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+{"segments": [{"id": 1, "seek": 4923, "start": 21.45, "end": 49.23, "text": "Okay إذا احنا في المحاضرة الأخيرة أخدنا الـ monotone convergence theorem وشوفنا أنه في النظرية هذه لو في عندي sequence و ال sequence هذه monotone يعني increasing أو decreasing فعشان فبتكون convergent if and only if it is bounded", "tokens": [8297, 11933, 15730, 1975, 5016, 8315, 8978, 9673, 5016, 46958, 25720, 16247, 9778, 48923, 5551, 9778, 3215, 8315, 2423, 39184, 1108, 310, 546, 32181, 20904, 4032, 8592, 38688, 8315, 14739, 3224, 8978, 28239, 19913, 2288, 10632, 29538, 45164, 8978, 18871, 16254, 8310, 4032, 2423, 8310, 29538, 1108, 310, 546, 37495, 22653, 5662, 34051, 23223, 6156, 3615, 8592, 7649, 6156, 3555, 2655, 30544, 9652, 6930, 498, 293, 787, 498, 309, 307, 37498], "avg_logprob": -0.2000868007954624, "compression_ratio": 1.56, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 21.45, "end": 21.89, "word": "Okay", "probability": 0.06500244140625}, {"start": 21.89, "end": 22.23, "word": " 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هذه بالمناسبة ممكن نستخدمها في إثبات إنه monotone sequence معينة إما convergent أو divergent عشان أثبت إن ال monotone sequence إذا عندي أنا monotone sequence عشان أثبت إنها convergent لازم أثبت إنها bounded العكس لو في عنده monotone sequence", "tokens": [6027, 7649, 4724, 1863, 8592, 38688, 9122, 33911, 8717, 9566, 3555, 4587, 28239, 19913, 2288, 10632, 8978, 11933, 12984, 3555, 9307, 36145, 1629, 22978, 366, 9652, 6930, 34051, 18558, 6930, 28239, 19913, 2288, 10632, 29538, 20666, 2304, 8315, 35457, 3660, 3714, 43020, 8717, 14851, 9778, 40448, 11296, 8978, 11933, 12984, 3555, 9307, 36145, 3224, 1108, 310, 546, 8310, 20449, 9957, 3660, 11933, 15042, 9652, 6930, 34051, 18558, 6930, 6225, 8592, 7649, 5551, 12984, 3555, 2655, 36145, 2423, 1108, 310, 546, 8310, 11933, 15730, 18871, 16254, 41850, 1108, 310, 546, 8310, 6225, 8592, 7649, 5551, 12984, 3555, 2655, 36145, 11296, 9652, 6930, 5296, 31377, 2304, 5551, 12984, 3555, 2655, 36145, 11296, 37498, 18863, 4117, 3794, 45164, 8978, 43242, 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" اثبت", "probability": 0.977783203125}, {"start": 133.52, "end": 133.82, "word": " انها", "probability": 0.96240234375}, {"start": 133.82, "end": 134.64, "word": " unbounded", "probability": 0.826171875}, {"start": 134.64, "end": 134.94, "word": " not", "probability": 0.311767578125}, {"start": 134.94, "end": 135.46, "word": " bounded", "probability": 0.92041015625}, {"start": 135.46, "end": 138.3, "word": " فهي", "probability": 0.8038736979166666}, {"start": 138.3, "end": 138.5, "word": " ان", "probability": 0.440185546875}, {"start": 138.5, "end": 138.64, "word": " ال", "probability": 0.59423828125}, {"start": 138.64, "end": 139.26, "word": " sequence", "probability": 0.91845703125}, {"start": 139.26, "end": 140.18, "word": " xn", "probability": 0.513427734375}, {"start": 140.18, "end": 140.84, "word": " بساوي", "probability": 0.6241455078125}, {"start": 140.84, "end": 141.34, "word": " واحد", "probability": 0.863525390625}, {"start": 141.34, "end": 141.54, "word": " على", "probability": 0.74609375}, {"start": 141.54, "end": 141.84, "word": " n", "probability": 0.662109375}, {"start": 141.84, "end": 142.6, "word": " هاد", "probability": 0.439453125}, {"start": 142.6, "end": 142.72, "word": " ال", "probability": 0.97314453125}, {"start": 142.72, "end": 143.14, "word": " sequence", "probability": 0.96337890625}, {"start": 143.14, "end": 143.82, "word": " معروف", "probability": 0.9894205729166666}, {"start": 143.82, "end": 145.16, "word": " انه", "probability": 0.75537109375}, {"start": 145.16, "end": 145.38, "word": " ال", "probability": 0.8447265625}, {"start": 145.38, "end": 145.76, "word": " limit", "probability": 0.95654296875}, {"start": 145.76, "end": 146.5, "word": " انها", "probability": 0.908203125}, {"start": 146.5, "end": 147.24, "word": " convergent", "probability": 0.78515625}, {"start": 147.24, "end": 148.32, "word": " وits", "probability": 0.5908203125}, {"start": 148.32, "end": 148.7, "word": " limit", "probability": 0.96240234375}, {"start": 148.7, "end": 148.94, "word": " is", "probability": 0.5830078125}, {"start": 148.94, "end": 149.32, "word": " zero", "probability": 0.8076171875}, {"start": 149.32, "end": 151.18, "word": " زيها", "probability": 0.8816731770833334}, {"start": 151.18, "end": 151.54, "word": " زي", "probability": 0.984619140625}, {"start": 151.54, "end": 151.82, "word": " ال", "probability": 0.91162109375}, {"start": 151.82, "end": 152.26, "word": " sequence", "probability": 0.9873046875}, {"start": 152.26, "end": 152.66, "word": " واحد", "probability": 0.95654296875}, {"start": 152.66, "end": 152.82, "word": " على", "probability": 0.86767578125}, {"start": 152.82, "end": 153.08, "word": " n", "probability": 0.7958984375}], "temperature": 1.0}, {"id": 6, "seek": 18107, "start": 154.35, "end": 181.07, "text": "و ممكن تبرهن أن الـ sequence هذه convergence و نهايتها بالساعة و سفر باستخدام تعريف epsilon capital N لل limit بالظبط زي ما عملنا في برهان ال limit أن ال limit لل sequence واحد علي N 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"text": "اللي هو باستخدام تعريف epsilon capital N زائد الـarchimedean property بالظبط زي ما أثبتنا limit 1 على N بساوية 0 اليوم هنشوف برهان تاني باستخدام الـ monotone convergence theorem", "tokens": [6027, 20292, 31439, 4724, 995, 14851, 9778, 3215, 10943, 37279, 16572, 5172, 17889, 4238, 426, 30767, 16373, 3215, 2423, 39184, 1178, 332, 4858, 282, 4707, 20666, 19913, 3555, 9566, 30767, 1829, 19446, 5551, 12984, 3555, 2655, 8315, 4948, 502, 15844, 426, 4724, 3794, 995, 2407, 10632, 1958, 45595, 20498, 8032, 1863, 8592, 38688, 4724, 2288, 3224, 7649, 6055, 7649, 1829, 4724, 995, 14851, 9778, 3215, 10943, 2423, 39184, 1108, 310, 546, 32181, 20904], "avg_logprob": -0.2125211126498274, "compression_ratio": 1.3367875647668395, "no_speech_prob": 0.0, "words": [{"start": 181.71, "end": 182.05, "word": "اللي", "probability": 0.60791015625}, {"start": 182.05, "end": 182.29, "word": " هو", "probability": 0.953125}, {"start": 182.29, "end": 183.09, "word": " باستخدام", "probability": 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0.82666015625}, {"start": 225.5, "end": 226.06, "word": " معناه", "probability": 0.97119140625}, {"start": 226.06, "end": 226.86, "word": " أن", "probability": 0.4755859375}, {"start": 226.86, "end": 227.0, "word": " ال", "probability": 0.64306640625}, {"start": 227.0, "end": 227.48, "word": " sequence", "probability": 0.900390625}, {"start": 227.48, "end": 227.92, "word": " is", "probability": 0.9267578125}, {"start": 227.92, "end": 228.56, "word": " increasing", "probability": 0.9716796875}], "temperature": 1.0}, {"id": 9, "seek": 24568, "start": 229.82, "end": 245.68, "text": "كذلك الـ sequence هذه is bounded لأنه هي فيه عدد موجب M بساوي واحد عدد موجب بحيث أنه absolute xn أصغر من أو يساوي M لكل N لأن أنا فيها ال sequence increasing", "tokens": [4117, 8848, 23275, 2423, 39184, 8310, 29538, 307, 37498, 5296, 33456, 3224, 39896, 8978, 3224, 6225, 3215, 3215, 3714, 29245, 3555, 376, 4724, 3794, 995, 45865, 36764, 24401, 6225, 3215, 3215, 3714, 29245, 3555, 4724, 5016, 1829, 12984, 14739, 3224, 8236, 2031, 77, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 376, 5296, 28820, 426, 5296, 33456, 41850, 8978, 11296, 2423, 8310, 5662], "avg_logprob": -0.27367422978083294, "compression_ratio": 1.4268292682926829, "no_speech_prob": 0.0, "words": [{"start": 229.82, "end": 230.38, "word": "كذلك", "probability": 0.8702799479166666}, {"start": 230.38, "end": 230.58, "word": " الـ", "probability": 0.58203125}, {"start": 230.58, "end": 230.98, "word": " sequence", "probability": 0.81787109375}, {"start": 230.98, "end": 231.52, "word": " هذه", "probability": 0.455322265625}, {"start": 231.52, "end": 232.28, "word": " is", "probability": 0.75341796875}, {"start": 232.28, "end": 232.76, "word": " bounded", "probability": 0.9375}, {"start": 232.76, "end": 233.72, "word": " لأنه", "probability": 0.7330729166666666}, {"start": 233.72, "end": 234.12, "word": " هي", "probability": 0.475341796875}, {"start": 234.12, "end": 234.44, "word": " فيه", "probability": 0.6217041015625}, {"start": 234.44, "end": 234.74, "word": " عدد", "probability": 0.9728190104166666}, {"start": 234.74, "end": 235.24, "word": " موجب", "probability": 0.9376627604166666}, {"start": 235.24, "end": 235.54, "word": " M", "probability": 0.449951171875}, {"start": 235.54, "end": 236.12, "word": " بساوي", "probability": 0.8223876953125}, {"start": 236.12, "end": 236.54, "word": " واحد", "probability": 0.8583984375}, {"start": 236.54, "end": 236.84, "word": " عدد", "probability": 0.9715169270833334}, {"start": 236.84, "end": 237.32, "word": " موجب", "probability": 0.9928385416666666}, {"start": 237.32, "end": 238.26, "word": " بحيث", "probability": 0.66802978515625}, {"start": 238.26, "end": 238.62, "word": " أنه", "probability": 0.6474609375}, {"start": 238.62, "end": 238.96, "word": " absolute", "probability": 0.77783203125}, {"start": 238.96, "end": 239.7, "word": " xn", "probability": 0.4853515625}, {"start": 239.7, "end": 240.2, "word": " أصغر", "probability": 0.9853515625}, {"start": 240.2, "end": 240.4, "word": " من", "probability": 0.9736328125}, {"start": 240.4, "end": 240.6, "word": " أو", "probability": 0.8056640625}, {"start": 240.6, "end": 241.14, "word": " يساوي", "probability": 0.8570556640625}, {"start": 241.14, "end": 241.46, "word": " M", "probability": 0.8935546875}, {"start": 241.46, "end": 241.92, "word": " لكل", "probability": 0.9873046875}, {"start": 241.92, "end": 242.3, "word": " N", "probability": 0.6669921875}, {"start": 242.3, "end": 243.74, "word": " لأن", "probability": 0.58935546875}, {"start": 243.74, "end": 244.02, "word": " أنا", "probability": 0.62841796875}, {"start": 244.02, "end": 244.32, "word": " فيها", "probability": 0.716796875}, {"start": 244.32, "end": 244.44, "word": " ال", "probability": 0.395263671875}, {"start": 244.44, "end": 244.78, "word": " sequence", "probability": 0.724609375}, {"start": 244.78, "end": 245.68, "word": " increasing", "probability": 0.91845703125}], "temperature": 1.0}, {"id": 10, "seek": 26774, "start": 247.0, "end": 267.74, "text": "decreasing و bounded اذا by monotone convergence theorem ال sequence هذه هتكون convergent و ال limit تبعتها بساوي ال infimum طيب ال infimum للمجموعة هذه بتساوي سفر", "tokens": [1479, 14066, 3349, 4032, 37498, 1975, 15730, 538, 1108, 310, 546, 32181, 20904, 2423, 8310, 29538, 8032, 2655, 30544, 9652, 6930, 4032, 2423, 4948, 6055, 3555, 34268, 11296, 4724, 3794, 995, 45865, 2423, 1536, 332, 449, 23032, 1829, 3555, 2423, 1536, 332, 449, 5296, 19528, 7435, 2304, 2407, 27884, 29538, 39894, 3794, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.27774783968925476, "compression_ratio": 1.3885350318471337, "no_speech_prob": 0.0, "words": [{"start": 247.0, "end": 247.76, "word": "decreasing", "probability": 0.6033528645833334}, {"start": 247.76, "end": 249.66, "word": " و", "probability": 0.31103515625}, {"start": 249.66, "end": 250.26, "word": " bounded", "probability": 0.5849609375}, {"start": 250.26, "end": 251.16, "word": " اذا", "probability": 0.622802734375}, {"start": 251.16, "end": 251.46, "word": " by", "probability": 0.705078125}, {"start": 251.46, "end": 252.0, "word": " monotone", "probability": 0.715576171875}, {"start": 252.0, "end": 252.68, "word": " convergence", "probability": 0.93408203125}, {"start": 252.68, "end": 253.26, "word": " theorem", "probability": 0.89990234375}, {"start": 253.26, "end": 254.66, "word": " ال", "probability": 0.50439453125}, {"start": 254.66, "end": 255.26, "word": " sequence", "probability": 0.7255859375}, {"start": 255.26, "end": 255.82, "word": " هذه", "probability": 0.399169921875}, {"start": 255.82, "end": 256.62, "word": " هتكون", "probability": 0.96533203125}, {"start": 256.62, "end": 257.6, "word": " convergent", "probability": 0.784912109375}, {"start": 257.6, "end": 258.38, "word": " و", "probability": 0.61572265625}, {"start": 258.38, "end": 258.48, "word": " ال", "probability": 0.74755859375}, {"start": 258.48, "end": 258.72, "word": " limit", "probability": 0.96533203125}, {"start": 258.72, "end": 259.46, "word": " تبعتها", "probability": 0.904296875}, {"start": 259.46, "end": 260.42, "word": " بساوي", "probability": 0.71148681640625}, {"start": 260.42, "end": 260.58, "word": " ال", "probability": 0.85205078125}, {"start": 260.58, "end": 261.44, "word": " infimum", "probability": 0.7430013020833334}, {"start": 261.44, "end": 263.22, "word": " طيب", "probability": 0.8663736979166666}, {"start": 263.22, "end": 263.4, "word": " ال", "probability": 0.5068359375}, {"start": 263.4, "end": 263.92, "word": " infimum", "probability": 0.91748046875}, {"start": 263.92, "end": 264.66, "word": " للمجموعة", "probability": 0.8916829427083334}, {"start": 264.66, "end": 265.2, "word": " هذه", "probability": 0.92041015625}, {"start": 265.2, "end": 267.22, "word": " بتساوي", "probability": 0.963623046875}, {"start": 267.22, "end": 267.74, "word": " سفر", "probability": 0.819091796875}], "temperature": 1.0}, {"id": 11, "seek": 29039, "start": 270.57, "end": 290.39, "text": "وبرهان ذلك شبيه ببرهان الـ infimum للـ sequence 1 على n بالساوي 0 باستخدام الـ Archimedean property راجعوا برهان أن الـ infimum للـ sequence 1 على n وهذا ثمتناه في المحاضرات السابقة راجعوا البرهان وكتبوا برهان مشابه له", "tokens": [2407, 26890, 3224, 7649, 29910, 23275, 13412, 21292, 3224, 4724, 26890, 3224, 7649, 2423, 39184, 1536, 332, 449, 24976, 39184, 8310, 502, 15844, 297, 20666, 3794, 995, 45865, 1958, 4724, 995, 14851, 9778, 3215, 10943, 2423, 39184, 10984, 332, 4858, 282, 4707, 12602, 26108, 3615, 14407, 4724, 2288, 3224, 7649, 14739, 2423, 39184, 1536, 332, 449, 24976, 39184, 8310, 502, 15844, 297, 37037, 15730, 38637, 2304, 2655, 8315, 3224, 8978, 9673, 5016, 46958, 2288, 9307, 21136, 16758, 28671, 12602, 26108, 3615, 14407, 2423, 26890, 3224, 7649, 4032, 4117, 2655, 3555, 14407, 4724, 2288, 3224, 7649, 37893, 16758, 3224, 46740], "avg_logprob": -0.18640624433755876, "compression_ratio": 1.7692307692307692, "no_speech_prob": 0.0, "words": [{"start": 270.57, "end": 271.43, "word": "وبرهان", "probability": 0.822021484375}, {"start": 271.43, "end": 272.03, "word": " ذلك", "probability": 0.97607421875}, {"start": 272.03, "end": 272.81, "word": " شبيه", "probability": 0.8512369791666666}, {"start": 272.81, "end": 273.39, "word": " ببرهان", "probability": 0.950439453125}, {"start": 273.39, "end": 273.59, "word": " الـ", "probability": 0.52789306640625}, {"start": 273.59, "end": 274.19, "word": " infimum", "probability": 0.9007161458333334}, {"start": 274.19, "end": 274.91, "word": " للـ", "probability": 0.5147705078125}, {"start": 274.91, "end": 275.31, "word": " sequence", "probability": 0.8818359375}, {"start": 275.31, "end": 275.71, "word": " 1", "probability": 0.5888671875}, {"start": 275.71, "end": 275.89, "word": " على", "probability": 0.7470703125}, {"start": 275.89, "end": 276.11, "word": " n", "probability": 0.62939453125}, {"start": 276.11, "end": 276.73, "word": " بالساوي", "probability": 0.8131103515625}, {"start": 276.73, "end": 277.17, "word": " 0", "probability": 0.53173828125}, {"start": 277.17, "end": 278.87, "word": " باستخدام", "probability": 0.9698079427083334}, {"start": 278.87, "end": 279.09, "word": " الـ", "probability": 0.636474609375}, {"start": 279.09, "end": 279.73, "word": " Archimedean", "probability": 0.8460693359375}, {"start": 279.73, "end": 280.31, "word": " property", "probability": 0.7080078125}, {"start": 280.31, "end": 280.87, "word": " راجعوا", "probability": 0.9375}, {"start": 280.87, "end": 281.37, "word": " برهان", "probability": 0.9468994140625}, {"start": 281.37, "end": 282.51, "word": " أن", "probability": 0.305419921875}, {"start": 282.51, "end": 282.77, "word": " الـ", "probability": 0.637451171875}, {"start": 282.77, "end": 283.11, "word": " infimum", "probability": 0.9783528645833334}, {"start": 283.11, "end": 283.39, "word": " للـ", "probability": 0.642333984375}, {"start": 283.39, "end": 283.65, "word": " sequence", "probability": 0.97998046875}, {"start": 283.65, "end": 284.01, "word": " 1", "probability": 0.93505859375}, {"start": 284.01, "end": 284.21, "word": " على", "probability": 0.9140625}, {"start": 284.21, "end": 284.35, "word": " n", "probability": 0.904296875}, {"start": 284.35, "end": 284.61, "word": " وهذا", "probability": 0.596435546875}, {"start": 284.61, "end": 285.11, "word": " ثمتناه", "probability": 0.8171875}, {"start": 285.11, "end": 285.33, "word": " في", "probability": 0.97314453125}, {"start": 285.33, "end": 286.07, "word": " المحاضرات", "probability": 0.95341796875}, {"start": 286.07, "end": 286.65, "word": " السابقة", "probability": 0.9951171875}, {"start": 286.65, "end": 288.17, "word": " راجعوا", "probability": 0.90966796875}, {"start": 288.17, "end": 288.61, "word": " البرهان", "probability": 0.9346923828125}, {"start": 288.61, "end": 289.09, "word": " وكتبوا", "probability": 0.84765625}, {"start": 289.09, "end": 289.49, "word": " برهان", "probability": 0.991943359375}, {"start": 289.49, "end": 290.09, "word": " مشابه", "probability": 0.9876302083333334}, {"start": 290.09, "end": 290.39, "word": " له", "probability": 0.896484375}], "temperature": 1.0}, {"id": 12, "seek": 31256, "start": 292.46, "end": 312.56, "text": "بنفس الطريقة نثبت ان الانثرام لسيكوانس هادى او الست هادى سفر اذا حسب الـ monotone convergence theorem ال sequence واحد على جذر M is convergent و ال limit تبعتها بساوي الانثرام تبعها اللى هو سفر اذا هى مثال على تطبيق الـ monotone convergence theorem", "tokens": [3555, 1863, 36178, 41950, 16572, 28671, 8717, 12984, 3555, 2655, 16472, 2423, 7649, 12984, 2288, 10943, 5296, 3794, 1829, 4117, 2407, 7649, 3794, 8032, 18513, 7578, 1975, 2407, 2423, 14851, 8032, 18513, 7578, 8608, 5172, 2288, 1975, 15730, 11331, 35457, 2423, 39184, 1108, 310, 546, 32181, 20904, 2423, 8310, 36764, 24401, 15844, 10874, 8848, 2288, 376, 307, 9652, 6930, 4032, 2423, 4948, 6055, 3555, 34268, 11296, 4724, 3794, 995, 45865, 2423, 7649, 12984, 2288, 10943, 6055, 3555, 3615, 11296, 13672, 7578, 31439, 8608, 5172, 2288, 1975, 15730, 8032, 7578, 50113, 6027, 15844, 6055, 9566, 21292, 4587, 2423, 39184, 1108, 310, 546, 32181, 20904], "avg_logprob": -0.40384616129673445, "compression_ratio": 1.829268292682927, "no_speech_prob": 0.0, "words": [{"start": 292.46, "end": 293.32, "word": "بنفس", "probability": 0.8504231770833334}, {"start": 293.32, "end": 293.78, "word": " الطريقة", "probability": 0.9853515625}, {"start": 293.78, "end": 294.16, "word": " نثبت", "probability": 0.9132080078125}, {"start": 294.16, "end": 294.3, "word": " ان", "probability": 0.30908203125}, {"start": 294.3, "end": 294.8, "word": " الانثرام", "probability": 0.512109375}, {"start": 294.8, "end": 295.82, "word": " لسيكوانس", "probability": 0.660400390625}, {"start": 295.82, "end": 296.16, "word": " هادى", "probability": 0.4708658854166667}, {"start": 296.16, "end": 296.28, "word": " او", "probability": 0.70556640625}, {"start": 296.28, "end": 296.58, "word": " الست", "probability": 0.5537109375}, {"start": 296.58, "end": 296.9, "word": " هادى", "probability": 0.9498697916666666}, {"start": 296.9, "end": 297.22, "word": " سفر", "probability": 0.7529296875}, {"start": 297.22, "end": 298.02, "word": " اذا", "probability": 0.5670166015625}, {"start": 298.02, "end": 298.44, "word": " حسب", "probability": 0.920166015625}, {"start": 298.44, "end": 298.66, "word": " الـ", "probability": 0.469879150390625}, {"start": 298.66, "end": 298.9, "word": " monotone", "probability": 0.6710611979166666}, {"start": 298.9, "end": 299.48, "word": " convergence", "probability": 0.962890625}, {"start": 299.48, "end": 299.88, "word": " theorem", "probability": 0.77880859375}, {"start": 299.88, "end": 300.22, "word": " ال", "probability": 0.55810546875}, {"start": 300.22, "end": 300.72, "word": " sequence", "probability": 0.5419921875}, {"start": 300.72, "end": 301.24, "word": " واحد", "probability": 0.86376953125}, {"start": 301.24, "end": 301.4, "word": " على", "probability": 0.60009765625}, {"start": 301.4, "end": 301.78, "word": " جذر", "probability": 0.7099609375}, {"start": 301.78, "end": 302.02, "word": " M", "probability": 0.36083984375}, {"start": 302.02, "end": 302.66, "word": " is", "probability": 0.06561279296875}, {"start": 302.66, "end": 303.4, "word": " convergent", "probability": 0.95068359375}, {"start": 303.4, "end": 304.16, "word": " و", "probability": 0.640625}, {"start": 304.16, "end": 304.52, "word": " ال", "probability": 0.2069091796875}, {"start": 304.52, "end": 304.76, "word": " limit", "probability": 0.8720703125}, {"start": 304.76, "end": 305.22, "word": " تبعتها", "probability": 0.7550048828125}, {"start": 305.22, "end": 305.7, "word": " بساوي", "probability": 0.675048828125}, {"start": 305.7, "end": 306.22, "word": " الانثرام", "probability": 0.736669921875}, {"start": 306.22, "end": 306.68, "word": " تبعها", "probability": 0.70684814453125}, {"start": 306.68, "end": 306.84, "word": " اللى", "probability": 0.708984375}, {"start": 306.84, "end": 307.06, "word": " هو", "probability": 0.94091796875}, {"start": 307.06, "end": 307.56, "word": " سفر", "probability": 0.9596354166666666}, {"start": 307.56, "end": 308.76, "word": " اذا", "probability": 0.6424560546875}, {"start": 308.76, "end": 308.94, "word": " هى", "probability": 0.434326171875}, {"start": 308.94, "end": 309.38, "word": " مثال", "probability": 0.926025390625}, {"start": 309.38, "end": 309.58, "word": " على", "probability": 0.84521484375}, {"start": 309.58, "end": 310.24, "word": " تطبيق", "probability": 0.9871826171875}, {"start": 310.24, "end": 311.22, "word": " الـ", "probability": 0.706787109375}, {"start": 311.22, "end": 311.52, "word": " monotone", "probability": 0.9449869791666666}, {"start": 311.52, "end": 312.1, "word": " convergence", "probability": 0.9619140625}, {"start": 312.1, "end": 312.56, "word": " theorem", "probability": 0.91796875}], "temperature": 1.0}, {"id": 13, "seek": 34081, "start": 314.19, "end": 340.81, "text": "كذلك ممكن برضه زي ما قلتلكم نستخدم الـ monotone convergence theorem في أثبات أن سيكوانس زي هذه is divergent نشوف مع بعض كيف .. إذا هنا هاي سيكوانس الحد العام تبعها xn هذا الint partial sum بالمناسبة هذا الint partial sum في ال harmonic series", "tokens": [4117, 8848, 23275, 3714, 43020, 4724, 43042, 3224, 30767, 1829, 19446, 12174, 1211, 2655, 23275, 2304, 8717, 14851, 9778, 40448, 2423, 39184, 1108, 310, 546, 32181, 20904, 8978, 5551, 12984, 3555, 9307, 14739, 8608, 1829, 4117, 2407, 7649, 3794, 30767, 1829, 29538, 307, 18558, 6930, 8717, 8592, 38688, 20449, 45030, 11242, 9122, 33911, 4386, 11933, 15730, 34105, 8032, 47302, 8608, 1829, 4117, 2407, 7649, 3794, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 2031, 77, 23758, 2423, 686, 14641, 2408, 20666, 2304, 8315, 35457, 3660, 23758, 2423, 686, 14641, 2408, 8978, 2423, 32270, 2638], "avg_logprob": -0.2294407888462669, "compression_ratio": 1.5541125541125542, "no_speech_prob": 0.0, "words": [{"start": 314.19, "end": 314.73, "word": "كذلك", "probability": 0.87158203125}, {"start": 314.73, 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546.29, "end": 546.47, "word": " عند", "probability": 0.94970703125}, {"start": 546.47, "end": 546.95, "word": " المجموعة", "probability": 0.96748046875}, {"start": 546.95, "end": 547.41, "word": " واحد", "probability": 0.956787109375}, {"start": 547.41, "end": 547.65, "word": " زاد", "probability": 0.974365234375}, {"start": 547.65, "end": 547.99, "word": " نص", "probability": 0.9931640625}, {"start": 547.99, "end": 548.29, "word": " زاد", "probability": 0.9716796875}, {"start": 548.29, "end": 548.75, "word": " تلت", "probability": 0.9933268229166666}, {"start": 548.75, "end": 549.43, "word": " الى", "probability": 0.70849609375}, {"start": 549.43, "end": 549.95, "word": " اخر", "probability": 0.962158203125}, {"start": 549.95, "end": 550.25, "word": " حد", "probability": 0.99609375}, {"start": 550.25, "end": 550.65, "word": " واحد", "probability": 0.97509765625}, {"start": 550.65, "end": 550.81, "word": " على", "probability": 0.78369140625}, {"start": 550.81, "end": 551.13, "word": " 2", "probability": 0.8779296875}, {"start": 551.13, "end": 551.41, "word": " أس", "probability": 0.9677734375}, {"start": 551.41, "end": 551.63, "word": " n", "probability": 0.767578125}, {"start": 551.63, "end": 552.43, "word": " صح؟", "probability": 0.8004557291666666}, {"start": 552.43, "end": 552.67, "word": " هذا", "probability": 0.75}, {"start": 552.67, "end": 552.85, "word": " من", "probability": 0.99267578125}, {"start": 552.85, "end": 553.25, "word": " تعريف", "probability": 0.98828125}, {"start": 553.25, "end": 553.39, "word": " ال", "probability": 0.978515625}, {"start": 553.39, "end": 553.71, "word": " sequence", "probability": 0.9833984375}], "temperature": 1.0}, {"id": 22, "seek": 58154, "start": 555.68, "end": 581.54, "text": "الان الحدود هذه تبع المجموع هعملها blocks، بلوكات فواحد لوحده في block، نص لوحده، هاخد التلت والربع مع بعض، بعدين ال block الرابع هتكون خمس و سدس و سبعة و تمان، أربع حدود مع بعض، جمهم مع بعض", "tokens": [6027, 7649, 21542, 3215, 23328, 29538, 6055, 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معناه أن X على 2 نص M أكبر من M لكل M عدد موجب ما معناه أن ال limit لحد هذا أو ال sequence X المؤشرات تبقية 2 نص M تقول infinity معناته هذا الحد العام لها أكبر من أي عدد موجب", "tokens": [37746, 6027, 2655, 6027, 1829, 23758, 20449, 8315, 3224, 14739, 1783, 15844, 568, 8717, 9381, 376, 5551, 4117, 26890, 9154, 376, 5296, 28820, 376, 6225, 3215, 3215, 3714, 29245, 3555, 19446, 20449, 8315, 3224, 14739, 2423, 4948, 5296, 24401, 23758, 34051, 2423, 8310, 1783, 9673, 33604, 46309, 9307, 6055, 3555, 4587, 10632, 568, 8717, 9381, 376, 6055, 4587, 12610, 13202, 20449, 8315, 47395, 23758, 21542, 3215, 18863, 10943, 5296, 11296, 5551, 4117, 26890, 9154, 36632, 6225, 3215, 3215, 3714, 29245, 3555], "avg_logprob": -0.26543444940229743, "compression_ratio": 1.6777777777777778, "no_speech_prob": 0.0, "words": [{"start": 744.05, "end": 744.87, "word": "وبالتالي", "probability": 0.90966796875}, {"start": 744.87, "end": 745.19, "word": " هذا", "probability": 0.693359375}, {"start": 745.19, "end": 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3615, 9957], "avg_logprob": -0.06295138888888889, "compression_ratio": 9.317460317460318, "no_speech_prob": 0.0, "words": [{"start": 828.66, "end": 829.6, "word": "لإثبات", "probability": 0.71064453125}, {"start": 829.6, "end": 829.88, "word": " أن", "probability": 0.580078125}, {"start": 829.88, "end": 830.9, "word": " سيكوانس", "probability": 0.7408040364583334}, {"start": 830.9, "end": 831.36, "word": " معينة", "probability": 0.9703776041666666}, {"start": 831.36, "end": 831.92, "word": " مُعينة", "probability": 0.6619384765625}, {"start": 831.92, "end": 832.14, "word": " مُعينة", "probability": 0.844873046875}, {"start": 832.14, "end": 832.14, "word": " مُعينة", "probability": 0.85380859375}, {"start": 832.14, "end": 832.14, "word": " مُعينة", "probability": 0.8974609375}, {"start": 832.14, "end": 832.32, "word": " مُعينة", "probability": 0.9373046875}, {"start": 832.32, "end": 832.78, "word": " مُعينة", "probability": 0.95732421875}, {"start": 832.78, "end": 832.78, "word": " 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"text": "المثال التالت برضه هنستخدم .. هنطبق عليه اللي هو الـ monotone convergence theorem", "tokens": [45340, 12984, 6027, 16712, 6027, 2655, 4724, 43042, 3224, 8032, 1863, 14851, 9778, 40448, 4386, 8032, 1863, 9566, 3555, 4587, 47356, 13672, 1829, 31439, 2423, 39184, 1108, 310, 546, 32181, 20904], "avg_logprob": -0.13330078404396772, "compression_ratio": 1.196078431372549, "no_speech_prob": 0.0, "words": [{"start": 856.61, "end": 857.23, "word": "المثال", "probability": 0.9609375}, {"start": 857.23, "end": 857.61, "word": " التالت", "probability": 0.9498697916666666}, {"start": 857.61, "end": 857.95, "word": " برضه", "probability": 0.8797200520833334}, {"start": 857.95, "end": 858.79, "word": " هنستخدم", "probability": 0.888671875}, {"start": 858.79, "end": 859.19, "word": " ..", "probability": 0.309814453125}, {"start": 859.19, "end": 860.27, "word": " هنطبق", "probability": 0.94296875}, {"start": 860.27, "end": 860.59, "word": " عليه", "probability": 0.98486328125}, {"start": 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"word": " من", "probability": 0.99267578125}, {"start": 1169.2, "end": 1170.78, "word": " اتنين", "probability": 0.9344482421875}, {"start": 1170.78, "end": 1172.42, "word": " هنا", "probability": 0.201416015625}, {"start": 1172.42, "end": 1172.88, "word": " فرضنا", "probability": 0.9275716145833334}, {"start": 1172.88, "end": 1173.08, "word": " هذا", "probability": 0.5615234375}, {"start": 1173.08, "end": 1173.22, "word": " ال", "probability": 0.74267578125}, {"start": 1173.22, "end": 1173.66, "word": " induction", "probability": 0.95556640625}, {"start": 1173.66, "end": 1174.1, "word": " high", "probability": 0.2705078125}, {"start": 1174.1, "end": 1174.54, "word": " precision", "probability": 0.6005859375}, {"start": 1174.54, "end": 1177.36, "word": " وعايزين", "probability": 0.92578125}, {"start": 1177.36, "end": 1178.04, "word": " نثبت", "probability": 0.9898681640625}, {"start": 1178.04, "end": 1180.18, "word": " ان", "probability": 0.83740234375}, {"start": 1180.18, "end": 1180.52, "word": " هذا", "probability": 0.77783203125}, {"start": 1180.52, "end": 1181.04, "word": " بيقدي", "probability": 0.675537109375}, {"start": 1181.04, "end": 1181.26, "word": " ان", "probability": 0.9033203125}, {"start": 1181.26, "end": 1181.92, "word": " القبارة", "probability": 0.8848876953125}, {"start": 1181.92, "end": 1183.48, "word": " صحيحة", "probability": 0.95810546875}, {"start": 1183.48, "end": 1185.32, "word": " and", "probability": 0.66015625}, {"start": 1185.32, "end": 1185.68, "word": " N", "probability": 0.47998046875}, {"start": 1185.68, "end": 1186.26, "word": " بيساوي", "probability": 0.796142578125}, {"start": 1186.26, "end": 1186.66, "word": " K", "probability": 0.84619140625}, {"start": 1186.66, "end": 1187.08, "word": " زايد", "probability": 0.97314453125}, {"start": 1187.08, "end": 1187.5, "word": " واحد", "probability": 0.96728515625}, {"start": 1187.5, "end": 1187.84, "word": " يعني", "probability": 0.91650390625}, {"start": 1187.84, "end": 1188.14, "word": " بدي", "probability": 0.55047607421875}, {"start": 1188.14, "end": 1188.56, "word": " اثبت", "probability": 0.9212646484375}, {"start": 1188.56, "end": 1188.98, "word": " هذه", "probability": 0.82763671875}, {"start": 1188.98, "end": 1190.66, "word": " المتباينة", "probability": 0.943115234375}], "temperature": 1.0}, {"id": 46, "seek": 122249, "start": 1195.39, "end": 1222.49, "text": "بدي أثبت المتباينة هذه طبعا فتعالى نشوف كيف نثبت المتباينة هذه طيب أنا عندي", "tokens": [3555, 16254, 5551, 12984, 3555, 2655, 9673, 2655, 3555, 995, 9957, 3660, 29538, 23032, 3555, 3615, 995, 6156, 2655, 3615, 6027, 7578, 8717, 8592, 38688, 9122, 33911, 8717, 12984, 3555, 2655, 9673, 2655, 3555, 995, 9957, 3660, 29538, 23032, 1829, 3555, 41850, 18871, 16254], "avg_logprob": -0.2126736177338494, "compression_ratio": 1.5222222222222221, "no_speech_prob": 0.0, "words": [{"start": 1195.39, "end": 1195.81, "word": "بدي", "probability": 0.153564453125}, {"start": 1195.81, "end": 1196.39, "word": " أثبت", "probability": 0.910888671875}, {"start": 1196.39, "end": 1197.33, "word": " المتباينة", "probability": 0.9241536458333334}, {"start": 1197.33, "end": 1197.93, "word": " هذه", "probability": 0.417724609375}, {"start": 1197.93, "end": 1199.17, "word": " طبعا", "probability": 0.77032470703125}, {"start": 1199.17, "end": 1200.99, "word": " فتعالى", "probability": 0.88271484375}, {"start": 1200.99, "end": 1201.53, "word": " نشوف", "probability": 0.9864908854166666}, {"start": 1201.53, "end": 1201.93, "word": " كيف", "probability": 0.95556640625}, {"start": 1201.93, "end": 1202.59, "word": " نثبت", "probability": 0.9853515625}, {"start": 1202.59, "end": 1204.07, "word": " المتباينة", "probability": 0.9861653645833334}, {"start": 1204.07, "end": 1205.11, "word": " هذه", "probability": 0.93701171875}, {"start": 1205.11, "end": 1221.69, "word": " طيب", "probability": 0.8712565104166666}, {"start": 1221.69, "end": 1221.91, "word": " أنا", "probability": 0.59423828125}, {"start": 1221.91, "end": 1222.49, "word": " عندي", "probability": 0.8154296875}], "temperature": 1.0}, {"id": 47, "seek": 125328, "start": 1223.84, "end": 1253.28, "text": "هي عندي المتباينة هذه احنا فرضين ان المتباينة هذه صحيحة احنا فرضين من induction hypothesis ان هذه المتباينة صحيحة", "tokens": [3224, 1829, 18871, 16254, 9673, 2655, 3555, 995, 9957, 3660, 29538, 1975, 5016, 8315, 6156, 43042, 9957, 16472, 9673, 2655, 3555, 995, 9957, 3660, 29538, 20328, 5016, 1829, 5016, 3660, 1975, 5016, 8315, 6156, 43042, 9957, 9154, 33371, 17291, 16472, 29538, 9673, 2655, 3555, 995, 9957, 3660, 20328, 5016, 1829, 5016, 3660], "avg_logprob": -0.11497641509433962, "compression_ratio": 1.7339449541284404, "no_speech_prob": 0.0, "words": [{"start": 1223.84, "end": 1224.14, "word": "هي", "probability": 0.5521240234375}, {"start": 1224.14, "end": 1224.46, "word": " عندي", "probability": 0.768310546875}, {"start": 1224.46, "end": 1225.3, "word": " المتباينة", "probability": 0.955322265625}, {"start": 1225.3, "end": 1225.84, "word": " هذه", "probability": 0.7099609375}, {"start": 1225.84, "end": 1229.98, "word": " احنا", "probability": 0.8642578125}, {"start": 1229.98, "end": 1230.56, "word": " فرضين", "probability": 0.98388671875}, {"start": 1230.56, "end": 1230.8, "word": " ان", "probability": 0.8037109375}, {"start": 1230.8, "end": 1231.74, "word": " المتباينة", "probability": 0.93896484375}, {"start": 1231.74, "end": 1232.0, "word": " هذه", "probability": 0.69482421875}, {"start": 1232.0, "end": 1233.34, "word": " صحيحة", "probability": 0.91552734375}, {"start": 1233.34, "end": 1249.6, "word": " احنا", "probability": 0.9417317708333334}, {"start": 1249.6, "end": 1250.06, "word": " فرضين", "probability": 0.9933268229166666}, {"start": 1250.06, "end": 1250.2, "word": " من", "probability": 0.97265625}, {"start": 1250.2, "end": 1250.68, "word": " induction", "probability": 0.77978515625}, {"start": 1250.68, "end": 1251.34, "word": " hypothesis", "probability": 0.91455078125}, {"start": 1251.34, "end": 1251.76, "word": " ان", "probability": 0.7451171875}, {"start": 1251.76, "end": 1252.04, "word": " هذه", "probability": 0.56884765625}, {"start": 1252.04, "end": 1252.64, "word": " المتباينة", "probability": 0.9903157552083334}, {"start": 1252.64, "end": 1253.28, "word": " صحيحة", "probability": 0.9892578125}], "temperature": 1.0}, {"id": 48, "seek": 127157, "start": 1254.45, "end": 1271.57, "text": "أضرب المتباينة هذه في اتنين هي اضرب كل الأطراف في اتنين فبصير اتنين اصغر من اتنين XK اصغر من اتنين XK زائد واحد اصغر من اربع وهذا بيقدي ان واحد اصغر من جدر اتنين", "tokens": [10721, 11242, 25513, 9673, 2655, 3555, 995, 9957, 3660, 29538, 8978, 1975, 2655, 1863, 9957, 39896, 1975, 11242, 25513, 28242, 16247, 9566, 23557, 5172, 8978, 1975, 2655, 1863, 9957, 6156, 3555, 9381, 13546, 1975, 2655, 1863, 9957, 1975, 9381, 17082, 2288, 9154, 1975, 2655, 1863, 9957, 1783, 42, 1975, 9381, 17082, 2288, 9154, 1975, 2655, 1863, 9957, 1783, 42, 30767, 16373, 3215, 36764, 24401, 1975, 9381, 17082, 2288, 9154, 1975, 25513, 3615, 37037, 15730, 4724, 1829, 4587, 16254, 16472, 36764, 24401, 1975, 9381, 17082, 2288, 9154, 10874, 3215, 2288, 1975, 2655, 1863, 9957], "avg_logprob": -0.20113031899041317, "compression_ratio": 2.0802919708029197, "no_speech_prob": 0.0, "words": [{"start": 1254.45, "end": 1254.93, "word": "أضرب", "probability": 0.5813395182291666}, {"start": 1254.93, "end": 1255.65, "word": " المتباينة", "probability": 0.8685709635416666}, {"start": 1255.65, "end": 1255.87, "word": " هذه", "probability": 0.36083984375}, {"start": 1255.87, "end": 1256.01, "word": " في", "probability": 0.72119140625}, {"start": 1256.01, "end": 1256.39, "word": " اتنين", "probability": 0.76629638671875}, {"start": 1256.39, "end": 1257.83, "word": " هي", "probability": 0.1041259765625}, {"start": 1257.83, "end": 1258.23, "word": " اضرب", "probability": 0.88330078125}, {"start": 1258.23, "end": 1258.91, "word": " كل", "probability": 0.88330078125}, {"start": 1258.91, "end": 1259.39, "word": " الأطراف", "probability": 0.850830078125}, {"start": 1259.39, "end": 1259.53, "word": " في", "probability": 0.7958984375}, {"start": 1259.53, "end": 1259.87, "word": " اتنين", "probability": 0.9781494140625}, {"start": 1259.87, "end": 1260.51, "word": " فبصير", "probability": 0.81329345703125}, {"start": 1260.51, "end": 1260.93, "word": " اتنين", "probability": 0.9471435546875}, {"start": 1260.93, "end": 1261.35, "word": " اصغر", "probability": 0.874755859375}, {"start": 1261.35, "end": 1261.49, "word": " من", "probability": 0.98291015625}, {"start": 1261.49, "end": 1261.85, "word": " اتنين", "probability": 0.9820556640625}, {"start": 1261.85, "end": 1262.31, "word": " XK", "probability": 0.5582275390625}, {"start": 1262.31, "end": 1262.71, "word": " اصغر", "probability": 0.948974609375}, {"start": 1262.71, "end": 1262.83, "word": " من", "probability": 0.98828125}, {"start": 1262.83, "end": 1263.13, "word": " اتنين", "probability": 0.98779296875}, {"start": 1263.13, "end": 1263.59, "word": " XK", "probability": 0.95556640625}, {"start": 1263.59, "end": 1263.87, "word": " زائد", "probability": 0.5677490234375}, {"start": 1263.87, "end": 1264.29, "word": " واحد", "probability": 0.972900390625}, {"start": 1264.29, "end": 1265.39, "word": " اصغر", "probability": 0.9649658203125}, {"start": 1265.39, "end": 1265.55, "word": " من", "probability": 0.9951171875}, {"start": 1265.55, "end": 1266.07, "word": " اربع", "probability": 0.8172200520833334}, {"start": 1266.07, "end": 1268.39, "word": " وهذا", "probability": 0.80810546875}, {"start": 1268.39, "end": 1268.89, "word": " بيقدي", "probability": 0.6641845703125}, {"start": 1268.89, "end": 1269.29, "word": " ان", "probability": 0.86865234375}, {"start": 1269.29, "end": 1269.97, "word": " واحد", "probability": 0.981689453125}, {"start": 1269.97, "end": 1270.47, "word": " اصغر", "probability": 0.9774169921875}, {"start": 1270.47, "end": 1270.67, "word": " من", "probability": 0.990234375}, {"start": 1270.67, "end": 1271.05, "word": " جدر", "probability": 0.9573567708333334}, {"start": 1271.05, "end": 1271.57, "word": " اتنين", "probability": 0.9854736328125}], "temperature": 1.0}, {"id": 49, "seek": 130473, "start": 1275.73, "end": 1304.73, "text": "و اذا انا الان باخد الجذر التربيعى لكل الأطراف هذه اخد الجذر التربيعى فهي جذر اتنين طبعا اكبر من واحد اصغر منه يساوي جذر اتنين XK اللى هو XK زاد واحد هذا طبعا من التعريف تبع ال sequence من ال inductive formula جذر اتنين XK حسب التعريف بساوي XK زاد واحد", "tokens": [2407, 1975, 15730, 1975, 8315, 2423, 7649, 4724, 47283, 3215, 25724, 8848, 2288, 16712, 2288, 21292, 3615, 7578, 5296, 28820, 16247, 9566, 23557, 5172, 29538, 1975, 9778, 3215, 25724, 8848, 2288, 16712, 2288, 21292, 3615, 7578, 6156, 3224, 1829, 10874, 8848, 2288, 1975, 2655, 1863, 9957, 23032, 3555, 3615, 995, 1975, 4117, 26890, 9154, 36764, 24401, 1975, 9381, 17082, 2288, 9154, 3224, 7251, 3794, 995, 45865, 10874, 8848, 2288, 1975, 2655, 1863, 9957, 1783, 42, 13672, 7578, 31439, 1783, 42, 30767, 18513, 36764, 24401, 23758, 23032, 3555, 3615, 995, 9154, 16712, 3615, 16572, 5172, 6055, 3555, 3615, 2423, 8310, 9154, 2423, 31612, 488, 8513, 10874, 8848, 2288, 1975, 2655, 1863, 9957, 1783, 42, 11331, 35457, 16712, 3615, 16572, 5172, 4724, 3794, 995, 45865, 1783, 42, 30767, 18513, 36764, 24401], "avg_logprob": -0.15901441757495588, "compression_ratio": 2.0686274509803924, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1275.73, "end": 1276.69, "word": "و", "probability": 0.309326171875}, {"start": 1276.69, "end": 1277.65, "word": " اذا", "probability": 0.52154541015625}, {"start": 1277.65, "end": 1277.89, "word": " انا", "probability": 0.83251953125}, {"start": 1277.89, "end": 1278.23, "word": " الان", "probability": 0.61688232421875}, {"start": 1278.23, "end": 1278.73, "word": " باخد", "probability": 0.9744466145833334}, {"start": 1278.73, "end": 1279.21, "word": " الجذر", "probability": 0.87841796875}, {"start": 1279.21, "end": 1280.11, "word": " التربيعى", "probability": 0.82119140625}, {"start": 1280.11, "end": 1280.89, "word": " لكل", "probability": 0.91650390625}, {"start": 1280.89, "end": 1281.53, "word": " الأطراف", "probability": 0.9041748046875}, {"start": 1281.53, "end": 1281.83, "word": " هذه", "probability": 0.322021484375}, {"start": 1281.83, "end": 1282.13, "word": " اخد", "probability": 0.7151692708333334}, {"start": 1282.13, "end": 1282.51, "word": " الجذر", "probability": 0.9635416666666666}, {"start": 1282.51, "end": 1283.21, "word": " التربيعى", "probability": 0.965625}, {"start": 1283.21, "end": 1284.23, "word": " فهي", "probability": 0.78564453125}, {"start": 1284.23, "end": 1284.61, "word": " جذر", "probability": 0.9295247395833334}, {"start": 1284.61, "end": 1285.13, "word": " اتنين", "probability": 0.8204345703125}, {"start": 1285.13, "end": 1285.77, "word": " طبعا", "probability": 0.95751953125}, {"start": 1285.77, "end": 1286.13, "word": " اكبر", "probability": 0.9542643229166666}, {"start": 1286.13, "end": 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جذر", "probability": 0.9855143229166666}, {"start": 1299.71, "end": 1300.03, "word": " اتنين", "probability": 0.9871826171875}, {"start": 1300.03, "end": 1300.51, "word": " XK", "probability": 0.9775390625}, {"start": 1300.51, "end": 1302.01, "word": " حسب", "probability": 0.77490234375}, {"start": 1302.01, "end": 1302.51, "word": " التعريف", "probability": 0.99462890625}, {"start": 1302.51, "end": 1303.13, "word": " بساوي", "probability": 0.7833251953125}, {"start": 1303.13, "end": 1304.01, "word": " XK", "probability": 0.97265625}, {"start": 1304.01, "end": 1304.37, "word": " زاد", "probability": 0.950927734375}, {"start": 1304.37, "end": 1304.73, "word": " واحد", "probability": 0.989013671875}], "temperature": 1.0}, {"id": 50, "seek": 133420, "start": 1306.26, "end": 1334.2, "text": "وهذا أصغر من هنا جدر اتنين xk أصغر من جدر اتنين xk زائد واحد وهذا أصغر من جدر الأربع اللي هو الأتنين إذا هاي بيطلع عندي واحد أصغر من أو يساوي xk زائد واحد وهذا برضه من ال inductive formula الجدر التربيع 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induction أن xn أكبر من أوسع واحد أصغر من الأتنين و أثبتنا أن ال sequence هذه convergent، إذا حسب نظرية سابقة", "tokens": [1211, 33456, 1975, 12984, 3555, 2655, 8315, 34105, 538, 33371, 14739, 2031, 77, 5551, 4117, 26890, 9154, 34051, 3794, 3615, 36764, 24401, 5551, 9381, 17082, 2288, 9154, 16247, 2655, 1863, 9957, 4032, 5551, 12984, 3555, 2655, 8315, 14739, 2423, 8310, 29538, 9652, 6930, 12399, 11933, 15730, 11331, 35457, 8717, 19913, 2288, 10632, 8608, 16758, 28671], "avg_logprob": -0.29045759035008295, "compression_ratio": 1.3445945945945945, "no_speech_prob": 0.0, "words": [{"start": 1568.68, "end": 1569.2, "word": "لأن", "probability": 0.6163330078125}, {"start": 1569.2, "end": 1570.12, "word": " اثبتنا", "probability": 0.82412109375}, {"start": 1570.12, "end": 1570.4, "word": " هنا", "probability": 0.34130859375}, {"start": 1570.4, "end": 1570.7, "word": " by", "probability": 0.630859375}, {"start": 1570.7, "end": 1572.9, "word": " induction", "probability": 0.97607421875}, 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"word": " ممكن", "probability": 0.99267578125}, {"start": 1631.44, "end": 1631.88, "word": " تساوي", "probability": 0.935791015625}, {"start": 1631.88, "end": 1632.34, "word": " سفر", "probability": 0.88671875}, {"start": 1632.34, "end": 1633.7, "word": " مش", "probability": 0.716796875}, {"start": 1633.7, "end": 1634.04, "word": " ممكن", "probability": 0.992431640625}, {"start": 1634.04, "end": 1634.62, "word": " تساوي", "probability": 0.98779296875}, {"start": 1634.62, "end": 1635.42, "word": " سفر", "probability": 0.9928385416666666}, {"start": 1635.42, "end": 1636.38, "word": " اذا", "probability": 0.7587890625}, {"start": 1636.38, "end": 1636.9, "word": " لازم", "probability": 0.9853515625}, {"start": 1636.9, "end": 1637.54, "word": " الساوي", "probability": 0.8004557291666666}, {"start": 1637.54, "end": 1637.64, "word": " ..", "probability": 0.468505859375}, {"start": 1637.64, "end": 1637.94, "word": " وانا", "probability": 0.9235026041666666}, {"start": 1637.94, "end": 1638.3, "word": " عندي", "probability": 0.893310546875}, {"start": 1638.3, "end": 1638.8, "word": " سفر", "probability": 0.97314453125}, {"start": 1638.8, "end": 1638.94, "word": " او", "probability": 0.955810546875}, {"start": 1638.94, "end": 1639.3, "word": " اتنين", "probability": 0.99365234375}, {"start": 1639.3, "end": 1639.5, "word": " اذا", "probability": 0.784912109375}, {"start": 1639.5, "end": 1639.82, "word": " لازم", "probability": 0.9908854166666666}, {"start": 1639.82, "end": 1640.16, "word": " الساوي", "probability": 0.7537434895833334}, {"start": 1640.16, "end": 1640.46, "word": " اتنين", "probability": 0.98828125}], "temperature": 1.0}, {"id": 62, "seek": 166989, "start": 1641.55, "end": 1669.89, "text": "Okay إذا هين هيك استخدمنا الـ monotone convergence بالمثل في أد التمرين زي هذه sequences معرفة inductively و هتثبتوا أنها convergent و تجيبوا قيمة ال limit بنفس الطريقة و بنفس الأسلوب فحاولوا تستفيدوا من حل المثال الأخير هذا في حل مثل هذه التمرين Okay تمام واضح", "tokens": 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theorem، ال sub-sequences شوفنا قبل شوية sub-sequence", "tokens": [6027, 39184, 1422, 12, 11834, 2667, 293, 14331, 89, 3730, 12, 4360, 811, 9733, 640, 20904, 12399, 2423, 1422, 12, 11834, 2667, 13412, 38688, 8315, 12174, 36150, 13412, 2407, 10632, 1422, 12, 11834, 655], "avg_logprob": -0.3723214217594692, "compression_ratio": 1.202127659574468, "no_speech_prob": 0.0, "words": [{"start": 1789.63, "end": 1789.95, "word": "الـ", "probability": 0.685302734375}, {"start": 1789.95, "end": 1790.17, "word": " sub", "probability": 0.2213134765625}, {"start": 1790.17, "end": 1791.01, "word": "-sequences", "probability": 0.7611490885416666}, {"start": 1791.01, "end": 1793.03, "word": " and", "probability": 0.274169921875}, {"start": 1793.03, "end": 1793.87, "word": " Bolzano", "probability": 0.7632649739583334}, {"start": 1793.87, "end": 1794.61, "word": "-Weierstrass", "probability": 0.7654296875}, {"start": 1794.61, "end": 1796.07, "word": " theorem،", "probability": 0.596435546875}, {"start": 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{"start": 1856.34, "end": 1856.7, "word": " هذي", "probability": 0.93359375}, {"start": 1856.7, "end": 1857.28, "word": " سمنها", "probability": 0.8310546875}, {"start": 1857.28, "end": 1858.1, "word": " R2", "probability": 0.986328125}, {"start": 1858.1, "end": 1860.66, "word": " والتمانية", "probability": 0.8917236328125}, {"start": 1860.66, "end": 1861.34, "word": " R3", "probability": 0.973388671875}], "temperature": 1.0}, {"id": 70, "seek": 188576, "start": 1864.82, "end": 1885.76, "text": "فبنلاحظ أن R1 أكبر من أو ساوء واحد، عدد طبيعي أكبر من أو ساوء واحد وR2 أكبر من R1، اللي هو أربعة أكبر من اتنين وR3 اللي هو تمانية أكبر من R2", "tokens": [5172, 3555, 1863, 15040, 5016, 19913, 14739, 497, 16, 5551, 4117, 26890, 9154, 34051, 8608, 995, 2407, 38207, 36764, 24401, 12399, 6225, 3215, 3215, 23032, 21292, 3615, 1829, 5551, 4117, 26890, 9154, 34051, 8608, 995, 2407, 38207, 36764, 24401, 4032, 49, 17, 5551, 4117, 26890, 9154, 497, 16, 12399, 13672, 1829, 31439, 5551, 25513, 27884, 5551, 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{"start": 1869.92, "end": 1870.48, "word": " طبيعي", "probability": 0.94580078125}, {"start": 1870.48, "end": 1870.94, "word": " أكبر", "probability": 0.97216796875}, {"start": 1870.94, "end": 1871.14, "word": " من", "probability": 0.994140625}, {"start": 1871.14, "end": 1871.32, "word": " أو", "probability": 0.9677734375}, {"start": 1871.32, "end": 1871.66, "word": " ساوء", "probability": 0.9775390625}, {"start": 1871.66, "end": 1872.08, "word": " واحد", "probability": 0.9873046875}, {"start": 1872.08, "end": 1874.52, "word": " وR2", "probability": 0.7600911458333334}, {"start": 1874.52, "end": 1877.24, "word": " أكبر", "probability": 0.9720052083333334}, {"start": 1877.24, "end": 1877.42, "word": " من", "probability": 0.99560546875}, {"start": 1877.42, "end": 1878.32, "word": " R1،", "probability": 0.8570963541666666}, {"start": 1878.32, "end": 1878.36, "word": " اللي", "probability": 0.7308349609375}, {"start": 1878.36, "end": 1878.56, "word": " هو", "probability": 0.978515625}, {"start": 1878.56, "end": 1878.98, "word": " أربعة", "probability": 0.7980143229166666}, {"start": 1878.98, "end": 1879.32, "word": " أكبر", "probability": 0.9811197916666666}, {"start": 1879.32, "end": 1879.5, "word": " من", "probability": 0.99462890625}, {"start": 1879.5, "end": 1879.96, "word": " اتنين", "probability": 0.9090576171875}, {"start": 1879.96, "end": 1882.14, "word": " وR3", "probability": 0.80078125}, {"start": 1882.14, "end": 1882.44, "word": " اللي", "probability": 0.89111328125}, {"start": 1882.44, "end": 1882.64, "word": " هو", "probability": 0.9892578125}, {"start": 1882.64, "end": 1883.28, "word": " تمانية", "probability": 0.880859375}, {"start": 1883.28, "end": 1884.52, "word": " أكبر", "probability": 0.908203125}, {"start": 1884.52, "end": 1885.12, "word": " من", "probability": 0.99658203125}, {"start": 1885.12, "end": 1885.76, "word": " R2", "probability": 0.984375}], "temperature": 1.0}, {"id": 71, "seek": 191619, "start": 1887.01, "end": 1916.19, "text": "و هكذا اذا ال sub sequence المؤشرات تبعتها او ال indices انا بسميه index مجموعة index indices ال indices او المؤشرات لل sub sequence هي عداد طبيعية هذا هي اتنين اربعة تمانية هي عداد طبيعية والعداد الطبيعية هذه بتشكل sequence هذه عبارة عن sequence of natural numbers", "tokens": [2407, 8032, 4117, 15730, 1975, 15730, 2423, 1422, 8310, 9673, 33604, 46309, 9307, 6055, 3555, 34268, 11296, 1975, 2407, 2423, 43840, 1975, 8315, 4724, 38251, 1829, 3224, 8186, 3714, 7435, 2304, 2407, 27884, 8186, 43840, 2423, 43840, 1975, 2407, 9673, 33604, 46309, 9307, 24976, 1422, 8310, 39896, 6225, 3215, 18513, 23032, 21292, 3615, 10632, 23758, 39896, 1975, 2655, 1863, 9957, 1975, 25513, 27884, 46811, 7649, 10632, 39896, 6225, 3215, 18513, 23032, 21292, 3615, 10632, 16070, 22488, 18513, 41950, 21292, 3615, 10632, 29538, 39894, 8592, 28820, 8310, 29538, 6225, 3555, 9640, 3660, 18871, 8310, 295, 3303, 3547], "avg_logprob": -0.16196842291920455, "compression_ratio": 1.9752475247524752, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1887.01, "end": 1887.27, "word": "و", "probability": 0.85205078125}, {"start": 1887.27, "end": 1887.93, "word": " هكذا", "probability": 0.8375651041666666}, {"start": 1887.93, "end": 1889.05, "word": " اذا", "probability": 0.5625}, {"start": 1889.05, "end": 1889.35, "word": " ال", "probability": 0.9013671875}, {"start": 1889.35, "end": 1889.59, "word": " sub", "probability": 0.488037109375}, {"start": 1889.59, "end": 1890.13, "word": " sequence", "probability": 0.58740234375}, {"start": 1890.13, "end": 1891.19, "word": " المؤشرات", "probability": 0.95263671875}, {"start": 1891.19, "end": 1891.99, "word": " تبعتها", "probability": 0.8741455078125}, {"start": 1891.99, "end": 1892.89, "word": " او", "probability": 0.94091796875}, {"start": 1892.89, "end": 1893.03, "word": " ال", "probability": 0.93017578125}, {"start": 1893.03, "end": 1893.61, "word": " indices", "probability": 0.77197265625}, {"start": 1893.61, "end": 1894.81, "word": " انا", "probability": 0.691162109375}, {"start": 1894.81, "end": 1895.39, "word": " بسميه", "probability": 0.9149169921875}, {"start": 1895.39, "end": 1895.93, "word": " index", "probability": 0.79736328125}, {"start": 1895.93, "end": 1897.11, "word": " مجموعة", "probability": 0.882421875}, {"start": 1897.11, "end": 1897.55, "word": " index", "probability": 0.79541015625}, {"start": 1897.55, "end": 1898.33, "word": " indices", "probability": 0.72216796875}, {"start": 1898.33, "end": 1899.43, "word": " ال", "probability": 0.9501953125}, {"start": 1899.43, "end": 1899.89, "word": " indices", "probability": 0.87109375}, {"start": 1899.89, "end": 1900.33, "word": " او", "probability": 0.967529296875}, {"start": 1900.33, "end": 1901.15, "word": " المؤشرات", "probability": 0.98779296875}, {"start": 1901.15, "end": 1901.39, "word": " لل", "probability": 0.748046875}, {"start": 1901.39, "end": 1901.65, "word": " sub", "probability": 0.720703125}, {"start": 1901.65, "end": 1902.23, "word": " sequence", "probability": 0.9013671875}, {"start": 1902.23, "end": 1903.03, "word": " هي", "probability": 0.685546875}, {"start": 1903.03, "end": 1903.53, "word": " عداد", "probability": 0.9309895833333334}, {"start": 1903.53, "end": 1904.21, "word": " طبيعية", "probability": 0.9385986328125}, {"start": 1904.21, "end": 1904.49, "word": " هذا", "probability": 0.1153564453125}, {"start": 1904.49, "end": 1904.71, "word": " هي", "probability": 0.75341796875}, {"start": 1904.71, "end": 1905.07, "word": " اتنين", "probability": 0.8741455078125}, {"start": 1905.07, "end": 1905.49, "word": " اربعة", "probability": 0.8819986979166666}, {"start": 1905.49, "end": 1906.07, "word": " تمانية", "probability": 0.9571940104166666}, {"start": 1906.07, "end": 1906.77, "word": " هي", "probability": 0.6025390625}, {"start": 1906.77, "end": 1907.17, "word": " عداد", "probability": 0.9833984375}, {"start": 1907.17, "end": 1907.85, "word": " طبيعية", "probability": 0.9896240234375}, {"start": 1907.85, "end": 1909.23, "word": " والعداد", "probability": 0.84619140625}, {"start": 1909.23, "end": 1909.89, "word": " الطبيعية", "probability": 0.971923828125}, {"start": 1909.89, "end": 1910.27, "word": " هذه", "probability": 0.69189453125}, {"start": 1910.27, "end": 1910.97, "word": " بتشكل", "probability": 0.9718424479166666}, {"start": 1910.97, "end": 1911.65, "word": " sequence", "probability": 0.8896484375}, {"start": 1911.65, "end": 1913.57, "word": " هذه", "probability": 0.73681640625}, {"start": 1913.57, "end": 1913.99, "word": " عبارة", "probability": 0.99560546875}, {"start": 1913.99, "end": 1914.17, "word": " عن", "probability": 0.99658203125}, {"start": 1914.17, "end": 1914.81, "word": " sequence", "probability": 0.97998046875}, {"start": 1914.81, "end": 1915.17, "word": " of", "probability": 0.96923828125}, {"start": 1915.17, "end": 1915.69, "word": " natural", "probability": 0.9091796875}, {"start": 1915.69, "end": 1916.19, "word": " numbers", "probability": 0.8876953125}], "temperature": 1.0}, {"id": 72, "seek": 194578, "start": 1917.84, "end": 1945.78, "text": "صح؟ و ال sequence هذه is strictly .. strictly increasing .. strictly increasing يعني متزايدة زيادة صحيحة يعني R واحد أصغر منه مش أصغر منه أو يساوي R اتنين و R اتنين أصغر منه و لا تساوي R تلاتة و هكذا مظبوط؟ صح؟", "tokens": [9381, 5016, 22807, 4032, 2423, 8310, 29538, 307, 20792, 4386, 20792, 5662, 4386, 20792, 5662, 37495, 22653, 44650, 11622, 995, 25708, 3660, 30767, 1829, 18513, 3660, 20328, 5016, 1829, 5016, 3660, 37495, 22653, 497, 36764, 24401, 5551, 9381, 17082, 2288, 9154, 3224, 37893, 5551, 9381, 17082, 2288, 9154, 3224, 34051, 7251, 3794, 995, 45865, 497, 1975, 2655, 1863, 9957, 4032, 497, 1975, 2655, 1863, 9957, 5551, 9381, 17082, 2288, 9154, 3224, 4032, 20193, 6055, 3794, 995, 45865, 497, 6055, 1211, 9307, 3660, 4032, 8032, 4117, 15730, 3714, 19913, 3555, 2407, 9566, 22807, 20328, 5016, 22807], "avg_logprob": -0.1554361948122581, "compression_ratio": 1.7081081081081082, "no_speech_prob": 0.0, "words": [{"start": 1917.84, "end": 1918.76, "word": "صح؟", "probability": 0.8531901041666666}, {"start": 1918.76, "end": 1919.68, "word": " و", "probability": 0.625}, {"start": 1919.68, "end": 1919.92, "word": " ال", "probability": 0.921875}, {"start": 1919.92, "end": 1920.26, "word": " sequence", "probability": 0.88818359375}, {"start": 1920.26, "end": 1920.74, "word": " هذه", "probability": 0.56298828125}, {"start": 1920.74, "end": 1921.12, "word": " is", "probability": 0.92138671875}, {"start": 1921.12, "end": 1921.88, "word": " strictly", "probability": 0.96240234375}, {"start": 1921.88, "end": 1922.12, "word": " ..", "probability": 0.65576171875}, {"start": 1922.12, "end": 1924.84, "word": " strictly", "probability": 0.89697265625}, {"start": 1924.84, "end": 1928.2, "word": " increasing", "probability": 0.50732421875}, {"start": 1928.2, "end": 1928.58, "word": " ..", "probability": 0.369384765625}, {"start": 1928.58, "end": 1929.22, "word": " strictly", "probability": 0.96435546875}, {"start": 1929.22, "end": 1929.82, "word": " increasing", "probability": 0.96630859375}, {"start": 1929.82, "end": 1931.18, "word": " يعني", "probability": 0.94921875}, {"start": 1931.18, "end": 1932.9, "word": " متزايدة", "probability": 0.96650390625}, {"start": 1932.9, "end": 1933.64, "word": " زيادة", "probability": 0.9822998046875}, {"start": 1933.64, "end": 1934.58, "word": " صحيحة", "probability": 0.99580078125}, {"start": 1934.58, "end": 1935.44, "word": " يعني", "probability": 0.947998046875}, {"start": 1935.44, "end": 1935.68, "word": " R", "probability": 0.72216796875}, {"start": 1935.68, "end": 1936.16, "word": " واحد", "probability": 0.71484375}, {"start": 1936.16, "end": 1936.66, "word": " أصغر", "probability": 0.952392578125}, {"start": 1936.66, "end": 1936.96, "word": " منه", "probability": 0.9638671875}, {"start": 1936.96, "end": 1937.14, "word": " مش", "probability": 0.68310546875}, {"start": 1937.14, "end": 1937.52, "word": " أصغر", "probability": 0.976806640625}, {"start": 1937.52, "end": 1937.76, "word": " منه", "probability": 0.94287109375}, {"start": 1937.76, "end": 1937.92, "word": " أو", "probability": 0.60986328125}, {"start": 1937.92, "end": 1938.24, "word": " يساوي", "probability": 0.9483642578125}, {"start": 1938.24, "end": 1938.48, "word": " R", "probability": 0.9560546875}, {"start": 1938.48, "end": 1938.86, "word": " اتنين", "probability": 0.9111328125}, {"start": 1938.86, "end": 1939.46, "word": " و", "probability": 0.9052734375}, {"start": 1939.46, "end": 1939.7, "word": " R", "probability": 0.76416015625}, {"start": 1939.7, "end": 1940.1, "word": " اتنين", "probability": 0.9666748046875}, {"start": 1940.1, "end": 1940.6, "word": " أصغر", "probability": 0.9716796875}, {"start": 1940.6, "end": 1941.1, "word": " منه", "probability": 0.994140625}, {"start": 1941.1, "end": 1941.42, "word": " و", "probability": 0.366455078125}, {"start": 1941.42, "end": 1941.54, "word": " لا", "probability": 0.7998046875}, {"start": 1941.54, "end": 1941.98, "word": " تساوي", "probability": 0.941650390625}, {"start": 1941.98, "end": 1942.18, "word": " R", "probability": 0.9736328125}, {"start": 1942.18, "end": 1942.64, "word": " تلاتة", "probability": 0.845703125}, {"start": 1942.64, "end": 1942.8, "word": " و", "probability": 0.85205078125}, {"start": 1942.8, "end": 1943.28, "word": " هكذا", "probability": 0.671142578125}, {"start": 1943.28, "end": 1945.32, "word": " مظبوط؟", "probability": 0.7838541666666666}, {"start": 1945.32, "end": 1945.78, "word": " صح؟", "probability": 0.9768880208333334}], "temperature": 1.0}, {"id": 73, "seek": 197741, "start": 1949.03, "end": 1977.41, "text": "إذا السب سيكوانس السب سيكوانس من أي سيكوانس هي مجموعة جزئية منها صح لأن حدودها هي حدود حدود السب سيكوانس هي عناصر أو حدود من السيكوانس العصلية لكن مش أي حدود لازم تكون مرتبة بحيث أن المؤشرات تبعتها اتشكل strictly increasing sequence of natural numbers", "tokens": [28814, 15730, 21136, 3555, 8608, 1829, 4117, 2407, 7649, 3794, 21136, 3555, 8608, 1829, 4117, 2407, 7649, 3794, 9154, 36632, 8608, 1829, 4117, 2407, 7649, 3794, 39896, 3714, 7435, 2304, 2407, 27884, 10874, 11622, 19986, 10632, 9154, 11296, 20328, 5016, 5296, 33456, 11331, 3215, 23328, 11296, 39896, 11331, 3215, 23328, 11331, 3215, 23328, 21136, 3555, 8608, 1829, 4117, 2407, 7649, 3794, 39896, 18871, 33546, 2288, 34051, 11331, 3215, 23328, 9154, 21136, 1829, 4117, 2407, 7649, 3794, 18863, 9381, 1211, 10632, 44381, 37893, 36632, 11331, 3215, 23328, 5296, 31377, 2304, 6055, 30544, 3714, 43500, 49401, 4724, 5016, 1829, 12984, 14739, 9673, 33604, 46309, 9307, 6055, 3555, 34268, 11296, 1975, 2655, 8592, 28820, 20792, 5662, 8310, 295, 3303, 3547], "avg_logprob": -0.14208157133247892, "compression_ratio": 1.8823529411764706, "no_speech_prob": 0.0, "words": [{"start": 1949.03, "end": 1949.41, "word": "إذا", "probability": 0.588134765625}, {"start": 1949.41, "end": 1949.79, "word": " السب", "probability": 0.52288818359375}, {"start": 1949.79, "end": 1950.37, "word": " سيكوانس", "probability": 0.833984375}, {"start": 1950.37, "end": 1950.85, "word": " السب", "probability": 0.6309814453125}, {"start": 1950.85, "end": 1951.55, "word": " سيكوانس", "probability": 0.94775390625}, {"start": 1951.55, "end": 1951.87, "word": " من", "probability": 0.955078125}, {"start": 1951.87, "end": 1952.11, "word": " أي", "probability": 0.91015625}, {"start": 1952.11, "end": 1952.85, "word": " سيكوانس", "probability": 0.964599609375}, {"start": 1952.85, "end": 1953.43, "word": " هي", "probability": 0.82275390625}, {"start": 1953.43, "end": 1953.89, "word": " مجموعة", "probability": 0.95380859375}, {"start": 1953.89, "end": 1954.37, "word": " جزئية", "probability": 0.9326171875}, {"start": 1954.37, "end": 1954.81, "word": " منها", "probability": 0.990966796875}, {"start": 1954.81, "end": 1955.41, "word": " صح", "probability": 0.817626953125}, {"start": 1955.41, "end": 1956.23, "word": " لأن", "probability": 0.627197265625}, {"start": 1956.23, "end": 1956.93, "word": " حدودها", "probability": 0.976806640625}, {"start": 1956.93, "end": 1957.39, "word": " هي", "probability": 0.7861328125}, {"start": 1957.39, "end": 1958.17, "word": " حدود", "probability": 0.8792317708333334}, {"start": 1958.17, "end": 1959.01, "word": " حدود", "probability": 0.7621256510416666}, {"start": 1959.01, "end": 1959.35, "word": " السب", "probability": 0.816650390625}, {"start": 1959.35, "end": 1960.01, "word": " سيكوانس", "probability": 0.967529296875}, {"start": 1960.01, "end": 1961.01, "word": " هي", "probability": 0.82666015625}, {"start": 1961.01, "end": 1962.25, "word": " عناصر", "probability": 0.9860026041666666}, {"start": 1962.25, "end": 1962.81, "word": " أو", "probability": 0.6728515625}, {"start": 1962.81, "end": 1963.43, "word": " حدود", "probability": 0.9861653645833334}, {"start": 1963.43, "end": 1963.91, "word": " من", "probability": 0.990234375}, {"start": 1963.91, "end": 1964.43, "word": " السيكوانس", "probability": 0.939697265625}, {"start": 1964.43, "end": 1965.01, "word": " العصلية", "probability": 0.78997802734375}, {"start": 1965.01, "end": 1966.13, "word": " لكن", "probability": 0.8115234375}, {"start": 1966.13, "end": 1966.39, "word": " مش", "probability": 0.98095703125}, {"start": 1966.39, "end": 1966.61, "word": " أي", "probability": 0.72607421875}, {"start": 1966.61, "end": 1967.15, "word": " حدود", "probability": 0.9915364583333334}, {"start": 1967.15, "end": 1968.07, "word": " لازم", "probability": 0.9632161458333334}, {"start": 1968.07, "end": 1968.35, "word": " تكون", "probability": 0.974365234375}, {"start": 1968.35, "end": 1969.09, "word": " مرتبة", "probability": 0.97412109375}, {"start": 1969.09, "end": 1970.33, "word": " بحيث", "probability": 0.981689453125}, {"start": 1970.33, "end": 1970.51, "word": " أن", "probability": 0.453125}, {"start": 1970.51, "end": 1971.31, "word": " المؤشرات", "probability": 0.957275390625}, {"start": 1971.31, "end": 1972.17, "word": " تبعتها", "probability": 0.9527587890625}, {"start": 1972.17, "end": 1973.27, "word": " اتشكل", "probability": 0.882080078125}, {"start": 1973.27, "end": 1974.45, "word": " strictly", "probability": 0.7470703125}, {"start": 1974.45, "end": 1975.43, "word": " increasing", "probability": 0.94970703125}, {"start": 1975.43, "end": 1976.25, "word": " sequence", "probability": 0.95556640625}, {"start": 1976.25, "end": 1976.47, "word": " of", "probability": 0.96533203125}, {"start": 1976.47, "end": 1976.89, "word": " natural", "probability": 0.62451171875}, {"start": 1976.89, "end": 1977.41, "word": " numbers", "probability": 0.9267578125}], "temperature": 1.0}, {"id": 74, "seek": 200634, "start": 1978.58, "end": 2006.34, "text": "تمام؟ زي هيك إذاً هذا هو تعريف الـ subsequence إذا لو في أنا عندي sequence XN واخدت strictly increasing sequence of natural numbers فال sequence اللي المؤشرات تبعتها هي ال sequence RN اللي هي هذه عناصرها بنسميها subsequence من ال sequence XN", "tokens": [2655, 15042, 2304, 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1989.5, "end": 1990.14, "word": " strictly", "probability": 0.72509765625}, {"start": 1990.14, "end": 1990.84, "word": " increasing", "probability": 0.96044921875}, {"start": 1990.84, "end": 1991.72, "word": " sequence", "probability": 0.96533203125}, {"start": 1991.72, "end": 1992.06, "word": " of", "probability": 0.9453125}, {"start": 1992.06, "end": 1992.52, "word": " natural", "probability": 0.92236328125}, {"start": 1992.52, "end": 1993.12, "word": " numbers", "probability": 0.8916015625}, {"start": 1993.12, "end": 1994.94, "word": " فال", "probability": 0.949462890625}, {"start": 1994.94, "end": 1995.66, "word": " sequence", "probability": 0.82373046875}, {"start": 1995.66, "end": 1996.12, "word": " اللي", "probability": 0.914306640625}, {"start": 1996.12, "end": 1996.88, "word": " المؤشرات", "probability": 0.971435546875}, {"start": 1996.88, "end": 1997.62, "word": " تبعتها", "probability": 0.961669921875}, {"start": 1997.62, "end": 1998.78, "word": " هي", "probability": 0.92919921875}, {"start": 1998.78, "end": 1999.12, "word": " ال", "probability": 0.8017578125}, {"start": 1999.12, "end": 1999.54, "word": " sequence", "probability": 0.80322265625}, {"start": 1999.54, "end": 2000.36, "word": " RN", "probability": 0.7138671875}, {"start": 2000.36, "end": 2001.42, "word": " اللي", "probability": 0.92822265625}, {"start": 2001.42, "end": 2001.68, "word": " هي", "probability": 0.83349609375}, {"start": 2001.68, "end": 2001.86, "word": " هذه", "probability": 0.59228515625}, {"start": 2001.86, "end": 2002.58, "word": " عناصرها", "probability": 0.9390869140625}, {"start": 2002.58, "end": 2004.06, "word": " بنسميها", "probability": 0.9306640625}, {"start": 2004.06, "end": 2005.12, "word": " subsequence", "probability": 0.99169921875}, {"start": 2005.12, "end": 2005.32, "word": " من", "probability": 0.9912109375}, {"start": 2005.32, "end": 2005.48, "word": " ال", "probability": 0.84814453125}, {"start": 2005.48, "end": 2005.8, "word": " sequence", 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0.82470703125}, {"start": 2021.88, "end": 2022.68, "word": " او", "probability": 0.84814453125}, {"start": 2022.68, "end": 2022.96, "word": " even", "probability": 0.83935546875}, {"start": 2022.96, "end": 2023.36, "word": " natural", "probability": 0.7607421875}, {"start": 2023.36, "end": 2023.92, "word": " numbers", "probability": 0.8681640625}, {"start": 2023.92, "end": 2024.06, "word": " ده", "probability": 0.654052734375}, {"start": 2024.06, "end": 2024.38, "word": " هي", "probability": 0.70703125}, {"start": 2024.38, "end": 2024.94, "word": " على", "probability": 0.4189453125}, {"start": 2024.94, "end": 2025.3, "word": " سرعة", "probability": 0.7451171875}, {"start": 2025.3, "end": 2025.84, "word": " اتنين", "probability": 0.9071044921875}, {"start": 2025.84, "end": 2027.08, "word": " اربعة", "probability": 0.79638671875}, {"start": 2027.08, "end": 2028.48, "word": " ستة", "probability": 0.9034830729166666}, {"start": 2028.48, "end": 2029.14, "word": " و", "probability": 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"end": 2073.41, "word": " ستة،", "probability": 0.85009765625}, {"start": 2073.41, "end": 2073.65, "word": " ر", "probability": 0.462158203125}, {"start": 2073.65, "end": 2074.17, "word": " تلاتة", "probability": 0.9638671875}, {"start": 2074.17, "end": 2076.81, "word": " ستة", "probability": 0.9943033854166666}, {"start": 2076.81, "end": 2077.77, "word": " نفس", "probability": 0.8251953125}, {"start": 2077.77, "end": 2078.49, "word": " الحاجة،", "probability": 0.8583984375}, {"start": 2078.49, "end": 2078.49, "word": " يعني", "probability": 0.76220703125}, {"start": 2078.49, "end": 2079.13, "word": " هذه", "probability": 0.370361328125}, {"start": 2079.13, "end": 2079.87, "word": " subsequence", "probability": 0.68798828125}, {"start": 2079.87, "end": 2080.19, "word": " وهذه", "probability": 0.862060546875}, {"start": 2080.19, "end": 2080.85, "word": " subsequence", "probability": 0.998046875}, {"start": 2080.85, "end": 2081.05, "word": " من", "probability": 0.9052734375}, {"start": 2081.05, "end": 2081.19, "word": " ال", "probability": 0.60205078125}, {"start": 2081.19, "end": 2081.55, "word": " sequence", "probability": 0.73779296875}, {"start": 2081.55, "end": 2081.89, "word": " X", "probability": 0.93896484375}], "temperature": 1.0}, {"id": 78, "seek": 210784, "start": 2083.66, "end": 2107.84, "text": "لأن مأشراتهم كلهم بشكل strictly increasing sequences of natural numbers بالمثل ال sequence 1 على 2 n سالب 1 و ال sequence 1 على n factorial هدول برضه أيضا sub sequences من ال sequence 1 على n", "tokens": [1211, 33456, 3714, 10721, 46309, 9307, 16095, 28242, 16095, 4724, 8592, 28820, 20792, 5662, 22978, 295, 3303, 3547, 20666, 2304, 12984, 1211, 2423, 8310, 502, 15844, 568, 297, 8608, 6027, 3555, 502, 4032, 2423, 8310, 502, 15844, 297, 36916, 8032, 3215, 12610, 4724, 43042, 3224, 36632, 11242, 995, 1422, 22978, 9154, 2423, 8310, 502, 15844, 297], "avg_logprob": -0.2734375, "compression_ratio": 1.5151515151515151, "no_speech_prob": 0.0, "words": [{"start": 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sequence", "probability": 0.9541015625}, {"start": 2189.47, "end": 2189.97, "word": " هذه", "probability": 0.578125}, {"start": 2189.97, "end": 2190.85, "word": " هي", "probability": 0.66943359375}, {"start": 2190.85, "end": 2191.49, "word": " موجودة", "probability": 0.8916015625}, {"start": 2191.49, "end": 2191.73, "word": " هنا", "probability": 0.85546875}, {"start": 2191.73, "end": 2192.43, "word": " صح؟", "probability": 0.8907877604166666}], "temperature": 1.0}, {"id": 82, "seek": 221765, "start": 2193.79, "end": 2217.65, "text": "والمؤشرات تبعات ال sub-sequence هي M زاد واحد اصغر من R اتنين اللي هو M زاد اتنين وR اتنين اصغر من R تلاتة اللي هو M زاد تلاتة وكده هذا sub-sequence ولا مش sub-sequence؟ لو أخدت أي sequence X in فأي M تل هو sub-sequence منها", "tokens": [2407, 45340, 33604, 46309, 9307, 6055, 3555, 3615, 9307, 2423, 1422, 12, 11834, 655, 39896, 376, 30767, 18513, 36764, 24401, 1975, 9381, 17082, 2288, 9154, 497, 1975, 2655, 1863, 9957, 13672, 1829, 31439, 376, 30767, 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وكده", "probability": 0.7322998046875}, {"start": 2208.37, "end": 2209.23, "word": " هذا", "probability": 0.09698486328125}, {"start": 2209.23, "end": 2209.69, "word": " sub", "probability": 0.67041015625}, {"start": 2209.69, "end": 2210.13, "word": "-sequence", "probability": 0.9182942708333334}, {"start": 2210.13, "end": 2210.31, "word": " ولا", "probability": 0.80908203125}, {"start": 2210.31, "end": 2210.49, "word": " مش", "probability": 0.83447265625}, {"start": 2210.49, "end": 2210.71, "word": " sub", "probability": 0.95751953125}, {"start": 2210.71, "end": 2211.67, "word": "-sequence؟", "probability": 0.84814453125}, {"start": 2211.67, "end": 2212.55, "word": " لو", "probability": 0.69677734375}, {"start": 2212.55, "end": 2212.97, "word": " أخدت", "probability": 0.919677734375}, {"start": 2212.97, "end": 2213.15, "word": " أي", "probability": 0.6884765625}, {"start": 2213.15, "end": 2213.59, "word": " sequence", "probability": 0.93798828125}, {"start": 2213.59, "end": 2213.97, "word": " X", "probability": 0.6611328125}, {"start": 2213.97, "end": 2214.35, "word": " in", "probability": 0.3359375}, {"start": 2214.35, "end": 2214.95, "word": " فأي", "probability": 0.9192708333333334}, {"start": 2214.95, "end": 2215.31, "word": " M", "probability": 0.9189453125}, {"start": 2215.31, "end": 2215.71, "word": " تل", "probability": 0.83056640625}, {"start": 2215.71, "end": 2216.43, "word": " هو", "probability": 0.876953125}, {"start": 2216.43, "end": 2216.73, "word": " sub", "probability": 0.96435546875}, {"start": 2216.73, "end": 2217.23, "word": "-sequence", "probability": 0.9650065104166666}, {"start": 2217.23, "end": 2217.65, "word": " منها", "probability": 0.993896484375}], "temperature": 1.0}, {"id": 83, "seek": 224748, "start": 2220.14, "end": 2247.48, "text": "كذلك لو أخدت أي sequence xn فالـ sequence x اللي الحد اللي عم تبعها المؤشر تبعه 2 أس n هذي برضه subsequence زي ما شوفنا و x2n الحدود الزوجية لو أخدت الحدود الزوجية فقط فهذا بعطيني subsequence و لو أخدت 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"start": 2248.15, "end": 2266.99, "text": "الان سؤال اللى بهمنا احنا ما هي علاقة ال sequence بال subsequence من حيث ال convergence و ال divergence؟", "tokens": [6027, 7649, 8608, 33604, 6027, 13672, 7578, 4724, 16095, 8315, 1975, 5016, 8315, 19446, 39896, 11203, 995, 28671, 2423, 8310, 20666, 13924, 655, 9154, 11331, 1829, 12984, 2423, 32181, 4032, 2423, 47387, 22807], "avg_logprob": -0.2743566307951422, "compression_ratio": 1.3636363636363635, "no_speech_prob": 0.0, "words": [{"start": 2248.15, "end": 2248.51, "word": "الان", "probability": 0.31915283203125}, {"start": 2248.51, "end": 2258.47, "word": " سؤال", "probability": 0.8645833333333334}, {"start": 2258.47, "end": 2258.65, "word": " اللى", "probability": 0.699951171875}, {"start": 2258.65, "end": 2259.11, "word": " بهمنا", "probability": 0.8855794270833334}, {"start": 2259.11, "end": 2259.49, "word": " احنا", "probability": 0.9532877604166666}, {"start": 2259.49, "end": 2260.43, "word": " ما", "probability": 0.52880859375}, {"start": 2260.43, "end": 2260.69, "word": " هي", "probability": 0.50732421875}, {"start": 2260.69, "end": 2261.23, "word": " علاقة", "probability": 0.97265625}, {"start": 2261.23, "end": 2261.47, "word": " ال", "probability": 0.84912109375}, {"start": 2261.47, "end": 2261.93, "word": " sequence", "probability": 0.607421875}, {"start": 2261.93, "end": 2262.19, "word": " بال", "probability": 0.96484375}, {"start": 2262.19, "end": 2263.77, "word": " subsequence", "probability": 0.702880859375}, {"start": 2263.77, "end": 2264.51, "word": " من", "probability": 0.88720703125}, {"start": 2264.51, "end": 2264.87, "word": " حيث", "probability": 0.9676106770833334}, {"start": 2264.87, "end": 2265.01, "word": " ال", "probability": 0.91845703125}, {"start": 2265.01, "end": 2265.49, "word": " convergence", "probability": 0.88916015625}, {"start": 2265.49, "end": 2265.87, "word": " و", "probability": 0.52294921875}, {"start": 2265.87, "end": 2265.93, "word": " ال", "probability": 0.88427734375}, 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