diff --git "a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/nokw77ZubUw_raw.json" "b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/nokw77ZubUw_raw.json"
new file mode 100644--- /dev/null
+++ "b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/nokw77ZubUw_raw.json"
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4212, "start": 21.94, "end": 42.12, "text": "إذا في ال section هذا هن ان شاء الله هنتعلم ال limited theorems و بعض النظريات الخاصة بالنهايات فعشان نشوف النظريات هذه ناخد الأول تعريف", "tokens": [28814, 15730, 8978, 2423, 3541, 23758, 8032, 1863, 16472, 13412, 16606, 21984, 8032, 29399, 3615, 19528, 2423, 5567, 10299, 2592, 4032, 45030, 11242, 28239, 19913, 16572, 9307, 33962, 33546, 3660, 20666, 1863, 11296, 1829, 9307, 6156, 3615, 8592, 7649, 8717, 8592, 38688, 28239, 19913, 16572, 9307, 29538, 8717, 47283, 3215, 16247, 12610, 37279, 16572, 5172], "avg_logprob": -0.12074497594897236, "compression_ratio": 1.4966887417218544, "no_speech_prob": 0.0, "words": [{"start": 21.94, "end": 22.34, "word": "إذا", "probability": 0.59619140625}, {"start": 22.34, "end": 23.7, "word": " في", "probability": 0.9111328125}, {"start": 23.7, "end": 23.92, "word": " ال", "probability": 0.654296875}, {"start": 23.92, "end": 24.26, "word": " section", "probability": 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ومن", "probability": 0.58544921875}, {"start": 193.02, "end": 193.32, "word": " هنا", "probability": 0.9931640625}, {"start": 193.32, "end": 193.82, "word": " من", "probability": 0.300537109375}, {"start": 193.82, "end": 194.26, "word": " هنا", "probability": 0.9912109375}, {"start": 194.26, "end": 195.3, "word": " لكل", "probability": 0.97412109375}, {"start": 195.3, "end": 195.52, "word": " n", "probability": 0.430908203125}, {"start": 195.52, "end": 195.92, "word": " أكبر", "probability": 0.95556640625}, {"start": 195.92, "end": 196.06, "word": " من", "probability": 0.94873046875}, {"start": 196.06, "end": 196.18, "word": " أو", "probability": 0.8232421875}, {"start": 196.18, "end": 196.54, "word": " ساوي", "probability": 0.6195475260416666}, {"start": 196.54, "end": 196.96, "word": " capital", "probability": 0.45166015625}, {"start": 196.96, "end": 197.34, "word": " N", "probability": 0.7734375}, {"start": 197.34, "end": 198.76, "word": " المقدار", "probability": 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" ساوي", "probability": 0.6736653645833334}, {"start": 206.79, "end": 207.21, "word": " capital", "probability": 0.38818359375}, {"start": 207.21, "end": 207.47, "word": " N", "probability": 0.7119140625}, {"start": 207.47, "end": 209.27, "word": " أصغر", "probability": 0.70947265625}, {"start": 209.27, "end": 209.57, "word": " من", "probability": 0.9755859375}, {"start": 209.57, "end": 211.23, "word": " واحد", "probability": 0.773193359375}, {"start": 211.23, "end": 212.15, "word": " واحد", "probability": 0.860595703125}, {"start": 212.15, "end": 212.75, "word": " زائد", "probability": 0.841796875}, {"start": 212.75, "end": 213.25, "word": " absolute", "probability": 0.82421875}, {"start": 213.25, "end": 214.05, "word": " X", "probability": 0.47705078125}, {"start": 214.05, "end": 216.73, "word": " تمام؟", "probability": 0.65771484375}, {"start": 216.73, "end": 217.25, "word": " الآن", "probability": 0.6104736328125}, {"start": 217.25, "end": 217.51, "word": " لو", "probability": 0.9365234375}, {"start": 217.51, "end": 218.11, "word": " أخدت", "probability": 0.939453125}, {"start": 218.11, "end": 218.83, "word": " عرفت", "probability": 0.8819986979166666}, {"start": 218.83, "end": 219.27, "word": " capital", "probability": 0.75341796875}, {"start": 219.27, "end": 219.67, "word": " M", "probability": 0.98046875}, {"start": 219.67, "end": 220.55, "word": " على", "probability": 0.72265625}, {"start": 220.55, "end": 220.93, "word": " انها", "probability": 0.63525390625}], "temperature": 1.0}, {"id": 9, "seek": 24717, "start": 226.51, "end": 247.17, "text": "لو عرفت capital N و capital M علي انها ال supremum أو الأكبر بين الأعداد اللي هي absolute x1 و absolute x2 و هكذا إلى absolute x رقم capital N سالق واحد والعدد الأخير absolute x زائد واحد", "tokens": [1211, 2407, 6225, 28480, 2655, 4238, 426, 4032, 4238, 376, 25894, 16472, 11296, 2423, 23710, 449, 34051, 16247, 4117, 26890, 49374, 16247, 22488, 18513, 13672, 1829, 39896, 8236, 2031, 16, 4032, 8236, 2031, 17, 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"probability": 0.876953125}, {"start": 461.62, "end": 461.98, "word": " كل", "probability": 0.9541015625}, {"start": 461.98, "end": 462.48, "word": " bounded", "probability": 0.71630859375}, {"start": 462.48, "end": 463.06, "word": " sequence", "probability": 0.96484375}, {"start": 463.06, "end": 463.34, "word": " is", "probability": 0.943359375}, {"start": 463.34, "end": 464.04, "word": " convergent", "probability": 0.9775390625}, {"start": 464.04, "end": 464.76, "word": " هذا", "probability": 0.8623046875}, {"start": 464.76, "end": 465.0, "word": " مش", "probability": 0.9833984375}, {"start": 465.0, "end": 465.26, "word": " صح", "probability": 0.997802734375}], "temperature": 1.0}, {"id": 19, "seek": 47583, "start": 466.49, "end": 475.83, "text": "و هاي في counter example يثبت أو يوضح أن عكس نظرية 2.6 ليس صحيح", "tokens": [2407, 8032, 47302, 8978, 5682, 1365, 7251, 12984, 3555, 2655, 34051, 7251, 2407, 11242, 5016, 14739, 6225, 4117, 3794, 8717, 19913, 2288, 10632, 568, 13, 21, 32239, 3794, 20328, 5016, 1829, 5016], "avg_logprob": -0.2741477272727273, "compression_ratio": 0.96, "no_speech_prob": 0.0, "words": [{"start": 466.49, "end": 466.69, "word": "و", "probability": 0.71630859375}, {"start": 466.69, "end": 466.87, "word": " هاي", "probability": 0.527099609375}, {"start": 466.87, "end": 466.99, "word": " في", "probability": 0.86572265625}, {"start": 466.99, "end": 467.35, "word": " counter", "probability": 0.395263671875}, {"start": 467.35, "end": 469.75, "word": " example", "probability": 0.90380859375}, {"start": 469.75, "end": 471.95, "word": " يثبت", "probability": 0.83941650390625}, {"start": 471.95, "end": 472.27, "word": " أو", "probability": 0.73974609375}, {"start": 472.27, "end": 473.01, "word": " يوضح", "probability": 0.980712890625}, {"start": 473.01, "end": 473.33, "word": " أن", "probability": 0.4970703125}, {"start": 473.33, "end": 473.99, "word": " عكس", "probability": 0.96044921875}, {"start": 473.99, "end": 474.47, "word": " نظرية", "probability": 0.865478515625}, {"start": 474.47, "end": 474.73, "word": " 2", "probability": 0.499755859375}, {"start": 474.73, "end": 475.01, "word": ".6", "probability": 0.6671142578125}, {"start": 475.01, "end": 475.35, "word": " ليس", "probability": 0.7470703125}, {"start": 475.35, "end": 475.83, "word": " صحيح", "probability": 0.8792724609375}], "temperature": 1.0}, {"id": 20, "seek": 50185, "start": 476.75, "end": 501.85, "text": "السيكوانس ان الحد العام تبعها xn بساوي سالب واحد قص ان السيكوانس هذي bounded ليه bounded؟ لأن هاي في عدد موجب capital M بساوي واحد هذا عدد موجب إذا يوجد عدد موجب اللي هو الواحد بحيث ان absolute xn هذا ال absolute value العدد هذا واحد واحد أصغر من اذا بساوي واحد", "tokens": [6027, 3794, 1829, 4117, 2407, 7649, 3794, 16472, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 2031, 77, 4724, 3794, 995, 45865, 8608, 6027, 3555, 36764, 24401, 12174, 9381, 16472, 21136, 1829, 4117, 2407, 7649, 3794, 8032, 8848, 1829, 37498, 32239, 3224, 37498, 22807, 5296, 33456, 8032, 47302, 8978, 6225, 3215, 3215, 3714, 29245, 3555, 4238, 376, 4724, 3794, 995, 45865, 36764, 24401, 23758, 6225, 3215, 3215, 3714, 29245, 3555, 11933, 15730, 7251, 29245, 3215, 6225, 3215, 3215, 3714, 29245, 3555, 13672, 1829, 31439, 2423, 14407, 24401, 4724, 5016, 1829, 12984, 16472, 8236, 2031, 77, 23758, 2423, 8236, 2158, 18863, 3215, 3215, 23758, 36764, 24401, 36764, 24401, 5551, 9381, 17082, 2288, 9154, 1975, 15730, 4724, 3794, 995, 45865, 36764, 24401], "avg_logprob": -0.25994317590697735, "compression_ratio": 1.9906103286384977, "no_speech_prob": 0.0, "words": [{"start": 476.75, "end": 477.61, "word": "السيكوانس", "probability": 0.6936732700892857}, {"start": 477.61, "end": 478.05, "word": " ان", "probability": 0.470458984375}, {"start": 478.05, "end": 478.45, "word": " الحد", "probability": 0.9052734375}, {"start": 478.45, "end": 478.79, "word": " العام", "probability": 0.984619140625}, {"start": 478.79, "end": 479.25, "word": " تبعها", "probability": 0.8673095703125}, {"start": 479.25, "end": 479.89, "word": " xn", "probability": 0.531494140625}, {"start": 479.89, "end": 480.43, "word": " بساوي", "probability": 0.55133056640625}, {"start": 480.43, "end": 480.93, "word": " سالب", "probability": 0.8009440104166666}, {"start": 480.93, "end": 481.29, "word": " واحد", "probability": 0.976806640625}, {"start": 481.29, "end": 481.59, "word": " قص", "probability": 0.76318359375}, {"start": 481.59, "end": 481.91, "word": " ان", "probability": 0.48046875}, {"start": 481.91, "end": 483.37, "word": " السيكوانس", "probability": 0.8628336588541666}, {"start": 483.37, "end": 483.65, "word": " هذي", "probability": 0.4656982421875}, {"start": 483.65, "end": 484.03, "word": " bounded", "probability": 0.8603515625}, {"start": 484.03, "end": 484.47, "word": " ليه", "probability": 0.74560546875}, {"start": 484.47, "end": 486.09, "word": " bounded؟", "probability": 0.6361083984375}, {"start": 486.09, "end": 486.55, "word": " لأن", "probability": 0.879150390625}, {"start": 486.55, "end": 487.15, "word": " هاي", "probability": 0.35369873046875}, {"start": 487.15, "end": 487.37, "word": " في", "probability": 0.8603515625}, {"start": 487.37, "end": 487.81, "word": " عدد", "probability": 0.859375}, {"start": 487.81, "end": 488.27, "word": " موجب", "probability": 0.9851888020833334}, {"start": 488.27, "end": 488.79, "word": " capital", "probability": 0.53857421875}, {"start": 488.79, "end": 489.13, "word": " M", "probability": 0.892578125}, {"start": 489.13, "end": 489.65, "word": " بساوي", "probability": 0.9376220703125}, {"start": 489.65, "end": 490.11, "word": " واحد", "probability": 0.97509765625}, {"start": 490.11, "end": 490.35, "word": " هذا", "probability": 0.391845703125}, {"start": 490.35, "end": 490.65, "word": " عدد", "probability": 0.99365234375}, {"start": 490.65, "end": 491.13, "word": " موجب", "probability": 0.9930013020833334}, {"start": 491.13, "end": 491.53, "word": " إذا", "probability": 0.4884033203125}, {"start": 491.53, "end": 491.89, "word": " يوجد", "probability": 0.95458984375}, {"start": 491.89, "end": 492.19, "word": " عدد", "probability": 0.9925130208333334}, {"start": 492.19, "end": 492.67, "word": " موجب", "probability": 0.9921875}, {"start": 492.67, "end": 493.09, "word": " اللي", "probability": 0.95361328125}, {"start": 493.09, "end": 493.27, "word": " هو", "probability": 0.99560546875}, {"start": 493.27, "end": 493.81, "word": " الواحد", "probability": 0.9788411458333334}, {"start": 493.81, "end": 495.05, "word": " بحيث", "probability": 0.97265625}, {"start": 495.05, "end": 495.21, "word": " ان", "probability": 0.55859375}, {"start": 495.21, "end": 495.67, "word": " absolute", "probability": 0.84765625}, {"start": 495.67, "end": 496.75, "word": " xn", "probability": 0.956298828125}, {"start": 496.75, "end": 497.93, "word": " هذا", "probability": 0.5}, {"start": 497.93, "end": 498.43, "word": " ال", "probability": 0.418701171875}, {"start": 498.43, "end": 498.75, "word": " absolute", "probability": 0.8388671875}, {"start": 498.75, "end": 499.07, "word": " value", "probability": 0.9384765625}, {"start": 499.07, "end": 499.49, "word": " العدد", "probability": 0.88037109375}, {"start": 499.49, "end": 499.67, "word": " هذا", "probability": 0.66552734375}, {"start": 499.67, "end": 500.11, "word": " واحد", "probability": 0.98095703125}, {"start": 500.11, "end": 500.55, "word": " واحد", "probability": 0.70751953125}, {"start": 500.55, "end": 500.95, "word": " أصغر", "probability": 0.9466552734375}, {"start": 500.95, "end": 501.07, "word": " من", "probability": 0.953125}, {"start": 501.07, "end": 501.19, "word": " اذا", "probability": 0.2598876953125}, {"start": 501.19, "end": 501.49, "word": " بساوي", "probability": 0.726318359375}, {"start": 501.49, "end": 501.85, "word": " واحد", "probability": 0.992431640625}], "temperature": 1.0}, {"id": 21, "seek": 52253, "start": 503.09, "end": 522.53, "text": "إن ال absolute xn هي أصغر من أو ساوي عدد موجة بواحد لكل n إذا ال sequence هي bounded واضحة حسب التعريف الآن هذه ال sequence بنثبت إنها ليست convergent إنها divergent فلبرهان ذلك نعمل برهان بالتناقض", "tokens": [28814, 1863, 2423, 8236, 2031, 77, 39896, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 6225, 3215, 3215, 3714, 29245, 3660, 4724, 14407, 24401, 5296, 28820, 297, 11933, 15730, 2423, 8310, 39896, 37498, 4032, 46958, 5016, 3660, 11331, 35457, 16712, 3615, 16572, 5172, 6024, 48506, 29538, 2423, 8310, 44945, 12984, 3555, 2655, 36145, 11296, 32239, 14851, 9652, 6930, 36145, 11296, 18558, 6930, 6156, 46152, 2288, 3224, 7649, 29910, 23275, 8717, 25957, 1211, 4724, 2288, 3224, 7649, 20666, 2655, 8315, 4587, 11242], "avg_logprob": -0.23983434417161598, "compression_ratio": 1.5404040404040404, "no_speech_prob": 0.0, "words": [{"start": 503.09, "end": 503.41, "word": "إن", "probability": 0.44415283203125}, {"start": 503.41, "end": 503.53, "word": " ال", "probability": 0.4345703125}, {"start": 503.53, "end": 503.95, "word": " absolute", "probability": 0.2366943359375}, {"start": 503.95, "end": 504.63, "word": " xn", "probability": 0.523681640625}, {"start": 504.63, "end": 504.81, "word": " هي", "probability": 0.83447265625}, {"start": 504.81, "end": 505.25, "word": " أصغر", "probability": 0.978271484375}, {"start": 505.25, "end": 505.33, "word": " من", "probability": 0.95361328125}, {"start": 505.33, "end": 505.49, "word": " أو", "probability": 0.89013671875}, {"start": 505.49, "end": 505.85, "word": " ساوي", "probability": 0.8899739583333334}, {"start": 505.85, "end": 506.19, "word": " عدد", "probability": 0.9495442708333334}, {"start": 506.19, "end": 506.59, "word": " موجة", "probability": 0.8933919270833334}, {"start": 506.59, "end": 507.03, "word": " بواحد", "probability": 0.9578450520833334}, {"start": 507.03, "end": 507.45, "word": " لكل", "probability": 0.985595703125}, {"start": 507.45, "end": 507.67, "word": " n", "probability": 0.60546875}, {"start": 507.67, "end": 507.87, "word": " إذا", "probability": 0.5257568359375}, {"start": 507.87, "end": 508.03, "word": " ال", "probability": 0.61962890625}, {"start": 508.03, "end": 508.37, "word": " sequence", "probability": 0.92626953125}, {"start": 508.37, "end": 508.59, "word": " هي", "probability": 0.2939453125}, {"start": 508.59, "end": 508.95, "word": " bounded", "probability": 0.669921875}, {"start": 508.95, "end": 509.71, "word": " واضحة", "probability": 0.8402099609375}, {"start": 509.71, "end": 510.51, "word": " حسب", "probability": 0.91455078125}, {"start": 510.51, "end": 511.11, "word": " التعريف", "probability": 0.9857177734375}, {"start": 511.11, "end": 512.23, "word": " الآن", "probability": 0.716796875}, {"start": 512.23, "end": 512.51, "word": " هذه", "probability": 0.75341796875}, {"start": 512.51, "end": 512.63, "word": " ال", "probability": 0.95068359375}, {"start": 512.63, "end": 513.03, "word": " sequence", "probability": 0.9794921875}, {"start": 513.03, "end": 513.73, "word": " بنثبت", "probability": 0.7548065185546875}, {"start": 513.73, "end": 513.97, "word": " إنها", "probability": 0.706298828125}, {"start": 513.97, "end": 514.33, "word": " ليست", "probability": 0.8701171875}, {"start": 514.33, "end": 515.05, "word": " convergent", "probability": 0.781982421875}, {"start": 515.05, "end": 515.33, "word": " إنها", "probability": 0.890869140625}, {"start": 515.33, "end": 516.47, "word": " divergent", "probability": 0.6693115234375}, {"start": 516.47, "end": 519.95, "word": " فلبرهان", "probability": 0.8853515625}, {"start": 519.95, "end": 520.47, "word": " ذلك", "probability": 0.995849609375}, {"start": 520.47, "end": 521.39, "word": " نعمل", "probability": 0.90087890625}, {"start": 521.39, "end": 521.75, "word": " برهان", "probability": 0.9771728515625}, {"start": 521.75, "end": 522.53, "word": " بالتناقض", "probability": 0.96884765625}], "temperature": 1.0}, {"id": 22, "seek": 53807, "start": 523.53, "end": 538.07, "text": "أنا بدأ أثبت أن الـ sequence هذه is not convergent ف assume ال contrary يعني assume أنها convergent to some a belongs to the real numbers افرض أنها convergent وال limit تبعتها عدد a", "tokens": [10721, 8315, 4724, 3215, 10721, 5551, 12984, 3555, 2655, 14739, 2423, 39184, 8310, 29538, 307, 406, 9652, 6930, 6156, 6552, 2423, 19506, 37495, 22653, 6552, 14739, 11296, 9652, 6930, 281, 512, 257, 12953, 281, 264, 957, 3547, 1975, 5172, 43042, 14739, 11296, 9652, 6930, 16070, 4948, 6055, 3555, 34268, 11296, 6225, 3215, 3215, 257], "avg_logprob": -0.36505683010274714, "compression_ratio": 1.4110429447852761, "no_speech_prob": 0.0, "words": [{"start": 523.53, "end": 523.79, "word": "أنا", "probability": 0.5291748046875}, {"start": 523.79, "end": 524.07, "word": " بدأ", "probability": 0.4863077799479167}, {"start": 524.07, "end": 524.27, "word": " أثبت", "probability": 0.8936767578125}, {"start": 524.27, "end": 524.39, "word": " أن", "probability": 0.415771484375}, {"start": 524.39, "end": 524.43, "word": " الـ", "probability": 0.690185546875}, {"start": 524.43, "end": 524.71, "word": " sequence", "probability": 0.546875}, {"start": 524.71, "end": 525.21, "word": " هذه", "probability": 0.505859375}, {"start": 525.21, "end": 525.57, "word": " is", "probability": 0.2958984375}, {"start": 525.57, "end": 526.13, "word": " not", "probability": 0.93359375}, {"start": 526.13, "end": 526.95, "word": " convergent", "probability": 0.957275390625}, {"start": 526.95, "end": 527.43, "word": " ف", "probability": 0.66650390625}, {"start": 527.43, "end": 527.91, "word": " assume", "probability": 0.164794921875}, {"start": 527.91, "end": 528.07, "word": " ال", "probability": 0.8388671875}, {"start": 528.07, "end": 528.63, "word": " contrary", "probability": 0.494140625}, {"start": 528.63, "end": 529.45, "word": " يعني", "probability": 0.842041015625}, {"start": 529.45, "end": 529.91, "word": " assume", "probability": 0.69970703125}, {"start": 529.91, "end": 530.21, "word": " أنها", "probability": 0.80078125}, {"start": 530.21, "end": 531.05, "word": " convergent", "probability": 0.93359375}, {"start": 531.05, "end": 531.65, "word": " to", "probability": 0.94140625}, {"start": 531.65, "end": 532.07, "word": " some", "probability": 0.88671875}, {"start": 532.07, "end": 532.53, "word": " a", "probability": 0.72412109375}, {"start": 532.53, "end": 533.29, "word": " belongs", "probability": 0.377197265625}, {"start": 533.29, "end": 533.57, "word": " to", "probability": 0.9853515625}, {"start": 533.57, "end": 533.67, "word": " the", "probability": 0.8095703125}, {"start": 533.67, "end": 533.85, "word": " real", "probability": 0.96484375}, {"start": 533.85, "end": 534.45, "word": " numbers", "probability": 0.70947265625}, {"start": 534.45, "end": 535.51, "word": " افرض", "probability": 0.6980794270833334}, {"start": 535.51, "end": 535.77, "word": " أنها", "probability": 0.80126953125}, {"start": 535.77, "end": 536.49, "word": " convergent", "probability": 0.91845703125}, {"start": 536.49, "end": 536.67, "word": " وال", "probability": 0.388671875}, {"start": 536.67, "end": 536.95, "word": " limit", "probability": 0.5947265625}, {"start": 536.95, "end": 537.45, "word": " تبعتها", "probability": 0.872314453125}, {"start": 537.45, "end": 537.83, "word": " عدد", "probability": 0.9803059895833334}, {"start": 537.83, "end": 538.07, "word": " a", "probability": 0.84716796875}], "temperature": 1.0}, {"id": 23, "seek": 56794, "start": 539.68, "end": 567.94, "text": "فلو أخدت epsilon بساوي واحد عدد موجب إذا من تعريف ال convergence إذا يوجد capital N يعتمد على ال epsilon اللي أنا مختاره اللي هي الواحد بحيث لكل N أكبر من أو ساوي capital N المسافة بين xn و a أصغر من epsilon الآن ال N هذه اللي هي أكبر من أو ساوي capital N ممكن يكون عدد فردي أو زوجي", "tokens": [5172, 1211, 2407, 5551, 9778, 3215, 2655, 17889, 4724, 3794, 995, 45865, 36764, 24401, 6225, 3215, 3215, 3714, 29245, 3555, 11933, 15730, 9154, 37279, 16572, 5172, 2423, 32181, 11933, 15730, 7251, 29245, 3215, 4238, 426, 7251, 34268, 2304, 3215, 15844, 2423, 17889, 13672, 1829, 41850, 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"probability": 0.9749348958333334}, {"start": 593.47, "end": 593.65, "word": " من", "probability": 0.99560546875}, {"start": 593.65, "end": 593.99, "word": " سالب", "probability": 0.9557291666666666}, {"start": 593.99, "end": 594.33, "word": " اتنين", "probability": 0.864013671875}, {"start": 594.33, "end": 594.83, "word": " أصغر", "probability": 0.9720458984375}, {"start": 594.83, "end": 595.01, "word": " من", "probability": 0.99560546875}, {"start": 595.01, "end": 595.39, "word": " سفر", "probability": 0.68994140625}], "temperature": 1.0}, {"id": 25, "seek": 60992, "start": 597.41, "end": 609.93, "text": "لو كرت ال N اللي هي أكبر ما يساوي capital N even فهذا العدد بيصير واحد وبيصير المتباين هذا absolute واحد سالب a أصغر من واحد", "tokens": [1211, 2407, 9122, 43500, 2423, 426, 13672, 1829, 39896, 5551, 4117, 26890, 19446, 7251, 3794, 995, 45865, 4238, 426, 754, 6156, 3224, 15730, 18863, 3215, 3215, 4724, 1829, 9381, 13546, 36764, 24401, 4032, 3555, 1829, 9381, 13546, 9673, 2655, 3555, 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0.278564453125}, {"start": 600.27, "end": 600.59, "word": " N", "probability": 0.93310546875}, {"start": 600.59, "end": 601.07, "word": " even", "probability": 0.392822265625}, {"start": 601.07, "end": 603.67, "word": " فهذا", "probability": 0.9090169270833334}, {"start": 603.67, "end": 604.03, "word": " العدد", "probability": 0.9324544270833334}, {"start": 604.03, "end": 604.49, "word": " بيصير", "probability": 0.810791015625}, {"start": 604.49, "end": 605.01, "word": " واحد", "probability": 0.93701171875}, {"start": 605.01, "end": 605.55, "word": " وبيصير", "probability": 0.688623046875}, {"start": 605.55, "end": 606.17, "word": " المتباين", "probability": 0.87646484375}, {"start": 606.17, "end": 606.43, "word": " هذا", "probability": 0.237060546875}, {"start": 606.43, "end": 606.93, "word": " absolute", "probability": 0.90673828125}, {"start": 606.93, "end": 607.65, "word": " واحد", "probability": 0.9619140625}, {"start": 607.65, "end": 608.19, "word": " سالب", "probability": 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الأبوة", "probability": 0.8067626953125}, {"start": 699.14, "end": 699.4, "word": " ولا", "probability": 0.6865234375}, {"start": 699.4, "end": 700.04, "word": " يثبتها", "probability": 0.98134765625}], "temperature": 1.0}, {"id": 29, "seek": 71691, "start": 706.81, "end": 716.91, "text": "الملاحظة التانية بتقول إن نظرية 2.6 ممكن نستخدمها تثبت إن certain sequences are divergent", "tokens": [45340, 15040, 5016, 19913, 3660, 16712, 7649, 10632, 39894, 39648, 36145, 8717, 19913, 2288, 10632, 568, 13, 21, 3714, 43020, 8717, 14851, 9778, 40448, 11296, 6055, 12984, 3555, 2655, 36145, 1629, 22978, 366, 18558, 6930], "avg_logprob": -0.23719617683026525, "compression_ratio": 1.1166666666666667, "no_speech_prob": 0.0, "words": [{"start": 706.81, "end": 707.89, "word": "الملاحظة", "probability": 0.89365234375}, {"start": 707.89, "end": 708.23, "word": " التانية", "probability": 0.9287109375}, {"start": 708.23, "end": 708.63, "word": " بتقول", "probability": 0.626220703125}, {"start": 708.63, 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"seek": 75072, "start": 722.1, "end": 750.72, "text": "يعني نظرية هذه ممكن نستخدمها لإثبات أن ال sequence is معينة not convergent زي اختبار الدم بينفي الأبوة و لا يثبتها و هنا هذه نظرية بتنفي ال convergence و لا تثبته تمام مثلا ال sequence in هذه ال sequence of national numbers هذه ال sequence هذه bounded ولا مش bounded", "tokens": [40228, 22653, 8717, 19913, 2288, 10632, 29538, 3714, 43020, 8717, 14851, 9778, 40448, 11296, 5296, 28814, 12984, 3555, 9307, 14739, 2423, 8310, 307, 20449, 9957, 3660, 406, 9652, 6930, 30767, 1829, 1975, 46456, 3555, 9640, 32748, 2304, 4724, 9957, 41185, 16247, 3555, 2407, 3660, 4032, 20193, 7251, 12984, 3555, 2655, 11296, 4032, 34105, 29538, 8717, 19913, 2288, 10632, 39894, 1863, 41185, 2423, 32181, 4032, 20193, 6055, 12984, 3555, 2655, 3224, 46811, 10943, 50113, 15040, 2423, 8310, 294, 29538, 2423, 8310, 295, 4048, 3547, 29538, 2423, 8310, 29538, 37498, 49429, 37893, 37498], "avg_logprob": -0.31997282543907996, "compression_ratio": 1.7899543378995433, 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"word": " هذه", "probability": 0.55859375}, {"start": 745.14, "end": 745.56, "word": " ال", "probability": 0.42041015625}, {"start": 745.56, "end": 745.86, "word": " sequence", "probability": 0.85595703125}, {"start": 745.86, "end": 746.16, "word": " of", "probability": 0.64501953125}, {"start": 746.16, "end": 746.58, "word": " national", "probability": 0.5244140625}, {"start": 746.58, "end": 747.04, "word": " numbers", "probability": 0.7021484375}, {"start": 747.04, "end": 747.3, "word": " هذه", "probability": 0.6103515625}, {"start": 747.3, "end": 747.42, "word": " ال", "probability": 0.266357421875}, {"start": 747.42, "end": 747.88, "word": " sequence", "probability": 0.9384765625}, {"start": 747.88, "end": 749.5, "word": " هذه", "probability": 0.195068359375}, {"start": 749.5, "end": 749.86, "word": " bounded", "probability": 0.89501953125}, {"start": 749.86, "end": 750.14, "word": " ولا", "probability": 0.83056640625}, {"start": 750.14, "end": 750.34, "word": " مش", "probability": 0.9765625}, {"start": 750.34, "end": 750.72, "word": " bounded", "probability": 0.953125}], "temperature": 1.0}, {"id": 31, "seek": 77625, "start": 752.59, "end": 776.25, "text": "not bounded, unbounded، الـ sequence هذه unbounded، okay؟ إذا حسب نظرية 2.6، مدامها unbounded، إذا لازم تكون divergent، لبرهان ذلك، افرضي ال contrary، افرضي إنها convergent، إذا حسب نظرية 2.6، المفروض تطلع bounded، لكنها ليست bounded", "tokens": [2247, 37498, 11, 517, 18767, 292, 12399, 2423, 39184, 8310, 29538, 517, 18767, 292, 12399, 1392, 22807, 11933, 15730, 11331, 35457, 8717, 19913, 2288, 10632, 568, 13, 21, 12399, 3714, 3215, 10943, 11296, 517, 18767, 292, 12399, 11933, 15730, 5296, 31377, 2304, 6055, 30544, 18558, 6930, 12399, 5296, 26890, 3224, 7649, 29910, 23275, 12399, 1975, 5172, 43042, 1829, 2423, 19506, 12399, 1975, 5172, 43042, 1829, 36145, 11296, 9652, 6930, 12399, 11933, 15730, 11331, 35457, 8717, 19913, 2288, 10632, 568, 13, 21, 12399, 9673, 5172, 32887, 11242, 6055, 9566, 1211, 3615, 37498, 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{"start": 767.67, "end": 767.75, "word": " ال", "probability": 0.89697265625}, {"start": 767.75, "end": 768.39, "word": " contrary،", "probability": 0.728759765625}, {"start": 768.39, "end": 768.77, "word": " افرضي", "probability": 0.980224609375}, {"start": 768.77, "end": 769.15, "word": " إنها", "probability": 0.82177734375}, {"start": 769.15, "end": 771.09, "word": " convergent،", "probability": 0.8636067708333334}, {"start": 771.09, "end": 771.39, "word": " إذا", "probability": 0.902587890625}, {"start": 771.39, "end": 771.73, "word": " حسب", "probability": 0.99462890625}, {"start": 771.73, "end": 772.11, "word": " نظرية", "probability": 0.9884033203125}, {"start": 772.11, "end": 772.33, "word": " 2", "probability": 0.98876953125}, {"start": 772.33, "end": 772.85, "word": ".6،", "probability": 0.9680989583333334}, {"start": 772.85, "end": 773.13, "word": " المفروض", "probability": 0.9561767578125}, {"start": 773.13, "end": 773.51, "word": " تطلع", "probability": 0.968994140625}, {"start": 773.51, "end": 774.67, "word": " bounded،", "probability": 0.93359375}, {"start": 774.67, "end": 775.39, "word": " لكنها", "probability": 0.984619140625}, {"start": 775.39, "end": 775.87, "word": " ليست", "probability": 0.92822265625}, {"start": 775.87, "end": 776.25, "word": " bounded", "probability": 0.9462890625}], "temperature": 1.0}, {"id": 32, "seek": 80382, "start": 777.9, "end": 803.82, "text": "contradiction إذا ال sequence هذه كونها unbounded حسب نظرية نين سيفتر بتطلع divergent و احنا طبعا عارفين ان ال limit اللي عارفين انها divergent لأن limit n as n tends to infinity بساوي infinity ليس عدد حقيقي ال sequence هذه مالهاش limit okay تمام", "tokens": [9000, 6206, 4105, 11933, 15730, 2423, 8310, 29538, 9122, 11536, 11296, 517, 18767, 292, 11331, 35457, 8717, 19913, 2288, 10632, 8717, 9957, 8608, 1829, 5172, 2655, 2288, 39894, 9566, 1211, 3615, 18558, 6930, 4032, 1975, 5016, 8315, 23032, 3555, 3615, 995, 6225, 9640, 5172, 9957, 16472, 2423, 4948, 13672, 1829, 6225, 9640, 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حسب", "probability": 0.965087890625}, {"start": 784.96, "end": 785.4, "word": " نظرية", "probability": 0.96484375}, {"start": 785.4, "end": 785.68, "word": " نين", "probability": 0.455078125}, {"start": 785.68, "end": 785.98, "word": " سيفتر", "probability": 0.628564453125}, {"start": 785.98, "end": 786.44, "word": " بتطلع", "probability": 0.8819580078125}, {"start": 786.44, "end": 787.2, "word": " divergent", "probability": 0.74853515625}, {"start": 787.2, "end": 787.36, "word": " و", "probability": 0.7119140625}, {"start": 787.36, "end": 787.56, "word": " احنا", "probability": 0.74658203125}, {"start": 787.56, "end": 787.84, "word": " طبعا", "probability": 0.9727783203125}, {"start": 787.84, "end": 788.36, "word": " عارفين", "probability": 0.9781494140625}, {"start": 788.36, "end": 788.56, "word": " ان", "probability": 0.56640625}, {"start": 788.56, "end": 788.74, "word": " ال", "probability": 0.59423828125}, {"start": 788.74, "end": 789.04, "word": " limit", "probability": 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"seek": 83354, "start": 810.2, "end": 833.54, "text": "تابع الـ sequence in ليش unbounded؟ ليش الـ sequence هذه unbounded؟ هاي ال proof assume إنها bounded، in is bounded، بدنا نعمل برهان بالتناقل", "tokens": [2655, 16758, 3615, 2423, 39184, 8310, 294, 32239, 8592, 517, 18767, 292, 22807, 32239, 8592, 2423, 39184, 8310, 29538, 517, 18767, 292, 22807, 8032, 47302, 2423, 8177, 6552, 36145, 11296, 37498, 12399, 294, 307, 37498, 12399, 47525, 8315, 8717, 25957, 1211, 4724, 2288, 3224, 7649, 20666, 2655, 8315, 4587, 1211], "avg_logprob": -0.3645833216461481, "compression_ratio": 1.4477611940298507, "no_speech_prob": 0.0, "words": [{"start": 810.2, "end": 810.58, "word": "تابع", "probability": 0.3897298177083333}, {"start": 810.58, "end": 810.7, "word": " الـ", "probability": 0.4864501953125}, {"start": 810.7, "end": 811.14, "word": " sequence", "probability": 0.63916015625}, {"start": 811.14, "end": 811.4, "word": " in", "probability": 0.299072265625}, {"start": 811.4, "end": 811.76, 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"probability": 0.6566162109375}, {"start": 828.04, "end": 828.38, "word": " in", "probability": 0.3388671875}, {"start": 828.38, "end": 829.02, "word": " is", "probability": 0.9541015625}, {"start": 829.02, "end": 829.72, "word": " bounded،", "probability": 0.621826171875}, {"start": 829.72, "end": 832.02, "word": " بدنا", "probability": 0.6282958984375}, {"start": 832.02, "end": 832.28, "word": " نعمل", "probability": 0.9934895833333334}, {"start": 832.28, "end": 832.74, "word": " برهان", "probability": 0.931396484375}, {"start": 832.74, "end": 833.54, "word": " بالتناقل", "probability": 0.8017578125}], "temperature": 1.0}, {"id": 34, "seek": 85828, "start": 834.64, "end": 858.28, "text": "إذا يوجد عدد مجد M أكبر من سفر بحيث أنه absolute xn اللي هي M أصغر من M لكل M belonging to N طيب by Archimedean property", "tokens": [28814, 15730, 7251, 29245, 3215, 6225, 3215, 3215, 3714, 7435, 3215, 376, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 4724, 5016, 1829, 12984, 14739, 3224, 8236, 2031, 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1057.42, "word": " limit", "probability": 0.94580078125}], "temperature": 1.0}, {"id": 42, "seek": 107423, "start": 1059.65, "end": 1074.23, "text": "يبقى ان في جزء بيه عايزين نثبت ��ن limit xn في yn بساوي x في y فالبرهان ذلك", "tokens": [1829, 3555, 4587, 7578, 16472, 8978, 10874, 11622, 38207, 4724, 1829, 3224, 6225, 47302, 11622, 9957, 8717, 12984, 3555, 2655, 16472, 4948, 2031, 77, 8978, 17861, 4724, 3794, 995, 45865, 2031, 8978, 288, 6156, 6027, 26890, 3224, 7649, 29910, 23275], "avg_logprob": -0.27458080431310145, "compression_ratio": 1.2371134020618557, "no_speech_prob": 0.0, "words": [{"start": 1059.65, "end": 1060.09, "word": "يبقى", "probability": 0.569091796875}, {"start": 1060.09, "end": 1060.19, "word": " ان", "probability": 0.294921875}, {"start": 1060.19, "end": 1060.29, "word": " في", "probability": 0.7822265625}, {"start": 1060.29, "end": 1060.63, "word": " جزء", "probability": 0.8981119791666666}, {"start": 1060.63, "end": 1060.97, "word": " بيه", "probability": 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"probability": 0.9739990234375}, {"start": 1632.48, "end": 1632.8, "word": " أن", "probability": 0.46240234375}, {"start": 1632.8, "end": 1633.18, "word": " كل", "probability": 0.7568359375}, {"start": 1633.18, "end": 1633.56, "word": " حدود", "probability": 0.990234375}, {"start": 1633.56, "end": 1633.78, "word": " ال", "probability": 0.93798828125}, {"start": 1633.78, "end": 1634.36, "word": " sequence", "probability": 0.939453125}, {"start": 1634.36, "end": 1635.04, "word": " كلهم", "probability": 0.9521484375}, {"start": 1635.04, "end": 1636.52, "word": " غير", "probability": 0.989013671875}, {"start": 1636.52, "end": 1637.26, "word": " سالبين", "probability": 0.9468994140625}, {"start": 1637.26, "end": 1638.24, "word": " كلهم", "probability": 0.57452392578125}, {"start": 1638.24, "end": 1638.62, "word": " يعني", "probability": 0.8193359375}, {"start": 1638.62, "end": 1639.0, "word": " حدود", "probability": 0.99072265625}, {"start": 1639.0, "end": 1639.28, "word": " غير", "probability": 0.998046875}, {"start": 1639.28, "end": 1639.76, "word": " سالبة", "probability": 0.95751953125}], "temperature": 1.0}, {"id": 68, "seek": 166085, "start": 1640.37, "end": 1660.85, "text": "فكيف طلع الحد رقم N capital N سالب هذا بتناقض مع الفرض هذا بكمل البرهان تمام واضح البرهان طبعا على طريقة هذه إذا لو ال sequence كانت convergent وكل حدودها غير سالبة فنهايتها أيضا هتكون غير سالبة", "tokens": [5172, 4117, 33911, 23032, 1211, 3615, 21542, 3215, 12602, 4587, 2304, 426, 4238, 426, 8608, 6027, 3555, 23758, 39894, 8315, 4587, 11242, 20449, 27188, 43042, 23758, 4724, 24793, 1211, 2423, 26890, 3224, 7649, 46811, 10943, 4032, 46958, 5016, 2423, 26890, 3224, 7649, 23032, 3555, 3615, 995, 15844, 23032, 16572, 28671, 29538, 11933, 15730, 45164, 2423, 8310, 25961, 2655, 9652, 6930, 4032, 28820, 11331, 3215, 23328, 11296, 32771, 13546, 8608, 6027, 49401, 6156, 1863, 11296, 36081, 11296, 36632, 11242, 995, 8032, 2655, 30544, 32771, 13546, 8608, 6027, 49401], "avg_logprob": 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"word": " إذا", "probability": 0.695068359375}, {"start": 1652.71, "end": 1653.57, "word": " لو", "probability": 0.1533203125}, {"start": 1653.57, "end": 1653.57, "word": " ال", "probability": 0.88330078125}, {"start": 1653.57, "end": 1654.99, "word": " sequence", "probability": 0.90087890625}, {"start": 1654.99, "end": 1655.39, "word": " كانت", "probability": 0.968994140625}, {"start": 1655.39, "end": 1656.05, "word": " convergent", "probability": 0.6441650390625}, {"start": 1656.05, "end": 1657.07, "word": " وكل", "probability": 0.824462890625}, {"start": 1657.07, "end": 1657.57, "word": " حدودها", "probability": 0.986328125}, {"start": 1657.57, "end": 1657.83, "word": " غير", "probability": 0.996826171875}, {"start": 1657.83, "end": 1658.33, "word": " سالبة", "probability": 0.9446614583333334}, {"start": 1658.33, "end": 1659.23, "word": " فنهايتها", "probability": 0.857763671875}, {"start": 1659.23, "end": 1659.63, "word": " أيضا", "probability": 0.9168294270833334}, {"start": 1659.63, "end": 1660.11, "word": " هتكون", "probability": 0.7913411458333334}, {"start": 1660.11, "end": 1660.41, "word": " غير", "probability": 0.996826171875}, {"start": 1660.41, "end": 1660.85, "word": " سالبة", "probability": 0.9733072916666666}], "temperature": 1.0}, {"id": 69, "seek": 169165, "start": 1666.25, "end": 1691.65, "text": "طب لو كانت ال sequence convergent و حدودها غير موجبة كل حدودها غير موجبة فنهايتها ايضا هتكون غير موجبة و البرهان مشابه لبرهان نظرية السابقة النظرية اللي بعدها لو في عندي two sequences و التنتين convergent", "tokens": [9566, 3555, 45164, 25961, 2655, 2423, 8310, 9652, 6930, 4032, 11331, 3215, 23328, 11296, 32771, 13546, 3714, 29245, 49401, 28242, 11331, 3215, 23328, 11296, 32771, 13546, 3714, 29245, 49401, 6156, 1863, 11296, 36081, 11296, 1975, 1829, 11242, 995, 8032, 2655, 30544, 32771, 13546, 3714, 29245, 49401, 4032, 2423, 26890, 3224, 7649, 37893, 16758, 3224, 5296, 26890, 3224, 7649, 8717, 19913, 2288, 10632, 21136, 16758, 28671, 28239, 19913, 2288, 10632, 13672, 1829, 39182, 11296, 45164, 8978, 18871, 16254, 732, 22978, 4032, 16712, 29399, 9957, 9652, 6930], "avg_logprob": -0.18223110759674116, "compression_ratio": 1.9028571428571428, "no_speech_prob": 0.0, "words": [{"start": 1666.25, "end": 1666.57, "word": "طب", "probability": 0.52667236328125}, {"start": 1666.57, "end": 1666.71, "word": " لو", "probability": 0.96533203125}, {"start": 1666.71, "end": 1667.09, "word": " كانت", "probability": 0.982666015625}, {"start": 1667.09, "end": 1667.21, "word": " ال", "probability": 0.921875}, {"start": 1667.21, "end": 1667.49, "word": " sequence", "probability": 0.62744140625}, {"start": 1667.49, "end": 1668.33, "word": " convergent", "probability": 0.76220703125}, {"start": 1668.33, "end": 1668.57, "word": " و", "probability": 0.89697265625}, {"start": 1668.57, "end": 1669.09, "word": " حدودها", "probability": 0.85662841796875}, {"start": 1669.09, "end": 1669.37, "word": " غير", "probability": 0.9921875}, {"start": 1669.37, "end": 1669.93, "word": " موجبة", "probability": 0.986328125}, {"start": 1669.93, "end": 1671.25, "word": " كل", "probability": 0.478515625}, {"start": 1671.25, "end": 1671.67, "word": " حدودها", "probability": 0.987060546875}, {"start": 1671.67, "end": 1671.89, "word": " غير", "probability": 0.995361328125}, {"start": 1671.89, "end": 1672.45, "word": " موجبة", "probability": 0.9928385416666666}, {"start": 1672.45, "end": 1673.75, "word": " فنهايتها", "probability": 0.722607421875}, {"start": 1673.75, "end": 1673.99, "word": " ايضا", "probability": 0.821044921875}, {"start": 1673.99, "end": 1674.35, "word": " هتكون", "probability": 0.9041341145833334}, {"start": 1674.35, "end": 1674.61, "word": " غير", "probability": 0.995849609375}, {"start": 1674.61, "end": 1675.13, "word": " موجبة", "probability": 0.9939778645833334}, {"start": 1675.13, "end": 1675.35, "word": " و", "probability": 0.591796875}, {"start": 1675.35, "end": 1675.87, "word": " البرهان", "probability": 0.87060546875}, {"start": 1675.87, "end": 1676.59, "word": " مشابه", "probability": 0.9856770833333334}, {"start": 1676.59, "end": 1677.75, "word": " لبرهان", "probability": 0.941162109375}, {"start": 1677.75, "end": 1678.17, "word": " نظرية", "probability": 0.865234375}, {"start": 1678.17, "end": 1678.75, "word": " السابقة", "probability": 0.9407552083333334}, {"start": 1678.75, "end": 1682.43, "word": " النظرية", "probability": 0.8948974609375}, {"start": 1682.43, "end": 1682.57, "word": " اللي", "probability": 0.767333984375}, {"start": 1682.57, "end": 1683.71, "word": " بعدها", "probability": 0.9443359375}, {"start": 1683.71, "end": 1688.73, "word": " لو", "probability": 0.85302734375}, {"start": 1688.73, "end": 1688.95, "word": " في", "probability": 0.56494140625}, {"start": 1688.95, "end": 1689.19, "word": " عندي", "probability": 0.687255859375}, {"start": 1689.19, "end": 1689.37, "word": " two", "probability": 0.80712890625}, {"start": 1689.37, "end": 1690.15, "word": " sequences", "probability": 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-0.10233274542949569, "compression_ratio": 2.08, "no_speech_prob": 0.0, "words": [{"start": 1692.81, "end": 1693.39, "word": "والحد", "probability": 0.7233072916666666}, {"start": 1693.39, "end": 1693.97, "word": " العاملة", "probability": 0.9620768229166666}, {"start": 1693.97, "end": 1694.51, "word": " الأولى", "probability": 0.97119140625}, {"start": 1694.51, "end": 1694.95, "word": " أصغر", "probability": 0.9140625}, {"start": 1694.95, "end": 1695.01, "word": " من", "probability": 0.587890625}, {"start": 1695.01, "end": 1695.15, "word": " أو", "probability": 0.406005859375}, {"start": 1695.15, "end": 1695.39, "word": " ساوي", "probability": 0.8863932291666666}, {"start": 1695.39, "end": 1695.71, "word": " الحد", "probability": 0.933349609375}, {"start": 1695.71, "end": 1696.13, "word": " العاملة", "probability": 0.9851888020833334}, {"start": 1696.13, "end": 1696.67, "word": " التانية", "probability": 0.962890625}, {"start": 1696.67, "end": 1698.03, "word": " فنهاية", "probability": 0.885009765625}, {"start": 1698.03, "end": 1699.31, "word": " الأولى", "probability": 0.9646809895833334}, {"start": 1699.31, "end": 1699.71, "word": " أصغر", "probability": 0.9837646484375}, {"start": 1699.71, "end": 1699.81, "word": " من", "probability": 0.966796875}, {"start": 1699.81, "end": 1699.97, "word": " أو", "probability": 0.984375}, {"start": 1699.97, "end": 1700.49, "word": " ساوي", "probability": 0.9493815104166666}, {"start": 1700.49, "end": 1702.11, "word": " نهاية", "probability": 0.96435546875}, {"start": 1702.11, "end": 1703.07, "word": " التانية", "probability": 0.9788411458333334}, {"start": 1703.07, "end": 1704.81, "word": " والبرهان", "probability": 0.8270263671875}, {"start": 1704.81, "end": 1707.07, "word": " تطبيق", "probability": 0.9794921875}, {"start": 1707.07, "end": 1707.83, "word": " مباشر", "probability": 0.9932861328125}, {"start": 1707.83, "end": 1708.25, "word": " على", "probability": 0.8203125}, {"start": 1708.25, "end": 1708.71, "word": " نظرية", "probability": 0.8734130859375}, {"start": 1708.71, "end": 1708.89, "word": " اللى", "probability": 0.79638671875}, {"start": 1708.89, "end": 1709.37, "word": " فاتت", "probability": 0.9879557291666666}], "temperature": 1.0}, {"id": 71, "seek": 172970, "start": 1711.16, "end": 1729.7, "text": "لو اخدت انا عندي احنا فرضين ان xn أصغر من أو يساوي yn لكل n هذا معناه ان yn minus xn أكبر من أو يساوي سفر لكل n", "tokens": [1211, 2407, 1975, 9778, 3215, 2655, 1975, 8315, 18871, 16254, 1975, 5016, 8315, 6156, 43042, 9957, 16472, 2031, 77, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 17861, 5296, 28820, 297, 23758, 20449, 8315, 3224, 16472, 288, 77, 3175, 2031, 77, 5551, 4117, 26890, 9154, 34051, 7251, 3794, 995, 45865, 8608, 5172, 2288, 5296, 28820, 297], "avg_logprob": -0.22325212167481245, "compression_ratio": 1.4634146341463414, "no_speech_prob": 0.0, "words": [{"start": 1711.16, "end": 1711.52, "word": "لو", "probability": 0.64208984375}, {"start": 1711.52, "end": 1712.04, "word": " اخدت", "probability": 0.75433349609375}, {"start": 1712.04, "end": 1712.38, "word": " انا", "probability": 0.5986328125}, {"start": 1712.38, "end": 1713.16, "word": " عندي", "probability": 0.75927734375}, {"start": 1713.16, "end": 1713.96, "word": " احنا", "probability": 0.8994140625}, {"start": 1713.96, "end": 1714.46, "word": " فرضين", "probability": 0.984375}, {"start": 1714.46, "end": 1714.62, "word": " ان", "probability": 0.9033203125}, {"start": 1714.62, "end": 1715.42, "word": " xn", "probability": 0.2938232421875}, {"start": 1715.42, "end": 1717.34, "word": " أصغر", "probability": 0.85009765625}, {"start": 1717.34, "end": 1717.56, "word": " من", "probability": 0.98974609375}, {"start": 1717.56, "end": 1717.78, "word": " أو", "probability": 0.900390625}, {"start": 1717.78, "end": 1718.48, "word": " يساوي", "probability": 0.92626953125}, {"start": 1718.48, "end": 1719.0, "word": " yn", "probability": 0.76025390625}, {"start": 1719.0, "end": 1719.8, "word": " لكل", "probability": 0.981689453125}, {"start": 1719.8, "end": 1720.18, "word": " n", "probability": 0.87841796875}, {"start": 1720.18, "end": 1721.02, "word": " هذا", "probability": 0.578125}, {"start": 1721.02, "end": 1721.7, "word": " معناه", "probability": 0.9820963541666666}, {"start": 1721.7, "end": 1721.98, "word": " ان", "probability": 0.82421875}, {"start": 1721.98, "end": 1724.36, "word": " yn", "probability": 0.624755859375}, {"start": 1724.36, "end": 1724.98, "word": " minus", "probability": 0.361328125}, {"start": 1724.98, "end": 1725.82, "word": " xn", "probability": 0.991943359375}, {"start": 1725.82, "end": 1726.42, "word": " أكبر", "probability": 0.9016927083333334}, {"start": 1726.42, "end": 1726.68, "word": " من", "probability": 0.97998046875}, {"start": 1726.68, "end": 1726.94, "word": " أو", "probability": 0.95263671875}, {"start": 1726.94, "end": 1727.38, "word": " يساوي", "probability": 0.95361328125}, {"start": 1727.38, "end": 1727.9, "word": " سفر", "probability": 0.7823893229166666}, {"start": 1727.9, "end": 1729.42, "word": " لكل", "probability": 0.986572265625}, {"start": 1729.42, "end": 1729.7, "word": " n", "probability": 0.923828125}], "temperature": 1.0}, {"id": 72, "seek": 175040, "start": 1733.62, "end": 1750.4, "text": "فلو أخدت zn عرفت zn على أنه الفرق بين yn و xn فقلنا الفرق هذا غير سالب لكل n إذن هذه ال sequence جديدة حد العام تبعها zn وهذا الحد العام غير سالب لكل n", "tokens": [5172, 1211, 2407, 5551, 9778, 3215, 2655, 710, 77, 6225, 28480, 2655, 710, 77, 15844, 14739, 3224, 27188, 2288, 4587, 49374, 17861, 4032, 2031, 77, 6156, 4587, 1211, 8315, 27188, 2288, 4587, 23758, 32771, 13546, 8608, 6027, 3555, 5296, 28820, 297, 11933, 8848, 1863, 29538, 2423, 8310, 10874, 16254, 41891, 11331, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 710, 77, 37037, 15730, 21542, 3215, 18863, 10943, 32771, 13546, 8608, 6027, 3555, 5296, 28820, 297], "avg_logprob": -0.20104166905085247, "compression_ratio": 1.6423841059602649, "no_speech_prob": 0.0, "words": [{"start": 1733.62, "end": 1734.24, "word": "فلو", "probability": 0.5553385416666666}, {"start": 1734.24, "end": 1734.86, "word": " أخدت", "probability": 0.8643798828125}, {"start": 1734.86, "end": 1735.54, "word": " zn", "probability": 0.3443603515625}, {"start": 1735.54, "end": 1736.08, "word": " عرفت", "probability": 0.7821451822916666}, {"start": 1736.08, "end": 1736.64, "word": " zn", "probability": 0.86962890625}, {"start": 1736.64, "end": 1736.82, "word": " على", "probability": 0.599609375}, {"start": 1736.82, "end": 1737.26, "word": " أنه", "probability": 0.764892578125}, {"start": 1737.26, "end": 1738.22, "word": " الفرق", "probability": 0.9646809895833334}, {"start": 1738.22, "end": 1738.48, "word": " بين", "probability": 0.92529296875}, {"start": 1738.48, "end": 1738.8, "word": " yn", "probability": 0.7353515625}, {"start": 1738.8, "end": 1739.12, "word": " و", "probability": 0.9599609375}, {"start": 1739.12, "end": 1739.62, "word": " xn", "probability": 0.861328125}, {"start": 1739.62, "end": 1740.08, "word": " فقلنا", "probability": 0.81597900390625}, {"start": 1740.08, "end": 1740.5, "word": " الفرق", "probability": 0.9742838541666666}, {"start": 1740.5, "end": 1740.8, "word": " هذا", "probability": 0.8955078125}, {"start": 1740.8, "end": 1741.2, "word": " غير", "probability": 0.970703125}, {"start": 1741.2, "end": 1742.14, "word": " سالب", "probability": 0.87890625}, {"start": 1742.14, "end": 1742.62, "word": " لكل", "probability": 0.98583984375}, {"start": 1742.62, "end": 1742.78, "word": " n", "probability": 0.515625}, {"start": 1742.78, "end": 1743.0, "word": " إذن", "probability": 0.5371907552083334}, {"start": 1743.0, "end": 1743.2, "word": " هذه", "probability": 0.81201171875}, {"start": 1743.2, "end": 1743.3, "word": " ال", "probability": 0.91455078125}, {"start": 1743.3, "end": 1743.58, "word": " sequence", "probability": 0.6552734375}, {"start": 1743.58, "end": 1744.56, "word": " جديدة", "probability": 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"end": 1777.53, "text": "والـ sequence xn convergent وyn convergent حسب قوانين النهايات limit الفرق هذا موجود أو بساوي فرق النهايات إذا ال sequence zn حدودها كلها غير سالبة وconvergent لأنها الفرق بين two convergent sequences", "tokens": [2407, 6027, 39184, 8310, 2031, 77, 9652, 6930, 4032, 2534, 9652, 6930, 11331, 35457, 12174, 2407, 7649, 9957, 28239, 11296, 1829, 9307, 4948, 27188, 2288, 4587, 23758, 3714, 29245, 23328, 34051, 4724, 3794, 995, 45865, 6156, 2288, 4587, 28239, 11296, 1829, 9307, 11933, 15730, 2423, 8310, 710, 77, 11331, 3215, 23328, 11296, 28242, 11296, 32771, 13546, 8608, 6027, 49401, 4032, 1671, 331, 6930, 5296, 33456, 11296, 27188, 2288, 4587, 49374, 732, 9652, 6930, 22978], "avg_logprob": -0.240000003973643, "compression_ratio": 1.6666666666666667, "no_speech_prob": 0.0, "words": [{"start": 1751.71, "end": 1752.33, "word": "والـ", "probability": 0.5057779947916666}, {"start": 1752.33, "end": 1752.65, "word": " sequence", "probability": 0.70947265625}, {"start": 1752.65, "end": 1753.25, "word": " xn", "probability": 0.4512939453125}, {"start": 1753.25, "end": 1754.01, "word": " convergent", "probability": 0.692138671875}, {"start": 1754.01, "end": 1754.53, "word": " وyn", "probability": 0.6864013671875}, {"start": 1754.53, "end": 1755.53, "word": " convergent", "probability": 0.95068359375}, {"start": 1755.53, "end": 1756.77, "word": " حسب", "probability": 0.696533203125}, {"start": 1756.77, "end": 1760.51, "word": " قوانين", "probability": 0.9337158203125}, {"start": 1760.51, "end": 1761.13, "word": " النهايات", "probability": 0.8931884765625}, {"start": 1761.13, "end": 1763.03, "word": " limit", "probability": 0.1484375}, {"start": 1763.03, "end": 1764.47, "word": " الفرق", "probability": 0.9430338541666666}, {"start": 1764.47, "end": 1765.01, "word": " هذا", "probability": 0.56884765625}, {"start": 1765.01, "end": 1766.77, "word": " موجود", "probability": 0.9147135416666666}, {"start": 1766.77, "end": 1766.97, "word": " أو", "probability": 0.80517578125}, {"start": 1766.97, "end": 1767.43, "word": " بساوي", "probability": 0.7276611328125}, {"start": 1767.43, "end": 1767.79, "word": " فرق", "probability": 0.98583984375}, {"start": 1767.79, "end": 1768.45, "word": " النهايات", "probability": 0.9752197265625}, {"start": 1768.45, "end": 1770.63, "word": " إذا", "probability": 0.4444580078125}, {"start": 1770.63, "end": 1770.81, "word": " ال", "probability": 0.87744140625}, {"start": 1770.81, "end": 1771.11, "word": " sequence", "probability": 0.56494140625}, {"start": 1771.11, "end": 1771.77, "word": " zn", "probability": 0.710693359375}, {"start": 1771.77, "end": 1772.31, "word": " حدودها", "probability": 0.981201171875}, {"start": 1772.31, "end": 1772.61, "word": " كلها", "probability": 0.885986328125}, {"start": 1772.61, "end": 1772.91, "word": " غير", "probability": 0.996337890625}, {"start": 1772.91, "end": 1773.43, "word": " سالبة", "probability": 0.8992513020833334}, {"start": 1773.43, "end": 1774.73, "word": " وconvergent", "probability": 0.92333984375}, {"start": 1774.73, "end": 1775.23, "word": " لأنها", "probability": 0.91455078125}, {"start": 1775.23, "end": 1775.71, "word": " الفرق", "probability": 0.93505859375}, {"start": 1775.71, "end": 1776.07, "word": " بين", "probability": 0.94189453125}, {"start": 1776.07, "end": 1776.25, "word": " two", "probability": 0.8583984375}, {"start": 1776.25, "end": 1776.95, "word": " convergent", "probability": 0.8720703125}, {"start": 1776.95, "end": 1777.53, "word": " sequences", "probability": 0.92333984375}], "temperature": 1.0}, {"id": 74, "seek": 180673, "start": 1780.87, "end": 1806.73, "text": "وبالتالي حسب النظرية السابقة إذا ال limit ال sequence zn هذه بتطلع غير سالبة طب limit ال zn عسب قوانين النهيات بيساوي limit yn سالب limit xn و ادى هذه عن ناحية التانية فبيطلع limit yn أكبر من لو ساوي limit xn وهذا هو المظلومة okay تمام؟ راضى؟ دى اي سؤال؟", "tokens": [37746, 6027, 2655, 6027, 1829, 11331, 35457, 28239, 19913, 2288, 10632, 21136, 16758, 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سؤال؟", "probability": 0.840087890625}], "temperature": 1.0}, {"id": 75, "seek": 183567, "start": 1812.55, "end": 1835.67, "text": "النتيجة هذه بتقول لو كان في عندي sequence و ال sequence هذي convergent و الحدود تبعتها معصورة بين a و b", "tokens": [6027, 1863, 31371, 7435, 3660, 29538, 39894, 39648, 45164, 25961, 8978, 18871, 16254, 8310, 4032, 2423, 8310, 8032, 8848, 1829, 9652, 6930, 4032, 21542, 3215, 23328, 6055, 3555, 34268, 11296, 20449, 9381, 13063, 3660, 49374, 257, 4032, 272], "avg_logprob": -0.3888221276112092, "compression_ratio": 1.264, "no_speech_prob": 0.0, "words": [{"start": 1812.55, "end": 1813.55, "word": "النتيجة", "probability": 0.6970947265625}, {"start": 1813.55, "end": 1814.05, "word": " هذه", "probability": 0.27685546875}, {"start": 1814.05, "end": 1822.37, "word": " بتقول", "probability": 0.6824951171875}, {"start": 1822.37, "end": 1822.57, "word": " لو", "probability": 0.332763671875}, {"start": 1822.57, "end": 1822.87, "word": " كان", "probability": 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"probability": 0.9508056640625}, {"start": 1833.37, "end": 1834.75, "word": " بين", "probability": 0.58447265625}, {"start": 1834.75, "end": 1835.15, "word": " a", "probability": 0.599609375}, {"start": 1835.15, "end": 1835.35, "word": " و", "probability": 0.92919921875}, {"start": 1835.35, "end": 1835.67, "word": " b", "probability": 0.73486328125}], "temperature": 1.0}, {"id": 76, "seek": 186385, "start": 1839.05, "end": 1863.85, "text": "فلازم نهايتها ايضا .. نهايتها تطلع محصورة بين العددين a وb فبرهان النظرية هذه بنطبق نظرية 2.9 مرتين مرة", "tokens": [5172, 1211, 31377, 2304, 8717, 11296, 36081, 11296, 1975, 1829, 11242, 995, 4386, 8717, 11296, 36081, 11296, 6055, 9566, 1211, 3615, 3714, 5016, 9381, 13063, 3660, 49374, 18863, 3215, 3215, 9957, 257, 4032, 65, 6156, 26890, 3224, 7649, 28239, 19913, 2288, 10632, 29538, 44945, 9566, 3555, 4587, 8717, 19913, 2288, 10632, 568, 13, 24, 3714, 43500, 9957, 3714, 25720], "avg_logprob": -0.16666667064030966, "compression_ratio": 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من الفرض أنا عندي الـ sequence xn أصغر من أو ساوي الـ sequence اللي الحد العام تبعها ثابت بيه إذا ال limit حسب النظرية 8 إذا ال limit xn أصغر من أو ساوي limit ال sequence اللي الحد العام تبعها ثابت اللي هو بيه", "tokens": [4117, 8848, 23275, 41850, 18871, 16254, 2423, 39184, 8310, 2031, 77, 9154, 27188, 43042, 41850, 18871, 16254, 2423, 39184, 8310, 2031, 77, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 2423, 39184, 8310, 13672, 1829, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 38637, 16758, 2655, 4724, 1829, 3224, 11933, 15730, 2423, 4948, 11331, 35457, 28239, 19913, 2288, 10632, 1649, 11933, 15730, 2423, 4948, 2031, 77, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 4948, 2423, 8310, 13672, 1829, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 38637, 16758, 2655, 13672, 1829, 31439, 4724, 1829, 3224], "avg_logprob": -0.17976641323831347, "compression_ratio": 2.245508982035928, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1894.93, "end": 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0.9583333333333334}, {"start": 1971.99, "end": 1972.51, "word": " بينهم", "probability": 0.976806640625}, {"start": 1972.51, "end": 1973.15, "word": " هكذا", "probability": 0.95458984375}, {"start": 1973.15, "end": 1974.71, "word": " YN", "probability": 0.768798828125}, {"start": 1974.71, "end": 1975.49, "word": " محصورة", "probability": 0.95224609375}, {"start": 1975.49, "end": 1975.75, "word": " بين", "probability": 0.94677734375}, {"start": 1975.75, "end": 1976.41, "word": " XN", "probability": 0.9736328125}, {"start": 1976.41, "end": 1976.67, "word": " و", "probability": 0.9912109375}, {"start": 1976.67, "end": 1977.43, "word": " ZN", "probability": 0.9443359375}], "temperature": 1.0}, {"id": 81, "seek": 199415, "start": 1979.59, "end": 1994.15, "text": "و لو كانت الـ sequences الحدود العامة تبعتها على الأطراف convergent يعني ال sequence x in convergent و ال sequence z in convergent و التنتين ال limit تبعتهم متساوية", "tokens": [2407, 45164, 25961, 2655, 2423, 39184, 22978, 21542, 3215, 23328, 18863, 10943, 3660, 6055, 3555, 34268, 11296, 15844, 16247, 9566, 23557, 5172, 9652, 6930, 37495, 22653, 2423, 8310, 2031, 294, 9652, 6930, 4032, 2423, 8310, 710, 294, 9652, 6930, 4032, 16712, 29399, 9957, 2423, 4948, 6055, 3555, 34268, 16095, 44650, 3794, 995, 2407, 10632], "avg_logprob": -0.2055397786877372, "compression_ratio": 1.5810810810810811, "no_speech_prob": 0.0, "words": [{"start": 1979.59, "end": 1979.79, "word": "و", "probability": 0.4833984375}, {"start": 1979.79, "end": 1979.99, "word": " لو", "probability": 0.314453125}, {"start": 1979.99, "end": 1980.37, "word": " كانت", "probability": 0.954345703125}, {"start": 1980.37, "end": 1980.49, "word": " الـ", "probability": 0.48681640625}, {"start": 1980.49, "end": 1981.01, "word": " sequences", "probability": 0.67578125}, {"start": 1981.01, "end": 1982.05, "word": " الحدود", "probability": 0.9597981770833334}, {"start": 1982.05, "end": 1982.55, "word": " العامة", "probability": 0.9793294270833334}, {"start": 1982.55, "end": 1983.07, "word": " تبعتها", "probability": 0.8377685546875}, {"start": 1983.07, "end": 1983.21, "word": " على", "probability": 0.88671875}, {"start": 1983.21, "end": 1984.01, "word": " الأطراف", "probability": 0.951171875}, {"start": 1984.01, "end": 1985.47, "word": " convergent", "probability": 0.6771240234375}, {"start": 1985.47, "end": 1986.67, "word": " يعني", "probability": 0.765625}, {"start": 1986.67, "end": 1986.79, "word": " ال", "probability": 0.81396484375}, {"start": 1986.79, "end": 1987.05, "word": " sequence", "probability": 0.63671875}, {"start": 1987.05, "end": 1987.41, "word": " x", "probability": 0.52294921875}, {"start": 1987.41, "end": 1987.59, "word": " in", "probability": 0.432861328125}, {"start": 1987.59, "end": 1988.39, "word": " convergent", "probability": 0.8720703125}, {"start": 1988.39, "end": 1989.43, "word": " و", "probability": 0.630859375}, {"start": 1989.43, "end": 1989.55, "word": " ال", "probability": 0.8681640625}, {"start": 1989.55, "end": 1989.97, "word": " sequence", "probability": 0.97998046875}, {"start": 1989.97, "end": 1990.29, "word": " z", "probability": 0.95849609375}, {"start": 1990.29, "end": 1990.53, "word": " in", "probability": 0.93017578125}, {"start": 1990.53, "end": 1991.21, "word": " convergent", "probability": 0.964111328125}, {"start": 1991.21, "end": 1991.35, "word": " و", "probability": 0.68212890625}, {"start": 1991.35, "end": 1991.99, "word": " التنتين", "probability": 0.8336588541666666}, {"start": 1991.99, "end": 1992.23, "word": " ال", "probability": 0.69873046875}, {"start": 1992.23, "end": 1992.51, "word": " limit", "probability": 0.8857421875}, {"start": 1992.51, "end": 1993.25, "word": " تبعتهم", "probability": 0.956787109375}, {"start": 1993.25, "end": 1994.15, "word": " متساوية", "probability": 0.96826171875}], "temperature": 1.0}, {"id": 82, "seek": 202109, "start": 1996.99, "end": 2021.09, "text": "فلابد أو لازم أن الـ sequence المحصورة بينهم بتكون أيضًا convergent ونهايتها بتساوي القيمة المشتركة لنهايات للنهايات limit yn بتكون موجودة ونهايتها بتساوي نهاية xn ونهاية zn البرهان برضه مش صعب", "tokens": [5172, 15040, 44510, 34051, 5296, 31377, 2304, 14739, 2423, 39184, 8310, 9673, 5016, 9381, 13063, 3660, 49374, 16095, 39894, 30544, 36632, 11242, 14111, 995, 9652, 6930, 4032, 1863, 11296, 36081, 11296, 39894, 3794, 995, 45865, 25062, 32640, 3660, 9673, 8592, 2655, 31747, 3660, 5296, 1863, 11296, 1829, 9307, 24976, 1863, 11296, 1829, 9307, 4948, 17861, 39894, 30544, 3714, 29245, 23328, 3660, 4032, 1863, 11296, 36081, 11296, 39894, 3794, 995, 45865, 8717, 11296, 10632, 2031, 77, 4032, 1863, 11296, 10632, 710, 77, 2423, 26890, 3224, 7649, 4724, 43042, 3224, 37893, 20328, 3615, 3555], "avg_logprob": -0.16666667115303777, "compression_ratio": 1.7301587301587302, "no_speech_prob": 0.0, "words": [{"start": 1996.99, "end": 1998.39, "word": "فلابد", "probability": 0.5844319661458334}, {"start": 1998.39, "end": 1998.67, "word": " أو", "probability": 0.66064453125}, {"start": 1998.67, "end": 1999.21, "word": " لازم", "probability": 0.9807942708333334}, {"start": 1999.21, "end": 1999.41, "word": " أن", "probability": 0.51708984375}, {"start": 1999.41, "end": 1999.57, "word": " الـ", "probability": 0.751953125}, {"start": 1999.57, "end": 2000.01, "word": " sequence", "probability": 0.5791015625}, {"start": 2000.01, "end": 2000.77, "word": " المحصورة", "probability": 0.9708984375}, {"start": 2000.77, "end": 2001.35, "word": " بينهم", "probability": 0.967041015625}, {"start": 2001.35, "end": 2002.39, "word": " بتك��ن", "probability": 0.65869140625}, {"start": 2002.39, "end": 2002.73, "word": " أيضًا", "probability": 0.7894287109375}, {"start": 2002.73, "end": 2003.53, "word": " convergent", "probability": 0.78125}, {"start": 2003.53, "end": 2004.45, "word": " ونهايتها", "probability": 0.85693359375}, {"start": 2004.45, "end": 2005.75, "word": " بتساوي", "probability": 0.83251953125}, {"start": 2005.75, "end": 2006.51, "word": " القيمة", "probability": 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"probability": 0.925048828125}, {"start": 2015.89, "end": 2016.81, "word": " zn", "probability": 0.717529296875}, {"start": 2016.81, "end": 2019.91, "word": " البرهان", "probability": 0.85748291015625}, {"start": 2019.91, "end": 2020.29, "word": " برضه", "probability": 0.9768880208333334}, {"start": 2020.29, "end": 2020.53, "word": " مش", "probability": 0.9814453125}, {"start": 2020.53, "end": 2021.09, "word": " صعب", "probability": 0.96923828125}], "temperature": 1.0}, {"id": 83, "seek": 204639, "start": 2026.21, "end": 2046.39, "text": "أحنا فرضين أن limit sequence x in موجودة و limit sequence z in موجودة وتنتين متساويات فدعونا نسمي ال limit هذه مشتركة a عدد a الأن ناخد let epsilon أكبر من صفر b", "tokens": [10721, 5016, 8315, 6156, 43042, 9957, 14739, 4948, 8310, 2031, 294, 3714, 29245, 23328, 3660, 4032, 4948, 8310, 710, 294, 3714, 29245, 23328, 3660, 34683, 29399, 9957, 44650, 3794, 995, 45865, 9307, 6156, 3215, 3615, 2407, 8315, 8717, 38251, 1829, 2423, 4948, 29538, 37893, 2655, 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{"start": 2030.37, "end": 2030.63, "word": " limit", "probability": 0.646484375}, {"start": 2030.63, "end": 2031.87, "word": " sequence", "probability": 0.97265625}, {"start": 2031.87, "end": 2032.03, "word": " z", "probability": 0.9599609375}, {"start": 2032.03, "end": 2032.21, "word": " in", "probability": 0.71875}, {"start": 2032.21, "end": 2032.81, "word": " موجودة", "probability": 0.9820556640625}, {"start": 2032.81, "end": 2033.33, "word": " وتنتين", "probability": 0.6858723958333334}, {"start": 2033.33, "end": 2034.53, "word": " متساويات", "probability": 0.97666015625}, {"start": 2034.53, "end": 2035.77, "word": " فدعونا", "probability": 0.89794921875}, {"start": 2035.77, "end": 2037.13, "word": " نسمي", "probability": 0.9742838541666666}, {"start": 2037.13, "end": 2037.39, "word": " ال", "probability": 0.492431640625}, {"start": 2037.39, "end": 2037.73, "word": " limit", "probability": 0.8955078125}, {"start": 2037.73, "end": 2038.11, "word": " هذه", "probability": 0.259521484375}, {"start": 2038.11, "end": 2038.81, "word": " مشتركة", "probability": 0.85601806640625}, {"start": 2038.81, "end": 2039.11, "word": " a", "probability": 0.3818359375}, {"start": 2039.11, "end": 2040.01, "word": " عدد", "probability": 0.8470052083333334}, {"start": 2040.01, "end": 2040.27, "word": " a", "probability": 0.78466796875}, {"start": 2040.27, "end": 2043.25, "word": " الأن", "probability": 0.617919921875}, {"start": 2043.25, "end": 2044.39, "word": " ناخد", "probability": 0.9065755208333334}, {"start": 2044.39, "end": 2044.83, "word": " let", "probability": 0.9296875}, {"start": 2044.83, "end": 2045.23, "word": " epsilon", "probability": 0.8193359375}, {"start": 2045.23, "end": 2045.61, "word": " أكبر", "probability": 0.94775390625}, {"start": 2045.61, "end": 2045.81, "word": " من", "probability": 0.99267578125}, {"start": 2045.81, "end": 2046.23, "word": " صفر", "probability": 0.7049967447916666}, {"start": 2046.23, "end": 2046.39, "word": " b", "probability": 0.472900390625}], "temperature": 1.0}, {"id": 84, "seek": 206269, "start": 2048.61, "end": 2062.69, "text": "بما أن ال sequence xn converge ل a، إذا يوجد عدد طبيعي capital N يعتمد على إبسلون، بحيث لكل N أكبر من وسوء capital N، المسافة بين xn و a أصغر من إبسلون", "tokens": [3555, 15042, 14739, 2423, 8310, 2031, 77, 41881, 5296, 257, 12399, 11933, 15730, 7251, 29245, 3215, 6225, 3215, 3215, 23032, 21292, 3615, 1829, 4238, 426, 7251, 34268, 2304, 3215, 15844, 11933, 3555, 3794, 1211, 11536, 12399, 4724, 5016, 1829, 12984, 5296, 28820, 426, 5551, 4117, 26890, 9154, 46952, 2407, 38207, 4238, 426, 12399, 9673, 3794, 31845, 3660, 49374, 2031, 77, 4032, 257, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 1211, 11536], "avg_logprob": -0.23994007175915863, "compression_ratio": 1.3832335329341316, "no_speech_prob": 0.0, "words": [{"start": 2048.61, "end": 2049.05, "word": "بما", "probability": 0.9736328125}, {"start": 2049.05, "end": 2049.23, "word": " أن", "probability": 0.630859375}, 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"probability": 0.9862060546875}, {"start": 2059.43, "end": 2059.73, "word": " بين", "probability": 0.955078125}, {"start": 2059.73, "end": 2060.57, "word": " xn", "probability": 0.944580078125}, {"start": 2060.57, "end": 2060.91, "word": " و", "probability": 0.85546875}, {"start": 2060.91, "end": 2061.29, "word": " a", "probability": 0.4658203125}, {"start": 2061.29, "end": 2061.91, "word": " أصغر", "probability": 0.990966796875}, {"start": 2061.91, "end": 2062.11, "word": " من", "probability": 0.9931640625}, {"start": 2062.11, "end": 2062.69, "word": " إبسلون", "probability": 0.967578125}], "temperature": 1.0}, {"id": 85, "seek": 208948, "start": 2064.75, "end": 2089.49, "text": "كذلك بما أن ال sequence zm converge ل a إذا بقدر ألاقي لكل .. لنفس ال epsilon .. لنفس ال epsilon بقدر ألاقي capital N ممكن ال capital N مختلف عن ال capital N الأولى نية ففي الحالة هذه باخد capital N هذا ال maximum لل N الأولى و التانية زي ما شوفنا في القرآن السابق", "tokens": [4117, 8848, 23275, 4724, 15042, 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" هنا", "probability": 0.765625}, {"start": 2194.72, "end": 2196.02, "word": " هاندي", "probability": 0.527099609375}, {"start": 2196.02, "end": 2196.28, "word": " z", "probability": 0.8408203125}, {"start": 2196.28, "end": 2196.58, "word": " n", "probability": 0.931640625}, {"start": 2196.58, "end": 2197.14, "word": " minus", "probability": 0.994140625}, {"start": 2197.14, "end": 2197.6, "word": " a", "probability": 0.9912109375}, {"start": 2197.6, "end": 2198.2, "word": " من", "probability": 0.9521484375}, {"start": 2198.2, "end": 2199.32, "word": " هذا", "probability": 0.8310546875}, {"start": 2199.32, "end": 2199.86, "word": " الجزء", "probability": 0.986328125}, {"start": 2199.86, "end": 2200.92, "word": " z", "probability": 0.50048828125}, {"start": 2200.92, "end": 2201.32, "word": " n", "probability": 0.97216796875}, {"start": 2201.32, "end": 2201.82, "word": " minus", "probability": 0.994140625}, {"start": 2201.82, "end": 2202.26, "word": " a", "probability": 0.99560546875}, {"start": 2202.26, "end": 2202.94, "word": " أصغر", "probability": 0.9923095703125}, {"start": 2202.94, "end": 2203.1, "word": " من", "probability": 0.99462890625}, {"start": 2203.1, "end": 2203.46, "word": " إبسن", "probability": 0.5550537109375}], "temperature": 1.0}, {"id": 91, "seek": 223434, "start": 2208.86, "end": 2234.34, "text": "إذاً هذه الـ implication بتقول باختصار لكل N أكبر من أو ساوي capital N أنا عندي طلع يطلع عندي YN minus A أصغر من أبسلون أكبر من سالب أبسلون أو absolute YN minus A أصغر من أبسلون لكل N أكبر من أو ساوي capital N", "tokens": [28814, 15730, 14111, 29538, 2423, 39184, 37814, 39894, 39648, 4724, 47283, 2655, 9381, 9640, 5296, 28820, 426, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 4238, 426, 41850, 18871, 16254, 23032, 1211, 3615, 7251, 9566, 1211, 3615, 18871, 16254, 398, 45, 3175, 316, 5551, 9381, 17082, 2288, 9154, 5551, 3555, 3794, 1211, 11536, 5551, 4117, 26890, 9154, 8608, 6027, 3555, 5551, 3555, 3794, 1211, 11536, 34051, 8236, 398, 45, 3175, 316, 5551, 9381, 17082, 2288, 9154, 5551, 3555, 3794, 1211, 11536, 5296, 28820, 426, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 4238, 426], "avg_logprob": -0.229769734332436, "compression_ratio": 1.8771929824561404, "no_speech_prob": 0.0, "words": [{"start": 2208.86, "end": 2209.82, "word": "إذاً", "probability": 0.412353515625}, {"start": 2209.82, "end": 2210.78, "word": " هذه", "probability": 0.76513671875}, {"start": 2210.78, "end": 2211.32, "word": " الـ", "probability": 0.6541748046875}, {"start": 2211.32, "end": 2211.88, "word": " implication", "probability": 0.9580078125}, {"start": 2211.88, "end": 2212.1, "word": " بتقول", "probability": 0.760498046875}, {"start": 2212.1, "end": 2212.62, "word": " باختصار", "probability": 0.768408203125}, {"start": 2212.62, "end": 2213.7, "word": " لكل", "probability": 0.81201171875}, {"start": 2213.7, "end": 2214.0, "word": " N", "probability": 0.348876953125}, {"start": 2214.0, "end": 2214.46, "word": " أكبر", "probability": 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"probability": 0.494384765625}, {"start": 2221.32, "end": 2221.84, "word": " A", "probability": 0.84423828125}, {"start": 2221.84, "end": 2223.56, "word": " أصغر", "probability": 0.9820556640625}, {"start": 2223.56, "end": 2223.76, "word": " من", "probability": 0.9951171875}, {"start": 2223.76, "end": 2224.3, "word": " أبسلون", "probability": 0.72138671875}, {"start": 2224.3, "end": 2224.86, "word": " أكبر", "probability": 0.9638671875}, {"start": 2224.86, "end": 2225.1, "word": " من", "probability": 0.9970703125}, {"start": 2225.1, "end": 2225.72, "word": " سالب", "probability": 0.9482421875}, {"start": 2225.72, "end": 2227.46, "word": " أبسلون", "probability": 0.958984375}, {"start": 2227.46, "end": 2228.62, "word": " أو", "probability": 0.80078125}, {"start": 2228.62, "end": 2229.18, "word": " absolute", "probability": 0.62890625}, {"start": 2229.18, "end": 2229.9, "word": " YN", "probability": 0.86328125}, {"start": 2229.9, "end": 2230.4, "word": " minus", "probability": 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0.99267578125}], "temperature": 1.0}, {"id": 92, "seek": 226302, "start": 2235.6, "end": 2263.02, "text": "أذن هين أثبتنا أنه for any epsilon أكبر من سفر يوجد capital N يعتمد على epsilon عدد طبيعي بحيث لكل N أكبر من أو ساوي capital N ال absolute value هذي أصغر من epsilon اذا by epsilon capital N definition of limit بطلع عندي limit هذا معناه ان limit ال sequence yn as n tends to infinity بتساوي العدد A", "tokens": [10721, 8848, 1863, 8032, 9957, 5551, 12984, 3555, 2655, 8315, 14739, 3224, 337, 604, 17889, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 7251, 29245, 3215, 4238, 426, 7251, 34268, 2304, 3215, 15844, 17889, 6225, 3215, 3215, 23032, 21292, 3615, 1829, 4724, 5016, 1829, 12984, 5296, 28820, 426, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 4238, 426, 2423, 8236, 2158, 8032, 8848, 1829, 5551, 9381, 17082, 2288, 9154, 17889, 1975, 15730, 538, 17889, 4238, 426, 7123, 295, 4948, 4724, 9566, 1211, 3615, 18871, 16254, 4948, 23758, 20449, 8315, 3224, 16472, 4948, 2423, 8310, 17861, 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"probability": 0.6796875}, {"start": 2250.72, "end": 2251.0, "word": " اذا", "probability": 0.53265380859375}, {"start": 2251.0, "end": 2251.24, "word": " by", "probability": 0.79296875}, {"start": 2251.24, "end": 2251.64, "word": " epsilon", "probability": 0.90771484375}, {"start": 2251.64, "end": 2252.08, "word": " capital", "probability": 0.59912109375}, {"start": 2252.08, "end": 2252.32, "word": " N", "probability": 0.96923828125}, {"start": 2252.32, "end": 2252.72, "word": " definition", "probability": 0.8974609375}, {"start": 2252.72, "end": 2252.94, "word": " of", "probability": 0.9775390625}, {"start": 2252.94, "end": 2253.28, "word": " limit", "probability": 0.96533203125}, {"start": 2253.28, "end": 2254.2, "word": " بطلع", "probability": 0.66790771484375}, {"start": 2254.2, "end": 2254.52, "word": " عندي", "probability": 0.7376708984375}, {"start": 2254.52, "end": 2255.04, "word": " limit", "probability": 0.80615234375}, {"start": 2255.04, "end": 2255.64, "word": " هذا", 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ال bus على limit المقام حسب قوانين النهايات limit ال bus سفر limit المقام واحد اذا ال limit في النهاية تمتها سفر تمام المثال التاني هذا", "tokens": [4197, 270, 33251, 49115, 23758, 4724, 1829, 3794, 995, 45865, 4948, 33251, 49115, 13672, 1829, 8032, 7649, 37037, 15730, 23032, 3555, 3615, 995, 5296, 33456, 4948, 9673, 4587, 10943, 4724, 1829, 3794, 995, 45865, 8592, 8608, 5172, 2288, 6156, 3555, 3794, 995, 45865, 4948, 2423, 1255, 15844, 4948, 9673, 4587, 10943, 11331, 35457, 12174, 2407, 7649, 9957, 28239, 11296, 1829, 9307, 4948, 2423, 1255, 8608, 5172, 2288, 4948, 9673, 4587, 10943, 36764, 24401, 1975, 15730, 2423, 4948, 8978, 28239, 11296, 10632, 46811, 2655, 11296, 8608, 5172, 2288, 46811, 10943, 9673, 12984, 6027, 16712, 7649, 1829, 23758], "avg_logprob": -0.25918169119923384, "compression_ratio": 2.101123595505618, "no_speech_prob": 0.0, "words": [{"start": 2402.99, "end": 2403.87, "word": "limit", "probability": 0.549163818359375}, {"start": 2403.87, "end": 2404.35, "word": " 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