{"segments": [{"id": 1, "seek": 3638, "start": 20.92, "end": 36.38, "text": "بسم الله الرحمن الرحيم اليوم هناخد أخر لقاء في ال course وهو تكملة section خمسة أربعة في الكتاب المقرر اللي بتكلم عن ال uniform continuity", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 45595, 20498, 8032, 1863, 47283, 3215, 5551, 34740, 5296, 4587, 16606, 8978, 2423, 1164, 37037, 2407, 6055, 24793, 37977, 3541, 16490, 2304, 3794, 3660, 5551, 25513, 27884, 8978, 33251, 2655, 16758, 9673, 4587, 2288, 2288, 13672, 1829, 39894, 4117, 19528, 18871, 2423, 9452, 23807], "avg_logprob": -0.10995370259991398, "compression_ratio": 1.414012738853503, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 20.92, "end": 21.28, "word": "بسم", "probability": 0.913330078125}, {"start": 21.28, "end": 21.46, "word": " الله", "probability": 0.96923828125}, {"start": 21.46, "end": 21.88, "word": " الرحمن", "probability": 0.9763997395833334}, {"start": 21.88, "end": 22.6, "word": " الرحيم", 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"start": 67.89, "end": 87.65, "text": "محددة جزئية من الأعداد الحقيقية فكان في عندي non uniform continuity criterion و آخر نظرية أثبتنا نظرية مهمة هو هي ال uniform continuity criterion اللي بتقول أنه لو كانت ال function تبعتي متصلة", "tokens": [2304, 24401, 41891, 10874, 11622, 19986, 10632, 9154, 16247, 22488, 18513, 21542, 38436, 4587, 10632, 6156, 41361, 8978, 18871, 16254, 2107, 9452, 23807, 46691, 4032, 19753, 34740, 8717, 19913, 2288, 10632, 5551, 12984, 3555, 2655, 8315, 8717, 19913, 2288, 10632, 3714, 16095, 3660, 31439, 39896, 2423, 9452, 23807, 46691, 13672, 1829, 39894, 39648, 14739, 3224, 45164, 25961, 2655, 2423, 2445, 6055, 3555, 3615, 31371, 44650, 36520, 3660], "avg_logprob": -0.13269760876017458, "compression_ratio": 1.5879120879120878, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 67.89, "end": 68.75, "word": "محددة", "probability": 0.9435221354166666}, {"start": 68.75, "end": 69.45, "word": " جزئية", "probability": 0.963623046875}, {"start": 69.45, 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نفس الفترة وبالتالي الاتصال العادي لا يؤدي للاتصال المنطم", "tokens": [5172, 9778, 3215, 8315, 50113, 6027, 15844, 11778, 6027, 3660, 2445, 11778, 6027, 3660, 36764, 24401, 15844, 1783, 13412, 5172, 8315, 14739, 11296, 44650, 36520, 3660, 10957, 15844, 27188, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 9154, 8608, 5172, 2288, 30731, 3714, 15040, 8717, 11296, 10632, 457, 309, 390, 406, 48806, 10957, 15844, 8717, 36178, 27188, 2655, 25720, 46599, 6027, 2655, 6027, 1829, 2423, 9307, 9381, 6027, 18863, 995, 16254, 20193, 7251, 33604, 16254, 24976, 9307, 9381, 6027, 9673, 1863, 9566, 2304], "avg_logprob": -0.20052083989694006, "compression_ratio": 1.7179487179487178, "no_speech_prob": 0.0, "words": [{"start": 112.64000000000001, "end": 113.76, "word": "فخدنا", "probability": 0.70501708984375}, {"start": 113.76, "end": 114.4, "word": " مثال", "probability": 0.975341796875}, {"start": 114.4, "end": 116.06, "word": " على", "probability": 0.7705078125}, {"start": 116.06, "end": 117.02, 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"probability": 0.9208984375}, {"start": 130.26, "end": 130.58, "word": " نفس", "probability": 0.997314453125}, {"start": 130.58, "end": 131.14, "word": " الفترة", "probability": 0.9925130208333334}, {"start": 131.14, "end": 133.3, "word": " وبالتالي", "probability": 0.94130859375}, {"start": 133.3, "end": 134.58, "word": " الاتصال", "probability": 0.896484375}, {"start": 134.58, "end": 135.08, "word": " العادي", "probability": 0.8430989583333334}, {"start": 135.08, "end": 135.3, "word": " لا", "probability": 0.9384765625}, {"start": 135.3, "end": 135.78, "word": " يؤدي", "probability": 0.9230143229166666}, {"start": 135.78, "end": 136.66, "word": " للاتصال", "probability": 0.9195556640625}, {"start": 136.66, "end": 137.32, "word": " المنطم", "probability": 0.67144775390625}], "temperature": 1.0}, {"id": 6, "seek": 16474, "start": 138.66, "end": 164.74, "text": "اليوم هنتعرف على نوع جديد من ال functions وهو لبسش functions و ال functions هدول هتكونوا دائما كلهم uniformly continuous فنعرف 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"start": 821.54, "end": 847.64, "text": "على الفترة I إذاً هي مثال على function uniform ل continuous على المجال تبعها هنشوف الآن إن هذه ال function ما هياش لبسش على نفس الفترة إذا ال claim", "tokens": [3615, 23942, 27188, 2655, 25720, 286, 11933, 15730, 14111, 39896, 50113, 6027, 15844, 2445, 9452, 5296, 10957, 15844, 9673, 7435, 6027, 6055, 3555, 3615, 11296, 8032, 1863, 8592, 38688, 6024, 48506, 36145, 29538, 2423, 2445, 19446, 39896, 33599, 5296, 3555, 3794, 8592, 15844, 8717, 36178, 27188, 2655, 25720, 11933, 15730, 2423, 3932], "avg_logprob": -0.26901532569021547, "compression_ratio": 1.4645161290322581, "no_speech_prob": 0.0, "words": [{"start": 821.54, "end": 822.12, "word": "على", "probability": 0.825927734375}, {"start": 822.12, "end": 823.0, "word": " الفترة", "probability": 0.9773763020833334}, {"start": 823.0, "end": 823.4, "word": " I", "probability": 0.45849609375}, {"start": 823.4, "end": 825.32, "word": " إذاً", "probability": 0.4336344401041667}, {"start": 825.32, 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"word": " إن", "probability": 0.57177734375}, {"start": 832.32, "end": 832.72, "word": " هذه", "probability": 0.5966796875}, {"start": 832.72, "end": 832.88, "word": " ال", "probability": 0.97705078125}, {"start": 832.88, "end": 833.28, "word": " function", "probability": 0.87060546875}, {"start": 833.28, "end": 833.56, "word": " ما", "probability": 0.9111328125}, {"start": 833.56, "end": 834.28, "word": " هياش", "probability": 0.63037109375}, {"start": 834.28, "end": 835.32, "word": " لبسش", "probability": 0.8748779296875}, {"start": 835.32, "end": 835.52, "word": " على", "probability": 0.7880859375}, {"start": 835.52, "end": 835.72, "word": " نفس", "probability": 0.99169921875}, {"start": 835.72, "end": 836.32, "word": " الفترة", "probability": 0.9931640625}, {"start": 836.32, "end": 847.06, "word": " إذا", "probability": 0.7490234375}, {"start": 847.06, "end": 847.3, "word": " ال", "probability": 0.276123046875}, {"start": 847.3, "end": 847.64, "word": " claim", "probability": 0.9208984375}], "temperature": 1.0}, {"id": 31, "seek": 87867, "start": 853.37, "end": 878.67, "text": "if is not .. if is not لبسش على الفترة I فلبرحان ذلك assume on contrary", "tokens": [351, 307, 406, 4386, 498, 307, 406, 5296, 3555, 3794, 8592, 15844, 27188, 2655, 25720, 286, 6156, 46152, 2288, 5016, 7649, 29910, 23275, 6552, 322, 19506], "avg_logprob": -0.10662615519982797, "compression_ratio": 1.032967032967033, "no_speech_prob": 0.0, "words": [{"start": 853.37, "end": 853.93, "word": "if", "probability": 0.78955078125}, {"start": 853.93, "end": 854.57, "word": " is", "probability": 0.947265625}, {"start": 854.57, "end": 855.11, "word": " not", "probability": 0.9716796875}, {"start": 855.11, "end": 855.65, "word": " ..", "probability": 0.70703125}, {"start": 855.65, "end": 856.85, "word": " if", "probability": 0.935546875}, {"start": 856.85, "end": 857.23, "word": " is", "probability": 0.9697265625}, {"start": 857.23, "end": 857.53, "word": " not", "probability": 0.9677734375}, {"start": 857.53, "end": 859.15, "word": " لبسش", "probability": 0.9600830078125}, {"start": 859.15, "end": 863.65, "word": " على", "probability": 0.84912109375}, {"start": 863.65, "end": 864.81, "word": " الفترة", "probability": 0.9736328125}, {"start": 864.81, "end": 865.39, "word": " I", "probability": 0.71435546875}, {"start": 865.39, "end": 868.59, "word": " فلبرحان", "probability": 0.823046875}, {"start": 868.59, "end": 869.21, "word": " ذلك", "probability": 0.9755859375}, {"start": 869.21, "end": 873.99, "word": " assume", "probability": 0.916015625}, {"start": 873.99, "end": 877.95, "word": " on", "probability": 0.95263671875}, {"start": 877.95, "end": 878.67, "word": " contrary", "probability": 0.8720703125}], "temperature": 1.0}, {"id": 32, "seek": 90409, "start": 883.19, "end": 904.09, "text": "assume on contrary that if is لبسش on I then", "tokens": [640, 2540, 322, 19506, 300, 498, 307, 5296, 3555, 3794, 8592, 322, 286, 550], "avg_logprob": -0.18359375198682149, "compression_ratio": 0.9056603773584906, "no_speech_prob": 0.0, "words": [{"start": 883.19, "end": 883.99, "word": "assume", "probability": 0.820068359375}, {"start": 883.99, "end": 884.41, "word": " on", "probability": 0.939453125}, {"start": 884.41, "end": 885.35, "word": " contrary", "probability": 0.91015625}, {"start": 885.35, "end": 888.55, "word": " that", "probability": 0.93798828125}, {"start": 888.55, "end": 890.93, "word": " if", "probability": 0.4296875}, {"start": 890.93, "end": 891.47, "word": " is", "probability": 0.8125}, {"start": 891.47, "end": 892.21, "word": " لبسش", "probability": 0.958984375}, {"start": 892.21, "end": 901.65, "word": " on", "probability": 0.88134765625}, {"start": 901.65, "end": 902.23, "word": " I", "probability": 0.8818359375}, {"start": 902.23, "end": 904.09, "word": " then", "probability": 0.76416015625}], "temperature": 1.0}, {"id": 33, "seek": 93037, "start": 906.57, "end": 930.37, "text": "there exists k أكبر من السفر بحيث أنه absolute f of x minus f of u أصغر منها ساوي k في absolute x minus u لكل x", "tokens": [15456, 8198, 350, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 4724, 5016, 1829, 12984, 14739, 3224, 8236, 283, 295, 2031, 3175, 283, 295, 344, 5551, 9381, 17082, 2288, 9154, 11296, 8608, 995, 45865, 350, 8978, 8236, 2031, 3175, 344, 5296, 28820, 2031], "avg_logprob": -0.23037790143212608, "compression_ratio": 1.2066115702479339, "no_speech_prob": 0.0, "words": [{"start": 906.57, "end": 907.03, "word": "there", "probability": 0.08740234375}, {"start": 907.03, "end": 907.65, "word": " exists", "probability": 0.65234375}, {"start": 907.65, "end": 908.25, "word": " k", "probability": 0.5625}, {"start": 908.25, "end": 909.07, "word": " أكبر", "probability": 0.9239908854166666}, {"start": 909.07, "end": 909.29, "word": " من", "probability": 0.9931640625}, {"start": 909.29, "end": 909.95, "word": " السفر", "probability": 0.8238932291666666}, {"start": 909.95, "end": 911.33, "word": " بحيث", "probability": 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"end": 926.33, "word": " k", "probability": 0.8251953125}, {"start": 926.33, "end": 927.47, "word": " في", "probability": 0.4384765625}, {"start": 927.47, "end": 928.01, "word": " absolute", "probability": 0.95654296875}, {"start": 928.01, "end": 928.61, "word": " x", "probability": 0.8681640625}, {"start": 928.61, "end": 929.03, "word": " minus", "probability": 0.9833984375}, {"start": 929.03, "end": 929.39, "word": " u", "probability": 0.97998046875}, {"start": 929.39, "end": 929.91, "word": " لكل", "probability": 0.9765625}, {"start": 929.91, "end": 930.37, "word": " x", "probability": 0.96923828125}], "temperature": 1.0}, {"id": 34, "seek": 93997, "start": 931.63, "end": 939.97, "text": "هو you تنتمي للفترة I اللى هى الفترة المغلطة من سفر لاتنين", "tokens": [3224, 2407, 291, 6055, 29399, 2304, 1829, 24976, 5172, 2655, 25720, 286, 13672, 7578, 8032, 7578, 27188, 2655, 25720, 9673, 17082, 1211, 9566, 3660, 9154, 8608, 5172, 2288, 5296, 9307, 1863, 9957], "avg_logprob": 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عندي N أصغر من أو ساوي K for all N في N وهذا بتناقض مع ال Archimedean property which contradicts", "tokens": [1211, 28820, 426, 8978, 426, 1975, 11242, 25513, 9673, 2655, 3215, 9957, 3660, 29538, 8978, 426, 6055, 25513, 10632, 6156, 3555, 9566, 1211, 3615, 18871, 16254, 426, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 591, 337, 439, 426, 8978, 426, 37037, 15730, 39894, 8315, 4587, 11242, 20449, 2423, 10984, 332, 4858, 282, 4707, 597, 28900, 82], "avg_logprob": -0.2711864396677179, "compression_ratio": 1.2560975609756098, "no_speech_prob": 0.0, "words": [{"start": 1116.68, "end": 1117.6, "word": "لكل", "probability": 0.5875244140625}, {"start": 1117.6, "end": 1118.02, "word": " N", "probability": 0.151123046875}, {"start": 1118.02, "end": 1118.38, "word": " في", "probability": 0.92138671875}, {"start": 1118.38, "end": 1118.9, "word": " N", "probability": 0.89892578125}, {"start": 1118.9, "end": 1123.52, "word": " اضرب", "probability": 0.73193359375}, {"start": 1123.52, 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"end": 1132.2, "word": " K", "probability": 0.6103515625}, {"start": 1132.2, "end": 1133.4, "word": " for", "probability": 0.89501953125}, {"start": 1133.4, "end": 1134.02, "word": " all", "probability": 0.91162109375}, {"start": 1134.02, "end": 1134.44, "word": " N", "probability": 0.87060546875}, {"start": 1134.44, "end": 1134.9, "word": " في", "probability": 0.97119140625}, {"start": 1134.9, "end": 1135.44, "word": " N", "probability": 0.8828125}, {"start": 1135.44, "end": 1138.18, "word": " وهذا", "probability": 0.925048828125}, {"start": 1138.18, "end": 1138.92, "word": " بتناقض", "probability": 0.81146240234375}, {"start": 1138.92, "end": 1139.16, "word": " مع", "probability": 0.8349609375}, {"start": 1139.16, "end": 1139.32, "word": " ال", "probability": 0.90576171875}, {"start": 1139.32, "end": 1140.36, "word": " Archimedean", "probability": 0.746124267578125}, {"start": 1140.36, "end": 1141.06, "word": " property", "probability": 0.75927734375}, {"start": 1141.06, "end": 1142.54, "word": " which", "probability": 0.7578125}, {"start": 1142.54, "end": 1146.04, "word": " contradicts", "probability": 0.826904296875}], "temperature": 1.0}, {"id": 42, "seek": 115925, "start": 1147.33, "end": 1159.25, "text": "التي تتناقض مع مين؟ التي تتناقض مع الـ Archimedean property", "tokens": [6027, 31371, 6055, 2655, 8315, 4587, 11242, 20449, 3714, 9957, 22807, 2423, 31371, 6055, 2655, 8315, 4587, 11242, 20449, 2423, 39184, 10984, 332, 4858, 282, 4707], "avg_logprob": -0.4678819356141267, "compression_ratio": 1.2857142857142858, "no_speech_prob": 0.0, "words": [{"start": 1147.33, "end": 1147.83, "word": "التي", "probability": 0.45843505859375}, {"start": 1147.83, "end": 1151.13, "word": " تتناقض", "probability": 0.87275390625}, {"start": 1151.13, "end": 1151.39, "word": " مع", "probability": 0.64990234375}, {"start": 1151.39, "end": 1152.47, "word": " مين؟", "probability": 0.4612630208333333}, {"start": 1152.47, "end": 1153.39, "word": " التي", "probability": 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"word": " continuous", "probability": 0.8720703125}, {"start": 1239.3, "end": 1240.76, "word": " على", "probability": 0.916015625}, {"start": 1240.76, "end": 1241.98, "word": " set", "probability": 0.98046875}, {"start": 1241.98, "end": 1242.66, "word": " معينة", "probability": 0.98193359375}], "temperature": 1.0}, {"id": 46, "seek": 125877, "start": 1243.03, "end": 1258.77, "text": "لكنها ليست لبسش لكن أثبتنا قبل ايه ان كل لبسش function is always uniformly continuous ناخد بعض الأمثلة", "tokens": [1211, 19452, 11296, 32239, 14851, 5296, 3555, 3794, 8592, 44381, 5551, 12984, 3555, 2655, 8315, 12174, 36150, 1975, 1829, 3224, 16472, 28242, 5296, 3555, 3794, 8592, 2445, 307, 1009, 48806, 10957, 8717, 47283, 3215, 45030, 11242, 16247, 2304, 12984, 37977], "avg_logprob": -0.2612423896789551, "compression_ratio": 1.1968503937007875, "no_speech_prob": 0.0, "words": [{"start": 1243.03, "end": 1243.75, "word": "لكنها", "probability": 0.7493489583333334}, {"start": 1243.75, "end": 1244.23, "word": " ليست", "probability": 0.931396484375}, {"start": 1244.23, "end": 1244.81, "word": " لبسش", "probability": 0.78875732421875}, {"start": 1244.81, "end": 1245.89, "word": " لكن", "probability": 0.41259765625}, {"start": 1245.89, "end": 1246.47, "word": " أثبتنا", "probability": 0.930078125}, {"start": 1246.47, "end": 1246.73, "word": " قبل", "probability": 0.6455078125}, {"start": 1246.73, "end": 1246.89, "word": " ايه", "probability": 0.61474609375}, {"start": 1246.89, "end": 1247.05, "word": " ان", "probability": 0.52880859375}, {"start": 1247.05, "end": 1247.39, "word": " كل", "probability": 0.85302734375}, {"start": 1247.39, "end": 1247.81, "word": " لبسش", "probability": 0.8408203125}, {"start": 1247.81, "end": 1248.29, "word": " function", "probability": 0.6416015625}, {"start": 1248.29, "end": 1248.87, "word": " is", "probability": 0.67431640625}, {"start": 1248.87, "end": 1250.45, "word": " always", "probability": 0.8212890625}, {"start": 1250.45, "end": 1251.19, "word": " uniformly", "probability": 0.94384765625}, {"start": 1251.19, "end": 1252.39, "word": " continuous", "probability": 0.91650390625}, {"start": 1252.39, "end": 1257.75, "word": " ناخد", "probability": 0.742431640625}, {"start": 1257.75, "end": 1258.13, "word": " بعض", "probability": 0.9765625}, {"start": 1258.13, "end": 1258.77, "word": " الأمثلة", "probability": 0.9755859375}], "temperature": 1.0}, {"id": 47, "seek": 130772, "start": 1286.12, "end": 1307.72, "text": "example led f of x بساوي x تربية و x ينتمي للمجموعة a اللي هي الفترة المغلقة من سفر إلى بي حيث بي أي عدد موجب بي أي عدد موجب", "tokens": [3121, 335, 781, 4684, 283, 295, 2031, 4724, 3794, 995, 45865, 2031, 6055, 25513, 10632, 4032, 2031, 7251, 29399, 2304, 1829, 5296, 19528, 7435, 2304, 2407, 27884, 257, 13672, 1829, 39896, 27188, 2655, 25720, 9673, 17082, 1211, 28671, 9154, 8608, 5172, 2288, 30731, 4724, 1829, 11331, 1829, 12984, 4724, 1829, 36632, 6225, 3215, 3215, 3714, 29245, 3555, 4724, 1829, 36632, 6225, 3215, 3215, 3714, 29245, 3555], "avg_logprob": -0.17583954601145502, "compression_ratio": 1.4962962962962962, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1286.12, "end": 1287.32, "word": "example", "probability": 0.7457682291666666}, {"start": 1287.32, "end": 1288.52, "word": " led", "probability": 0.69580078125}, {"start": 1288.52, "end": 1288.9, "word": " f", "probability": 0.5390625}, {"start": 1288.9, "end": 1289.18, "word": " of", "probability": 0.61474609375}, {"start": 1289.18, "end": 1289.6, "word": " x", "probability": 0.91259765625}, {"start": 1289.6, "end": 1290.76, "word": " بساوي", "probability": 0.7744140625}, {"start": 1290.76, "end": 1291.24, "word": " x", "probability": 0.8779296875}, {"start": 1291.24, "end": 1292.06, "word": " تربية", "probability": 0.768310546875}, {"start": 1292.06, "end": 1293.52, "word": " و", "probability": 0.70068359375}, {"start": 1293.52, "end": 1294.26, "word": " x", "probability": 0.7041015625}, {"start": 1294.26, "end": 1295.22, "word": " ينتمي", "probability": 0.963623046875}, {"start": 1295.22, "end": 1296.52, "word": " للمجموعة", "probability": 0.897705078125}, {"start": 1296.52, "end": 1296.92, "word": " a", "probability": 0.7216796875}, {"start": 1296.92, "end": 1298.14, "word": " اللي", "probability": 0.8212890625}, {"start": 1298.14, "end": 1298.4, "word": " هي", "probability": 0.83544921875}, {"start": 1298.4, "end": 1299.16, "word": " الفترة", "probability": 0.9894205729166666}, {"start": 1299.16, "end": 1300.04, "word": " المغلقة", "probability": 0.968994140625}, {"start": 1300.04, "end": 1300.42, "word": " من", "probability": 0.99072265625}, {"start": 1300.42, "end": 1301.06, "word": " سفر", "probability": 0.7889811197916666}, {"start": 1301.06, "end": 1301.38, "word": " إلى", "probability": 0.81982421875}, {"start": 1301.38, "end": 1301.8, "word": " بي", "probability": 0.605224609375}, {"start": 1301.8, "end": 1303.12, "word": " حيث", "probability": 0.83349609375}, {"start": 1303.12, "end": 1303.66, "word": " بي", "probability": 0.94140625}, {"start": 1303.66, "end": 1303.96, "word": " أي", "probability": 0.62841796875}, {"start": 1303.96, "end": 1304.44, "word": " عدد", "probability": 0.99072265625}, {"start": 1304.44, "end": 1304.9, "word": " موجب", "probability": 0.779296875}, {"start": 1304.9, "end": 1305.5, "word": " بي", "probability": 0.845458984375}, {"start": 1305.5, "end": 1306.6, "word": " أي", "probability": 0.80615234375}, {"start": 1306.6, "end": 1307.12, "word": " عدد", "probability": 0.9957682291666666}, {"start": 1307.12, "end": 1307.72, "word": " موجب", "probability": 0.98583984375}], "temperature": 1.0}, {"id": 48, "seek": 133551, "start": 1309.23, "end": 1335.51, "text": "بنأثبت أن الـ function هذه تطلع uniformly continuous show that show أن f is uniformly continuous on a ففيه برهنين", "tokens": [3555, 1863, 10721, 12984, 3555, 2655, 14739, 2423, 39184, 2445, 29538, 6055, 9566, 1211, 3615, 48806, 10957, 855, 300, 855, 14739, 283, 307, 48806, 10957, 322, 257, 6156, 41185, 3224, 4724, 2288, 3224, 1863, 9957], "avg_logprob": -0.3159722106324302, "compression_ratio": 1.2327586206896552, "no_speech_prob": 0.0, "words": [{"start": 1309.23, "end": 1310.07, "word": "بنأثبت", "probability": 0.7078653971354166}, {"start": 1310.07, "end": 1310.25, "word": " أن", "probability": 0.440673828125}, {"start": 1310.25, "end": 1310.41, "word": " الـ", "probability": 0.816162109375}, {"start": 1310.41, "end": 1310.75, "word": " function", "probability": 0.8212890625}, {"start": 1310.75, "end": 1311.31, "word": " هذه", "probability": 0.6845703125}, {"start": 1311.31, "end": 1312.57, "word": " تطلع", "probability": 0.9112548828125}, {"start": 1312.57, "end": 1313.05, "word": " uniformly", "probability": 0.63232421875}, {"start": 1313.05, "end": 1314.41, "word": " continuous", "probability": 0.783203125}, {"start": 1314.41, "end": 1319.95, "word": " show", "probability": 0.79248046875}, {"start": 1319.95, "end": 1320.55, "word": " that", "probability": 0.93603515625}, {"start": 1320.55, "end": 1325.95, "word": " show", "probability": 0.409423828125}, {"start": 1325.95, "end": 1326.29, "word": " أن", "probability": 0.5458984375}, {"start": 1326.29, "end": 1326.69, "word": " f", "probability": 0.3310546875}, {"start": 1326.69, "end": 1327.25, "word": " is", "probability": 0.91748046875}, {"start": 1327.25, "end": 1328.37, "word": " uniformly", "probability": 0.9736328125}, {"start": 1328.37, "end": 1331.67, "word": " continuous", "probability": 0.89208984375}, {"start": 1331.67, "end": 1332.41, "word": " on", "probability": 0.90380859375}, {"start": 1332.41, "end": 1332.91, "word": " a", "probability": 0.70703125}, {"start": 1332.91, "end": 1334.87, "word": " ففيه", "probability": 0.7156575520833334}, {"start": 1334.87, "end": 1335.51, "word": " برهنين", "probability": 0.83740234375}], "temperature": 1.0}, {"id": 49, "seek": 135944, "start": 1337.38, "end": 1359.44, "text": "او حالين proof one حال الأول since if is continuous on a being a polynomial", "tokens": [995, 2407, 11331, 6027, 9957, 8177, 472, 11331, 6027, 16247, 12610, 1670, 498, 307, 10957, 322, 257, 885, 257, 26110], "avg_logprob": -0.25930058388482957, "compression_ratio": 1.0227272727272727, "no_speech_prob": 0.0, "words": [{"start": 1337.38, "end": 1337.76, "word": "او", "probability": 0.74853515625}, {"start": 1337.76, "end": 1338.38, "word": " حالين", "probability": 0.85888671875}, {"start": 1338.38, "end": 1338.84, "word": " proof", "probability": 0.469970703125}, {"start": 1338.84, "end": 1339.78, "word": " one", "probability": 0.79638671875}, {"start": 1339.78, "end": 1341.0, "word": " حال", "probability": 0.685791015625}, {"start": 1341.0, "end": 1341.54, "word": " الأول", "probability": 0.854248046875}, {"start": 1341.54, "end": 1343.72, "word": " since", "probability": 0.72998046875}, {"start": 1343.72, "end": 1348.4, "word": " if", "probability": 0.7607421875}, {"start": 1348.4, "end": 1349.14, "word": " is", "probability": 0.931640625}, {"start": 1349.14, "end": 1351.64, "word": " continuous", "probability": 0.88330078125}, {"start": 1351.64, "end": 1353.68, "word": " on", "probability": 0.95458984375}, {"start": 1353.68, "end": 1354.36, "word": " a", "probability": 0.7021484375}, {"start": 1354.36, "end": 1357.4, "word": " being", "probability": 0.6015625}, {"start": 1357.4, "end": 1358.88, "word": " a", "probability": 0.72509765625}, {"start": 1358.88, "end": 1359.44, "word": " polynomial", "probability": 0.87744140625}], "temperature": 1.0}, {"id": 50, "seek": 139408, "start": 1364.78, "end": 1394.08, "text": "لأنها polynomial و احنا قلنا كل polynomial function متصل على R وبالتالي على أي مجموعة جزئية من R زي المجموعة A اللي هي الفترة المغلقة من سفر إلى الـ B ف if is continuous على A كونها polynomial and بما انه and since", "tokens": [1211, 33456, 11296, 26110, 4032, 1975, 5016, 8315, 12174, 1211, 8315, 28242, 26110, 2445, 44650, 36520, 15844, 497, 46599, 6027, 2655, 6027, 1829, 15844, 36632, 3714, 7435, 2304, 2407, 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0.927734375}, {"start": 1372.84, "end": 1374.36, "word": " المجموعة", "probability": 0.95654296875}, {"start": 1374.36, "end": 1374.68, "word": " A", "probability": 0.76513671875}, {"start": 1374.68, "end": 1374.88, "word": " اللي", "probability": 0.77587890625}, {"start": 1374.88, "end": 1375.14, "word": " هي", "probability": 0.94140625}, {"start": 1375.14, "end": 1375.72, "word": " الفترة", "probability": 0.98828125}, {"start": 1375.72, "end": 1376.52, "word": " المغلقة", "probability": 0.9237060546875}, {"start": 1376.52, "end": 1379.0, "word": " من", "probability": 0.94482421875}, {"start": 1379.0, "end": 1379.76, "word": " سفر", "probability": 0.69580078125}, {"start": 1379.76, "end": 1380.32, "word": " إلى", "probability": 0.8955078125}, {"start": 1380.32, "end": 1381.4, "word": " الـ", "probability": 0.591796875}, {"start": 1381.4, "end": 1381.62, "word": " B", "probability": 0.435791015625}, {"start": 1381.62, "end": 1385.62, "word": " ف", "probability": 0.94482421875}, {"start": 1385.62, "end": 1385.94, "word": " if", "probability": 0.361083984375}, {"start": 1385.94, "end": 1386.2, "word": " is", "probability": 0.8271484375}, {"start": 1386.2, "end": 1386.76, "word": " continuous", "probability": 0.9169921875}, {"start": 1386.76, "end": 1387.14, "word": " على", "probability": 0.84619140625}, {"start": 1387.14, "end": 1387.36, "word": " A", "probability": 0.908203125}, {"start": 1387.36, "end": 1387.88, "word": " كونها", "probability": 0.9410807291666666}, {"start": 1387.88, "end": 1388.4, "word": " polynomial", "probability": 0.91357421875}, {"start": 1388.4, "end": 1390.4, "word": " and", "probability": 0.88330078125}, {"start": 1390.4, "end": 1390.92, "word": " بما", "probability": 0.973876953125}, {"start": 1390.92, "end": 1391.4, "word": " انه", "probability": 0.753173828125}, {"start": 1391.4, "end": 1393.46, "word": " and", "probability": 0.8505859375}, {"start": 1393.46, "end": 1394.08, "word": " since", "probability": 0.900390625}], "temperature": 1.0}, {"id": 51, "seek": 142498, "start": 1395.88, "end": 1424.98, "text": "الـ set A هذه اللي هي عبارة عن الفترة المغلقة من سفر لـ B is closed and bounded and bounded interval then by uniform continuity theorem", "tokens": [6027, 39184, 992, 316, 29538, 13672, 1829, 39896, 6225, 3555, 9640, 3660, 18871, 27188, 2655, 25720, 9673, 17082, 1211, 28671, 9154, 8608, 5172, 2288, 5296, 39184, 363, 307, 5395, 293, 37498, 293, 37498, 15035, 550, 538, 9452, 23807, 20904], "avg_logprob": -0.2259765576571226, "compression_ratio": 1.27007299270073, "no_speech_prob": 0.0, "words": [{"start": 1395.88, "end": 1396.4, "word": "الـ", "probability": 0.6517333984375}, {"start": 1396.4, "end": 1396.72, "word": " set", "probability": 0.568359375}, {"start": 1396.72, "end": 1397.08, "word": " A", "probability": 0.60400390625}, {"start": 1397.08, "end": 1397.64, "word": " هذه", "probability": 0.5966796875}, {"start": 1397.64, "end": 1397.84, "word": " اللي", "probability": 0.841064453125}, 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1607.92, "word": " المغلفة", "probability": 0.884033203125}, {"start": 1607.92, "end": 1608.58, "word": " من", "probability": 0.94482421875}, {"start": 1608.58, "end": 1609.04, "word": " سفر", "probability": 0.81298828125}, {"start": 1609.04, "end": 1609.26, "word": " إلى", "probability": 0.8876953125}, {"start": 1609.26, "end": 1610.68, "word": " بي", "probability": 0.9033203125}, {"start": 1610.68, "end": 1612.12, "word": " طبعا", "probability": 0.93896484375}, {"start": 1612.12, "end": 1612.52, "word": " هذا", "probability": 0.85595703125}, {"start": 1612.52, "end": 1613.42, "word": " بساوي", "probability": 0.907958984375}], "temperature": 1.0}, {"id": 59, "seek": 164180, "start": 1614.18, "end": 1641.8, "text": "اتنين بي في absolute x minus u for all x و u تنتمي الى a اذا هاي شرط لبسيش اتحقق with k بيساو اتنين بيعدد موجب اذا هنا take k بيساو اتنين بيعدد موجب", "tokens": [995, 2655, 1863, 9957, 4724, 1829, 8978, 8236, 2031, 3175, 344, 337, 439, 2031, 4032, 344, 6055, 29399, 2304, 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1618.04, "word": " u", "probability": 0.8564453125}, {"start": 1618.04, "end": 1619.56, "word": " for", "probability": 0.8701171875}, {"start": 1619.56, "end": 1620.22, "word": " all", "probability": 0.9482421875}, {"start": 1620.22, "end": 1620.74, "word": " x", "probability": 0.97705078125}, {"start": 1620.74, "end": 1621.12, "word": " و", "probability": 0.5537109375}, {"start": 1621.12, "end": 1621.66, "word": " u", "probability": 0.51025390625}, {"start": 1621.66, "end": 1622.78, "word": " تنتمي", "probability": 0.77178955078125}, {"start": 1622.78, "end": 1623.18, "word": " الى", "probability": 0.7174072265625}, {"start": 1623.18, "end": 1623.48, "word": " a", "probability": 0.77392578125}, {"start": 1623.48, "end": 1625.06, "word": " اذا", "probability": 0.5889892578125}, {"start": 1625.06, "end": 1625.28, "word": " هاي", "probability": 0.5211181640625}, {"start": 1625.28, "end": 1625.72, "word": " شرط", "probability": 0.8976236979166666}, {"start": 1625.72, "end": 1626.34, "word": " لبسيش", "probability": 0.71728515625}, {"start": 1626.34, "end": 1627.18, "word": " اتحقق", "probability": 0.94091796875}, {"start": 1627.18, "end": 1628.04, "word": " with", "probability": 0.71484375}, {"start": 1628.04, "end": 1628.36, "word": " k", "probability": 0.79931640625}, {"start": 1628.36, "end": 1628.82, "word": " بيساو", "probability": 0.755322265625}, {"start": 1628.82, "end": 1629.2, "word": " اتنين", "probability": 0.930908203125}, {"start": 1629.2, "end": 1629.72, "word": " بيعدد", "probability": 0.87939453125}, {"start": 1629.72, "end": 1630.2, "word": " موجب", "probability": 0.9391276041666666}, {"start": 1630.2, "end": 1631.72, "word": " اذا", "probability": 0.734130859375}, {"start": 1631.72, "end": 1631.94, "word": " هنا", "probability": 0.68505859375}, {"start": 1631.94, "end": 1632.54, "word": " take", "probability": 0.212890625}, {"start": 1632.54, "end": 1637.34, "word": " k", "probability": 0.427001953125}, {"start": 1637.34, "end": 1638.48, "word": " بيساو", "probability": 0.9580078125}, {"start": 1638.48, "end": 1640.44, "word": " اتنين", "probability": 0.98681640625}, {"start": 1640.44, "end": 1641.18, "word": " بيعدد", "probability": 0.9727783203125}, {"start": 1641.18, "end": 1641.8, "word": " موجب", "probability": 0.9925130208333334}], "temperature": 1.0}, {"id": 60, "seek": 165851, "start": 1656.69, "end": 1658.51, "text": "Okay طبعا", "tokens": [8297, 23032, 3555, 3615, 995], "avg_logprob": -0.5572916567325592, "compression_ratio": 0.5909090909090909, "no_speech_prob": 0.0, "words": [{"start": 1656.6899999999998, "end": 1658.09, "word": "Okay", "probability": 0.2413330078125}, {"start": 1658.09, "end": 1658.51, "word": " طبعا", "probability": 0.72998046875}], "temperature": 1.0}, {"id": 61, "seek": 170218, "start": 1674.18, "end": 1702.18, "text": "واضح البران في اي سؤال او استفسار في عندي نظرية تتعلق بال uniform الها علاقة بال uniform continuity وهي النظرية التالية", "tokens": [2407, 46958, 5016, 29739, 23557, 1863, 8978, 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"word": " النظرية", "probability": 0.9666748046875}, {"start": 1701.38, "end": 1702.18, "word": " التالية", "probability": 0.9923502604166666}], "temperature": 1.0}, {"id": 62, "seek": 174078, "start": 1718.26, "end": 1740.78, "text": "فيرم if if from a to r is uniformly is uniformly continuous on a then", "tokens": [5172, 13546, 2304, 498, 498, 490, 257, 281, 367, 307, 48806, 307, 48806, 10957, 322, 257, 550], "avg_logprob": -0.4661458416117562, "compression_ratio": 1.123076923076923, "no_speech_prob": 0.0, "words": [{"start": 1718.2599999999998, "end": 1719.6599999999999, "word": "فيرم", "probability": 0.4401143391927083}, {"start": 1719.6599999999999, "end": 1721.06, "word": " if", "probability": 0.432861328125}, {"start": 1721.06, "end": 1721.68, "word": " if", "probability": 0.2373046875}, {"start": 1721.68, "end": 1723.24, "word": " from", "probability": 0.8779296875}, {"start": 1723.24, "end": 1723.78, "word": " a", "probability": 0.58837890625}, {"start": 1723.78, "end": 1724.1, "word": " to", "probability": 0.96728515625}, {"start": 1724.1, "end": 1724.68, "word": " r", "probability": 0.8642578125}, {"start": 1724.68, "end": 1726.8, "word": " is", "probability": 0.9462890625}, {"start": 1726.8, "end": 1727.78, "word": " uniformly", "probability": 0.96728515625}, {"start": 1727.78, "end": 1728.34, "word": " is", "probability": 0.41162109375}, {"start": 1728.34, "end": 1729.44, "word": " uniformly", "probability": 0.9755859375}, {"start": 1729.44, "end": 1732.54, "word": " continuous", "probability": 0.90283203125}, {"start": 1732.54, "end": 1735.4, "word": " on", "probability": 0.9423828125}, {"start": 1735.4, "end": 1736.46, "word": " a", "probability": 0.93017578125}, {"start": 1736.46, "end": 1740.78, "word": " then", "probability": 0.83642578125}], "temperature": 1.0}, {"id": 63, "seek": 177158, "start": 1743.0, "end": 1771.58, "text": "For any Cauchy Sequence xn contained in A The sequence f of xn اللي هي ال image لسيقونس xn is Cauchy", "tokens": [12587, 604, 7544, 625, 88, 46859, 655, 2031, 77, 16212, 294, 316, 440, 8310, 283, 295, 2031, 77, 13672, 1829, 39896, 2423, 3256, 5296, 3794, 1829, 4587, 11536, 3794, 2031, 77, 307, 7544, 625, 88], "avg_logprob": -0.4025607638888889, "compression_ratio": 1.1057692307692308, "no_speech_prob": 0.0, "words": [{"start": 1743.0, "end": 1743.56, "word": "For", "probability": 0.077880859375}, {"start": 1743.56, "end": 1744.24, "word": " any", "probability": 0.6416015625}, {"start": 1744.24, "end": 1746.2, "word": " Cauchy", "probability": 0.8546549479166666}, {"start": 1746.2, "end": 1749.64, "word": " Sequence", "probability": 0.77978515625}, {"start": 1749.64, "end": 1752.14, "word": " xn", "probability": 0.436279296875}, {"start": 1752.14, "end": 1753.28, "word": " contained", "probability": 0.63427734375}, {"start": 1753.28, "end": 1754.72, "word": " in", "probability": 0.94873046875}, {"start": 1754.72, "end": 1755.3, "word": " A", "probability": 0.6474609375}, {"start": 1755.3, "end": 1758.78, "word": " The", "probability": 0.252197265625}, {"start": 1758.78, "end": 1759.52, "word": " sequence", "probability": 0.85888671875}, {"start": 1759.52, "end": 1762.7, "word": " f", "probability": 0.748046875}, {"start": 1762.7, "end": 1763.06, "word": " of", "probability": 0.3759765625}, {"start": 1763.06, "end": 1764.12, "word": " xn", "probability": 0.80224609375}, {"start": 1764.12, "end": 1765.0, "word": " اللي", "probability": 0.734619140625}, {"start": 1765.0, "end": 1765.2, "word": " هي", "probability": 0.8662109375}, {"start": 1765.2, "end": 1765.32, "word": " ال", "probability": 0.93701171875}, {"start": 1765.32, "end": 1765.78, "word": " image", "probability": 0.4560546875}, {"start": 1765.78, "end": 1767.22, "word": " لسيقونس", "probability": 0.6578776041666666}, {"start": 1767.22, "end": 1767.94, "word": " xn", "probability": 0.888427734375}, {"start": 1767.94, "end": 1768.54, "word": " is", "probability": 0.76416015625}, {"start": 1768.54, "end": 1771.58, "word": " Cauchy", "probability": 0.8675130208333334}], "temperature": 1.0}, {"id": 64, "seek": 180109, "start": 1773.11, "end": 1801.09, "text": "in R that is that is هذا يعني هذا يعني هذا يعني انه uniformly uniformly continuous", "tokens": [259, 497, 300, 307, 300, 307, 23758, 37495, 22653, 23758, 37495, 22653, 23758, 37495, 22653, 16472, 3224, 48806, 48806, 10957], "avg_logprob": -0.2416294529324486, "compression_ratio": 1.606060606060606, "no_speech_prob": 0.0, "words": [{"start": 1773.11, "end": 1773.51, "word": "in", "probability": 0.259765625}, {"start": 1773.51, "end": 1774.05, "word": " R", "probability": 0.57861328125}, {"start": 1774.05, "end": 1780.09, "word": " that", "probability": 0.83740234375}, {"start": 1780.09, "end": 1780.57, "word": " is", "probability": 0.974609375}, {"start": 1780.57, "end": 1785.95, "word": " that", "probability": 0.429931640625}, {"start": 1785.95, "end": 1787.39, "word": " is", "probability": 0.966796875}, {"start": 1787.39, "end": 1787.79, "word": " هذا", "probability": 0.73876953125}, {"start": 1787.79, "end": 1788.31, "word": " يعني", "probability": 0.975830078125}, {"start": 1788.31, "end": 1789.55, "word": " هذا", "probability": 0.8642578125}, {"start": 1789.55, "end": 1790.05, "word": " يعني", "probability": 0.984130859375}, {"start": 1790.05, "end": 1792.03, "word": " هذا", "probability": 0.9091796875}, {"start": 1792.03, "end": 1792.55, "word": " يعني", "probability": 0.988037109375}, {"start": 1792.55, "end": 1793.99, "word": " انه", "probability": 0.74658203125}, {"start": 1793.99, "end": 1796.03, "word": " uniformly", "probability": 0.9775390625}, {"start": 1796.03, "end": 1798.89, "word": " uniformly", "probability": 0.51416015625}, {"start": 1798.89, "end": 1801.09, "word": " continuous", "probability": 0.94091796875}], "temperature": 1.0}, {"id": 65, "seek": 182246, "start": 1804.96, "end": 1822.46, "text": "functions preserve كوشي sequences", "tokens": [15930, 3916, 15665, 9122, 2407, 8592, 1829, 22978], "avg_logprob": -0.5598958333333334, "compression_ratio": 0.8222222222222222, "no_speech_prob": 0.0, "words": [{"start": 1804.9599999999998, "end": 1806.36, "word": "functions", "probability": 0.502166748046875}, {"start": 1806.36, "end": 1807.76, "word": " preserve", "probability": 0.6494140625}, {"start": 1807.76, "end": 1818.04, "word": " كوشي", "probability": 0.789947509765625}, {"start": 1818.04, "end": 1822.46, "word": " sequences", "probability": 0.7890625}], "temperature": 1.0}, {"id": 66, "seek": 185208, "start": 1827.96, "end": 1852.08, "text": "يعني الدوال اللي بتكون متصل اتصال منتظم بتحافظ على cushy sequences بمعنى انه لو كانت xn cushy sequence في المجال تبع الدالة A فصورتها هتطلع cushy sequence في المجال المقابل R والبرهان سهل", "tokens": [40228, 22653, 32748, 2407, 6027, 13672, 1829, 39894, 30544, 44650, 36520, 1975, 2655, 9381, 6027, 9154, 2655, 19913, 2304, 39894, 5016, 31845, 19913, 15844, 18422, 88, 22978, 4724, 2304, 3615, 1863, 7578, 16472, 3224, 45164, 25961, 2655, 2031, 77, 18422, 88, 8310, 8978, 9673, 7435, 6027, 6055, 3555, 3615, 32748, 6027, 3660, 316, 6156, 9381, 13063, 2655, 11296, 8032, 2655, 9566, 1211, 3615, 18422, 88, 8310, 8978, 9673, 7435, 6027, 9673, 4587, 16758, 1211, 497, 16070, 26890, 3224, 7649, 8608, 3224, 1211], "avg_logprob": -0.14288403973521957, "compression_ratio": 1.6741573033707866, "no_speech_prob": 0.0, "words": [{"start": 1827.9600000000003, "end": 1829.0800000000002, "word": "يعني", "probability": 0.86767578125}, {"start": 1829.0800000000002, "end": 1830.2, "word": " الدوال", "probability": 0.77001953125}, {"start": 1830.2, "end": 1830.46, "word": " اللي", "probability": 0.72998046875}, {"start": 1830.46, "end": 1831.0, "word": " بتكون", "probability": 0.968505859375}, {"start": 1831.0, "end": 1831.54, "word": " متصل", "probability": 0.7099609375}, {"start": 1831.54, "end": 1832.08, "word": " اتصال", "probability": 0.8839111328125}, {"start": 1832.08, "end": 1832.7, "word": " منتظم", "probability": 0.904541015625}, {"start": 1832.7, "end": 1834.14, "word": " بتحافظ", "probability": 0.9630126953125}, {"start": 1834.14, "end": 1834.42, "word": " على", "probability": 0.84619140625}, {"start": 1834.42, "end": 1834.8, "word": " cushy", "probability": 0.536407470703125}, {"start": 1834.8, "end": 1835.46, "word": " sequences", "probability": 0.87646484375}, {"start": 1835.46, "end": 1836.86, "word": " بمعنى", "probability": 0.96474609375}, {"start": 1836.86, "end": 1837.9, "word": " انه", "probability": 0.7353515625}, {"start": 1837.9, "end": 1838.08, "word": " لو", "probability": 0.98095703125}, {"start": 1838.08, "end": 1838.72, "word": " كانت", "probability": 0.97705078125}, {"start": 1838.72, "end": 1839.42, "word": " xn", "probability": 0.425537109375}, {"start": 1839.42, "end": 1839.96, "word": " cushy", "probability": 0.811279296875}, {"start": 1839.96, "end": 1840.54, "word": " sequence", "probability": 0.94482421875}, {"start": 1840.54, "end": 1841.26, "word": " في", "probability": 0.798828125}, {"start": 1841.26, "end": 1841.82, "word": " المجال", "probability": 0.9549153645833334}, {"start": 1841.82, "end": 1842.18, "word": " تبع", "probability": 0.9407552083333334}, {"start": 1842.18, "end": 1842.92, "word": " الدالة", "probability": 0.9690755208333334}, {"start": 1842.92, "end": 1843.38, "word": " A", "probability": 0.499755859375}, {"start": 1843.38, "end": 1845.08, "word": " فصورتها", "probability": 0.98330078125}, {"start": 1845.08, "end": 1846.26, "word": " هتطلع", "probability": 0.97255859375}, {"start": 1846.26, "end": 1846.7, "word": " cushy", "probability": 0.912353515625}, {"start": 1846.7, "end": 1847.26, "word": " sequence", "probability": 0.96044921875}, {"start": 1847.26, "end": 1848.0, "word": " في", "probability": 0.93896484375}, {"start": 1848.0, "end": 1848.46, "word": " المجال", "probability": 0.99609375}, {"start": 1848.46, "end": 1849.14, "word": " المقابل", "probability": 0.9849853515625}, {"start": 1849.14, "end": 1849.66, "word": " R", "probability": 0.8447265625}, {"start": 1849.66, "end": 1851.6, "word": " والبرهان", "probability": 0.8905029296875}, {"start": 1851.6, "end": 1852.08, "word": " سهل", "probability": 0.9972330729166666}], "temperature": 1.0}, {"id": 67, "seek": 188177, "start": 1853.21, "end": 1881.77, "text": "طبعا هذا بس صحيح لل uniform ل continuous functions أما لو كانت ال function بس continuous فمش شرط اتحافظ على كوشي sequences والبرهان سهل بسيط prove let if from A to R", "tokens": [9566, 3555, 3615, 995, 23758, 4724, 3794, 20328, 5016, 1829, 5016, 24976, 9452, 5296, 10957, 6828, 5551, 15042, 45164, 25961, 2655, 2423, 2445, 4724, 3794, 10957, 6156, 2304, 8592, 13412, 2288, 9566, 1975, 2655, 5016, 31845, 19913, 15844, 9122, 2407, 8592, 1829, 22978, 16070, 26890, 3224, 7649, 8608, 3224, 1211, 4724, 3794, 1829, 9566, 7081, 718, 498, 490, 316, 281, 497], "avg_logprob": -0.16922883232755045, "compression_ratio": 1.3333333333333333, "no_speech_prob": 0.0, "words": [{"start": 1853.21, "end": 1853.59, "word": "طبعا", "probability": 0.96923828125}, {"start": 1853.59, "end": 1853.81, "word": " هذا", "probability": 0.66748046875}, {"start": 1853.81, "end": 1854.33, "word": " بس", "probability": 0.80712890625}, {"start": 1854.33, "end": 1855.47, "word": " صحيح", "probability": 0.9942626953125}, {"start": 1855.47, "end": 1855.69, "word": " لل", "probability": 0.65087890625}, {"start": 1855.69, "end": 1856.21, "word": " uniform", "probability": 0.260009765625}, {"start": 1856.21, "end": 1856.39, "word": " ل", "probability": 0.6748046875}, {"start": 1856.39, "end": 1856.79, "word": " continuous", "probability": 0.82958984375}, {"start": 1856.79, "end": 1857.39, "word": " functions", "probability": 0.8662109375}, {"start": 1857.39, "end": 1857.79, "word": " أما", "probability": 0.88525390625}, {"start": 1857.79, "end": 1858.65, "word": " لو", "probability": 0.947265625}, {"start": 1858.65, "end": 1858.97, "word": " كانت", "probability": 0.972900390625}, {"start": 1858.97, "end": 1859.09, "word": " ال", "probability": 0.97900390625}, {"start": 1859.09, "end": 1859.47, "word": " function", "probability": 0.9365234375}, {"start": 1859.47, "end": 1859.91, "word": " بس", "probability": 0.990966796875}, {"start": 1859.91, "end": 1860.71, "word": " continuous", "probability": 0.96533203125}, {"start": 1860.71, "end": 1861.87, "word": " فمش", "probability": 0.9640299479166666}, {"start": 1861.87, "end": 1862.35, "word": " شرط", "probability": 0.9794921875}, {"start": 1862.35, "end": 1863.31, "word": " اتحافظ", "probability": 0.93271484375}, {"start": 1863.31, "end": 1863.51, "word": " على", "probability": 0.8173828125}, {"start": 1863.51, "end": 1863.91, "word": " كوشي", "probability": 0.729736328125}, {"start": 1863.91, "end": 1864.41, "word": " sequences", "probability": 0.5966796875}, {"start": 1864.41, "end": 1867.51, "word": " والبرهان", "probability": 0.79901123046875}, {"start": 1867.51, "end": 1868.57, "word": " سهل", "probability": 0.9967447916666666}, {"start": 1868.57, "end": 1869.45, "word": " بسيط", "probability": 0.90869140625}, {"start": 1869.45, "end": 1872.19, "word": " prove", "probability": 0.595703125}, {"start": 1872.19, "end": 1878.67, "word": " let", "probability": 0.87890625}, {"start": 1878.67, "end": 1879.23, "word": " if", "probability": 0.4140625}, {"start": 1879.23, "end": 1880.61, "word": " from", "probability": 0.908203125}, {"start": 1880.61, "end": 1881.05, "word": " A", "probability": 0.48583984375}, {"start": 1881.05, "end": 1881.29, "word": " to", "probability": 0.98388671875}, {"start": 1881.29, "end": 1881.77, "word": " R", "probability": 0.99462890625}], "temperature": 1.0}, {"id": 68, "seek": 191148, "start": 1882.84, "end": 1911.48, "text": "ب uniformly continuous on a and let x in contained in a,b كوشي كوشي sequence و بدنا نثبت ان ال image لل sequence x in بتطلع كوشي طيب", "tokens": [3555, 48806, 10957, 322, 257, 293, 718, 2031, 294, 16212, 294, 257, 11, 65, 9122, 2407, 8592, 1829, 9122, 2407, 8592, 1829, 8310, 4032, 47525, 8315, 8717, 12984, 3555, 2655, 16472, 2423, 3256, 24976, 8310, 2031, 294, 39894, 9566, 1211, 3615, 9122, 2407, 8592, 1829, 23032, 1829, 3555], "avg_logprob": -0.2932079081632653, "compression_ratio": 1.282442748091603, "no_speech_prob": 0.0, "words": [{"start": 1882.84, "end": 1883.26, "word": "ب", "probability": 0.322265625}, {"start": 1883.26, "end": 1884.54, "word": " uniformly", "probability": 0.0926513671875}, {"start": 1884.54, "end": 1885.54, "word": " continuous", "probability": 0.806640625}, {"start": 1885.54, "end": 1889.88, "word": " on", "probability": 0.78759765625}, {"start": 1889.88, "end": 1890.44, "word": " a", "probability": 0.6328125}, {"start": 1890.44, "end": 1892.4, "word": " and", "probability": 0.7861328125}, {"start": 1892.4, "end": 1895.32, "word": " let", "probability": 0.87255859375}, {"start": 1895.32, "end": 1898.12, "word": " x", "probability": 0.8564453125}, {"start": 1898.12, "end": 1898.52, "word": " in", "probability": 0.61083984375}, {"start": 1898.52, "end": 1899.32, "word": " contained", "probability": 0.68017578125}, {"start": 1899.32, "end": 1899.6, "word": " in", "probability": 0.89306640625}, {"start": 1899.6, "end": 1899.94, "word": " a", "probability": 0.9296875}, {"start": 1899.94, "end": 1900.3, "word": ",b", "probability": 0.4217529296875}, {"start": 1900.3, "end": 1901.06, "word": " كوشي", "probability": 0.8096923828125}, {"start": 1901.06, "end": 1903.66, "word": " كوشي", "probability": 0.85711669921875}, {"start": 1903.66, "end": 1904.24, "word": " sequence", "probability": 0.89208984375}, {"start": 1904.24, "end": 1906.54, "word": " و", "probability": 0.5810546875}, {"start": 1906.54, "end": 1906.88, "word": " بدنا", "probability": 0.741943359375}, {"start": 1906.88, "end": 1907.26, "word": " نثبت", "probability": 0.990478515625}, {"start": 1907.26, "end": 1907.38, "word": " ان", "probability": 0.443115234375}, {"start": 1907.38, "end": 1907.54, "word": " ال", "probability": 0.9365234375}, {"start": 1907.54, "end": 1907.9, "word": " image", "probability": 0.8564453125}, {"start": 1907.9, "end": 1908.16, "word": " لل", "probability": 0.2880859375}, {"start": 1908.16, "end": 1908.56, "word": " sequence", "probability": 0.96533203125}, {"start": 1908.56, "end": 1908.96, "word": " x", "probability": 0.92724609375}, {"start": 1908.96, "end": 1909.36, "word": " in", "probability": 0.85693359375}, {"start": 1909.36, "end": 1910.42, "word": " بتطلع", "probability": 0.9259033203125}, {"start": 1910.42, "end": 1910.92, "word": " كوشي", "probability": 0.9888916015625}, {"start": 1910.92, "end": 1911.48, "word": " طيب", "probability": 0.9441731770833334}], "temperature": 1.0}, {"id": 69, "seek": 193970, "start": 1912.54, "end": 1939.7, "text": "to show ان ال image لسيكوينس XN is Cauchy لبرهان ان ال sequence هذه ال image لسيكوينس XN is Cauchy نحاول نطبق تعريف Cauchy", "tokens": [1353, 855, 16472, 2423, 3256, 5296, 3794, 1829, 4117, 2407, 9957, 3794, 1783, 45, 307, 7544, 625, 88, 5296, 26890, 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{"start": 2096.92, "end": 2098.16, "word": " star", "probability": 0.544921875}, {"start": 2098.16, "end": 2100.02, "word": " and", "probability": 0.82763671875}, {"start": 2100.02, "end": 2100.42, "word": " double", "probability": 0.93359375}, {"start": 2100.42, "end": 2101.06, "word": " star", "probability": 0.95458984375}, {"start": 2101.06, "end": 2103.44, "word": " بيقدّوا", "probability": 0.69794921875}, {"start": 2103.44, "end": 2106.36, "word": " أنه", "probability": 0.5775146484375}, {"start": 2106.36, "end": 2107.66, "word": " يوجد", "probability": 0.9837239583333334}, {"start": 2107.66, "end": 2109.34, "word": " capital", "probability": 0.79833984375}, {"start": 2109.34, "end": 2109.8, "word": " N", "probability": 0.728515625}, {"start": 2109.8, "end": 2110.62, "word": " يعتمد", "probability": 0.96484375}, {"start": 2110.62, "end": 2111.0, "word": " على", "probability": 0.8916015625}, {"start": 2111.0, "end": 2111.58, "word": " epsilon", "probability": 0.472900390625}, 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"end": 2160.71, "word": " فالمسافة", "probability": 0.99169921875}, {"start": 2160.71, "end": 2161.03, "word": " بين", "probability": 0.98486328125}, {"start": 2161.03, "end": 2161.83, "word": " صورهم", "probability": 0.9396158854166666}, {"start": 2161.83, "end": 2162.11, "word": " اللي", "probability": 0.864990234375}, {"start": 2162.11, "end": 2162.33, "word": " هي", "probability": 0.58740234375}, {"start": 2162.33, "end": 2163.09, "word": " xn", "probability": 0.904052734375}, {"start": 2163.09, "end": 2163.37, "word": " هنا", "probability": 0.958984375}, {"start": 2163.37, "end": 2165.91, "word": " وصورة", "probability": 0.938720703125}, {"start": 2165.91, "end": 2166.09, "word": " ال", "probability": 0.9326171875}, {"start": 2166.09, "end": 2166.87, "word": " xm", "probability": 0.91796875}, {"start": 2166.87, "end": 2167.57, "word": " تطلع", "probability": 0.8150634765625}, {"start": 2167.57, "end": 2168.19, "word": " أصغر", "probability": 0.989013671875}, {"start": 2168.19, 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"word": " X", "probability": 0.96826171875}, {"start": 2185.29, "end": 2185.51, "word": " M", "probability": 0.3173828125}, {"start": 2185.51, "end": 2185.61, "word": " و", "probability": 0.845703125}, {"start": 2185.61, "end": 2185.77, "word": " F", "probability": 0.55908203125}, {"start": 2185.77, "end": 2185.91, "word": " of", "probability": 0.9267578125}, {"start": 2185.91, "end": 2186.15, "word": " X", "probability": 0.99072265625}, {"start": 2186.15, "end": 2186.35, "word": " M", "probability": 0.76220703125}, {"start": 2186.35, "end": 2186.83, "word": " أصغر", "probability": 0.989501953125}, {"start": 2186.83, "end": 2186.99, "word": " من", "probability": 0.9912109375}, {"start": 2186.99, "end": 2187.47, "word": " إبسلون", "probability": 0.97255859375}, {"start": 2187.47, "end": 2188.33, "word": " إذا", "probability": 0.566650390625}, {"start": 2188.33, "end": 2188.95, "word": " بما", "probability": 0.942626953125}, {"start": 2188.95, "end": 2189.35, "word": " أنه", "probability": 0.61767578125}, {"start": 2189.35, "end": 2189.89, "word": " since", "probability": 0.724609375}, {"start": 2189.89, "end": 2191.65, "word": " إبسلون", "probability": 0.90205078125}, {"start": 2191.65, "end": 2192.09, "word": " أكبر", "probability": 0.98193359375}, {"start": 2192.09, "end": 2192.31, "word": " من", "probability": 0.9970703125}, {"start": 2192.31, "end": 2192.89, "word": " السفر", "probability": 0.9777018229166666}, {"start": 2192.89, "end": 2193.65, "word": " was", "probability": 0.93408203125}, {"start": 2193.65, "end": 2194.65, "word": " arbitrary", "probability": 0.78662109375}], "temperature": 1.0}, {"id": 80, "seek": 222423, "start": 2196.2, "end": 2224.24, "text": "إذا الـ sequence f of x in is Cauchy تطلع الـ sequence هذه Cauchy وهو المطلوب okay تمام ممكن نستخدم النظرية هذه ممكن نستخدم النظرية هذه في ال .. ان نثبت ان function معينة ليست", "tokens": [28814, 15730, 2423, 39184, 8310, 283, 295, 2031, 294, 307, 7544, 625, 88, 6055, 9566, 1211, 3615, 2423, 39184, 8310, 29538, 7544, 625, 88, 37037, 2407, 9673, 9566, 1211, 37746, 1392, 46811, 10943, 3714, 43020, 8717, 14851, 9778, 40448, 28239, 19913, 2288, 10632, 29538, 3714, 43020, 8717, 14851, 9778, 40448, 28239, 19913, 2288, 10632, 29538, 8978, 2423, 4386, 16472, 8717, 12984, 3555, 2655, 16472, 2445, 20449, 9957, 3660, 32239, 14851], "avg_logprob": -0.24317781480265335, "compression_ratio": 1.6319018404907975, "no_speech_prob": 0.0, "words": [{"start": 2196.2, "end": 2196.68, "word": "إذا", "probability": 0.44073486328125}, {"start": 2196.68, "end": 2197.02, "word": " الـ", "probability": 0.4830322265625}, {"start": 2197.02, "end": 2197.72, "word": " sequence", "probability": 0.8125}, {"start": 2197.72, "end": 2198.28, "word": " f", "probability": 0.6181640625}, {"start": 2198.28, "end": 2198.62, "word": " of", "probability": 0.58642578125}, {"start": 2198.62, "end": 2199.1, "word": " x", "probability": 0.9091796875}, {"start": 2199.1, "end": 2199.78, "word": " in", "probability": 0.8095703125}, {"start": 2199.78, "end": 2201.24, "word": " is", "probability": 0.6982421875}, {"start": 2201.24, "end": 2201.84, "word": " Cauchy", "probability": 0.7569173177083334}, {"start": 2201.84, "end": 2202.56, "word": " تطلع", "probability": 0.77410888671875}, {"start": 2202.56, "end": 2202.74, "word": " الـ", "probability": 0.768798828125}, {"start": 2202.74, "end": 2203.12, "word": " sequence", "probability": 0.97119140625}, {"start": 2203.12, "end": 2203.5, "word": " هذه", "probability": 0.492431640625}, {"start": 2203.5, "end": 2204.44, "word": " Cauchy", "probability": 0.9246419270833334}, {"start": 2204.44, "end": 2205.12, "word": " وهو", "probability": 0.779052734375}, {"start": 2205.12, "end": 2205.86, "word": " المطلوب", "probability": 0.9866943359375}, {"start": 2205.86, "end": 2207.24, "word": " okay", "probability": 0.14892578125}, {"start": 2207.24, "end": 2207.8, "word": " تمام", "probability": 0.909423828125}, {"start": 2207.8, "end": 2210.62, "word": " ممكن", "probability": 0.863525390625}, {"start": 2210.62, "end": 2211.24, "word": " نستخدم", "probability": 0.9935302734375}, {"start": 2211.24, "end": 2211.86, "word": " النظرية", "probability": 0.96435546875}, {"start": 2211.86, "end": 2212.36, "word": " هذه", "probability": 0.947265625}, {"start": 2212.36, "end": 2214.08, "word": " ممكن", "probability": 0.872314453125}, {"start": 2214.08, "end": 2214.62, "word": " نستخدم", "probability": 0.9962158203125}, {"start": 2214.62, "end": 2215.14, "word": " النظرية", "probability": 0.980712890625}, {"start": 2215.14, "end": 2215.6, "word": " هذه", "probability": 0.96533203125}, {"start": 2215.6, "end": 2216.0, "word": " في", "probability": 0.79638671875}, {"start": 2216.0, "end": 2217.04, "word": " ال", "probability": 0.71728515625}, {"start": 2217.04, "end": 2221.4, "word": " ..", "probability": 0.42431640625}, {"start": 2221.4, "end": 2222.0, "word": " ان", "probability": 0.450927734375}, {"start": 2222.0, "end": 2222.48, "word": " نثبت", "probability": 0.9725341796875}, {"start": 2222.48, "end": 2222.62, "word": " ان", "probability": 0.64990234375}, {"start": 2222.62, "end": 2223.04, "word": " function", "probability": 0.2587890625}, {"start": 2223.04, "end": 2223.7, "word": " معينة", "probability": 0.9803059895833334}, {"start": 2223.7, "end": 2224.24, "word": " ليست", "probability": 0.9521484375}], "temperature": 1.0}, {"id": 81, "seek": 225228, "start": 2225.54, "end": 2252.28, "text": "uniform and continuous هاي example use above theorem to show ال function f of x بالسعر واحد على x is not", "tokens": [409, 8629, 293, 10957, 8032, 47302, 1365, 764, 3673, 20904, 281, 855, 2423, 2445, 283, 295, 2031, 20666, 3794, 3615, 2288, 36764, 24401, 15844, 2031, 307, 406], "avg_logprob": -0.3200334683060646, "compression_ratio": 1.0701754385964912, "no_speech_prob": 0.0, "words": [{"start": 2225.54, "end": 2226.16, "word": "uniform", "probability": 0.58087158203125}, {"start": 2226.16, "end": 2226.32, "word": " and", "probability": 0.52392578125}, {"start": 2226.32, "end": 2227.0, "word": " continuous", "probability": 0.85205078125}, {"start": 2227.0, "end": 2227.82, "word": " هاي", "probability": 0.5531005859375}, {"start": 2227.82, "end": 2228.54, "word": " example", "probability": 0.85400390625}, {"start": 2228.54, "end": 2236.2, "word": " use", "probability": 0.72998046875}, {"start": 2236.2, "end": 2236.9, "word": " above", "probability": 0.91455078125}, {"start": 2236.9, "end": 2240.1, "word": " theorem", "probability": 0.8798828125}, {"start": 2240.1, "end": 2242.78, "word": " to", "probability": 0.95263671875}, {"start": 2242.78, "end": 2243.3, "word": " show", "probability": 0.96435546875}, {"start": 2243.3, "end": 2245.02, "word": " ال", "probability": 0.71337890625}, {"start": 2245.02, "end": 2245.6, "word": " function", "probability": 0.88427734375}, {"start": 2245.6, "end": 2247.36, "word": " f", "probability": 0.81982421875}, {"start": 2247.36, "end": 2247.6, "word": " of", "probability": 0.73681640625}, {"start": 2247.6, "end": 2248.06, "word": " x", "probability": 0.95458984375}, {"start": 2248.06, "end": 2249.58, "word": " بالسعر", "probability": 0.60845947265625}, {"start": 2249.58, "end": 2250.06, "word": " واحد", "probability": 0.976806640625}, {"start": 2250.06, "end": 2250.22, "word": " على", "probability": 0.484619140625}, {"start": 2250.22, "end": 2250.64, "word": " x", "probability": 0.62646484375}, {"start": 2250.64, "end": 2251.86, "word": " is", "probability": 0.9560546875}, {"start": 2251.86, "end": 2252.28, "word": " not", "probability": 0.96630859375}], "temperature": 1.0}, {"id": 82, "seek": 226467, "start": 2255.48, "end": 2264.68, "text": "uniformly continuous on a بساوي الفترة المفتوحة من صفر إلى ملا نهار", "tokens": [409, 8629, 356, 10957, 322, 257, 4724, 3794, 995, 45865, 27188, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 9154, 20328, 5172, 2288, 30731, 3714, 15040, 8717, 3224, 9640], "avg_logprob": -0.2565104295810064, "compression_ratio": 1.063157894736842, "no_speech_prob": 0.0, "words": [{"start": 2255.4800000000005, "end": 2256.6200000000003, "word": "uniformly", "probability": 0.7395833333333334}, {"start": 2256.6200000000003, "end": 2257.76, "word": " continuous", "probability": 0.6640625}, {"start": 2257.76, "end": 2258.42, "word": " on", "probability": 0.88623046875}, {"start": 2258.42, "end": 2260.3, "word": " a", "probability": 0.54931640625}, {"start": 2260.3, "end": 2261.76, "word": " بساوي", "probability": 0.62249755859375}, {"start": 2261.76, "end": 2262.24, "word": " الفترة", "probability": 0.982421875}, {"start": 2262.24, "end": 2263.02, "word": " المفتوحة", "probability": 0.9795735677083334}, {"start": 2263.02, "end": 2263.22, "word": " من", "probability": 0.98388671875}, {"start": 2263.22, "end": 2263.7, "word": " صفر", "probability": 0.8042805989583334}, {"start": 2263.7, "end": 2263.9, "word": " إلى", "probability": 0.806640625}, {"start": 2263.9, "end": 2264.24, "word": " ملا", "probability": 0.575439453125}, {"start": 2264.24, "end": 2264.68, "word": " نهار", "probability": 0.8025716145833334}], "temperature": 1.0}, {"id": 83, "seek": 230567, "start": 2277.8, "end": 2305.68, "text": "لحظة ان النظرية دي ايش بتقول لو كانت ال function uniform ل continuous فلازم تحافظ على كوشي sequence طب لو محافظتش على كوشي sequence مش ممكن تكون uniform ل continuous صح؟ مظبوط؟ اذا هنا proof by above theorem حسب النظرية على it suffices", "tokens": [1211, 5016, 19913, 3660, 16472, 28239, 19913, 2288, 10632, 11778, 1829, 1975, 1829, 8592, 39894, 39648, 45164, 25961, 2655, 2423, 2445, 9452, 5296, 10957, 6156, 1211, 31377, 2304, 6055, 5016, 31845, 19913, 15844, 9122, 2407, 8592, 1829, 8310, 23032, 3555, 45164, 3714, 5016, 31845, 19913, 2655, 8592, 15844, 9122, 2407, 8592, 1829, 8310, 37893, 3714, 43020, 6055, 30544, 9452, 5296, 10957, 20328, 5016, 22807, 3714, 19913, 3555, 2407, 9566, 22807, 1975, 15730, 34105, 8177, 538, 3673, 20904, 11331, 35457, 28239, 19913, 2288, 10632, 15844, 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2281.54, "word": " uniform", "probability": 0.77978515625}, {"start": 2281.54, "end": 2281.74, "word": " ل", "probability": 0.7080078125}, {"start": 2281.74, "end": 2282.32, "word": " continuous", "probability": 0.88916015625}, {"start": 2282.32, "end": 2283.5, "word": " فلازم", "probability": 0.9276123046875}, {"start": 2283.5, "end": 2284.08, "word": " تحافظ", "probability": 0.9620361328125}, {"start": 2284.08, "end": 2284.24, "word": " على", "probability": 0.80322265625}, {"start": 2284.24, "end": 2284.64, "word": " كوشي", "probability": 0.8487548828125}, {"start": 2284.64, "end": 2285.14, "word": " sequence", "probability": 0.861328125}, {"start": 2285.14, "end": 2286.1, "word": " طب", "probability": 0.8447265625}, {"start": 2286.1, "end": 2286.28, "word": " لو", "probability": 0.9697265625}, {"start": 2286.28, "end": 2286.94, "word": " محافظتش", "probability": 0.856689453125}, {"start": 2286.94, "end": 2287.1, "word": " على", "probability": 0.7080078125}, {"start": 2287.1, "end": 2287.44, "word": " كوشي", "probability": 0.97412109375}, {"start": 2287.44, "end": 2287.96, "word": " sequence", "probability": 0.97314453125}, {"start": 2287.96, "end": 2288.78, "word": " مش", "probability": 0.9482421875}, {"start": 2288.78, "end": 2289.08, "word": " ممكن", "probability": 0.986328125}, {"start": 2289.08, "end": 2289.44, "word": " تكون", "probability": 0.9912109375}, {"start": 2289.44, "end": 2289.84, "word": " uniform", "probability": 0.92529296875}, {"start": 2289.84, "end": 2290.06, "word": " ل", "probability": 0.98046875}, {"start": 2290.06, "end": 2290.72, "word": " continuous", "probability": 0.9462890625}, {"start": 2290.72, "end": 2291.76, "word": " صح؟", "probability": 0.8142903645833334}, {"start": 2291.76, "end": 2293.14, "word": " مظبوط؟", "probability": 0.8007405598958334}, {"start": 2293.14, "end": 2293.26, "word": " اذا", "probability": 0.677490234375}, {"start": 2293.26, "end": 2293.68, "word": " هنا", "probability": 0.982421875}, {"start": 2293.68, "end": 2297.26, "word": " proof", "probability": 0.330810546875}, {"start": 2297.26, "end": 2298.78, "word": " by", "probability": 0.95263671875}, {"start": 2298.78, "end": 2300.68, "word": " above", "probability": 0.9306640625}, {"start": 2300.68, "end": 2301.86, "word": " theorem", "probability": 0.8486328125}, {"start": 2301.86, "end": 2302.56, "word": " حسب", "probability": 0.9404296875}, {"start": 2302.56, "end": 2303.1, "word": " النظرية", "probability": 0.987548828125}, {"start": 2303.1, "end": 2303.42, "word": " على", "probability": 0.82373046875}, {"start": 2303.42, "end": 2304.64, "word": " it", "probability": 0.93994140625}, {"start": 2304.64, "end": 2305.68, "word": " suffices", "probability": 0.936279296875}], "temperature": 1.0}, {"id": 84, "seek": 233350, "start": 2308.36, "end": 2333.5, "text": "to show يكفي اثبات ان f is .. if does not .. if does .. does not preserve .. preserve Cauchy sequences ف consider", "tokens": [1353, 855, 7251, 4117, 41185, 1975, 12984, 3555, 9307, 16472, 283, 307, 4386, 498, 775, 406, 4386, 498, 775, 4386, 775, 406, 15665, 4386, 15665, 7544, 625, 88, 22978, 6156, 1949], "avg_logprob": -0.4270019428804517, "compression_ratio": 1.2254901960784315, "no_speech_prob": 0.0, "words": [{"start": 2308.36, "end": 2308.6, "word": "to", "probability": 0.059814453125}, {"start": 2308.6, "end": 2309.16, "word": " show", "probability": 0.9580078125}, {"start": 2309.16, "end": 2309.74, "word": " يكفي", "probability": 0.8466796875}, {"start": 2309.74, "end": 2310.42, "word": " اثبات", "probability": 0.8819580078125}, {"start": 2310.42, "end": 2311.26, "word": " ان", "probability": 0.77392578125}, {"start": 2311.26, "end": 2311.74, "word": " f", "probability": 0.248291015625}, {"start": 2311.74, "end": 2312.36, "word": " is", "probability": 0.69482421875}, {"start": 2312.36, "end": 2314.16, "word": " ..", "probability": 0.34716796875}, {"start": 2314.16, "end": 2314.78, "word": " if", "probability": 0.33642578125}, {"start": 2314.78, "end": 2315.2, "word": " does", "probability": 0.85107421875}, {"start": 2315.2, "end": 2315.66, "word": " not", "probability": 0.96630859375}, {"start": 2315.66, "end": 2315.9, "word": " ..", "probability": 0.63134765625}, {"start": 2315.9, "end": 2316.22, "word": " if", "probability": 0.7822265625}, {"start": 2316.22, "end": 2316.92, "word": " does", "probability": 0.958984375}, {"start": 2316.92, "end": 2318.86, "word": " ..", "probability": 0.59375}, {"start": 2318.86, "end": 2319.36, "word": " does", "probability": 0.8759765625}, {"start": 2319.36, "end": 2319.92, "word": " not", "probability": 0.9619140625}, {"start": 2319.92, "end": 2322.42, "word": " preserve", "probability": 0.4140625}, {"start": 2322.42, "end": 2322.72, "word": " ..", "probability": 0.78173828125}, {"start": 2322.72, "end": 2324.48, "word": " preserve", "probability": 0.884765625}, {"start": 2324.48, "end": 2326.96, "word": " Cauchy", "probability": 0.7146402994791666}, {"start": 2326.96, "end": 2327.76, "word": " sequences", "probability": 0.8125}, {"start": 2327.76, "end": 2332.86, "word": " ف", "probability": 0.9443359375}, {"start": 2332.86, "end": 2333.5, "word": " consider", "probability": 0.6806640625}], "temperature": 1.0}, {"id": 85, "seek": 236513, "start": 2336.93, "end": 2365.13, "text": "consider ال sequence xn اللي هي بساوي واحد على ن ال sequence هذه converge لصفر وبالتالي اذا xn is Cauchy تمام but صورة ال xn", "tokens": [21190, 1438, 2423, 8310, 2031, 77, 13672, 1829, 39896, 4724, 3794, 995, 45865, 36764, 24401, 15844, 8717, 2423, 8310, 29538, 41881, 5296, 9381, 5172, 2288, 46599, 6027, 2655, 6027, 1829, 1975, 15730, 2031, 77, 307, 7544, 625, 88, 46811, 10943, 457, 20328, 13063, 3660, 2423, 2031, 77], "avg_logprob": -0.3434244692325592, "compression_ratio": 1.2681159420289856, "no_speech_prob": 0.0, "words": [{"start": 2336.93, "end": 2337.73, "word": "consider", "probability": 0.59210205078125}, {"start": 2337.73, "end": 2338.11, "word": " ال", "probability": 0.5966796875}, {"start": 2338.11, "end": 2338.59, "word": " sequence", "probability": 0.72802734375}, {"start": 2338.59, "end": 2339.65, "word": " xn", "probability": 0.5694580078125}, {"start": 2339.65, "end": 2340.89, "word": " اللي", "probability": 0.416015625}, {"start": 2340.89, "end": 2341.07, "word": " هي", "probability": 0.495361328125}, {"start": 2341.07, "end": 2341.99, "word": " بساوي", "probability": 0.7940673828125}, {"start": 2341.99, "end": 2342.71, "word": " واحد", "probability": 0.923095703125}, {"start": 2342.71, "end": 2342.95, "word": " على", "probability": 0.626953125}, {"start": 2342.95, "end": 2343.27, "word": " ن", "probability": 0.251708984375}, {"start": 2343.27, "end": 2345.69, "word": " ال", "probability": 0.8408203125}, {"start": 2345.69, "end": 2346.19, "word": " sequence", "probability": 0.9375}, {"start": 2346.19, "end": 2346.61, "word": " هذه", "probability": 0.338623046875}, {"start": 2346.61, "end": 2347.37, "word": " converge", "probability": 0.8916015625}, {"start": 2347.37, "end": 2348.05, "word": " لصفر", "probability": 0.83721923828125}, {"start": 2348.05, "end": 2351.47, "word": " وبالتالي", "probability": 0.865673828125}, {"start": 2351.47, "end": 2352.61, "word": " اذا", "probability": 0.6400146484375}, {"start": 2352.61, "end": 2353.73, "word": " xn", "probability": 0.756103515625}, {"start": 2353.73, "end": 2355.87, "word": " is", "probability": 0.89599609375}, {"start": 2355.87, "end": 2358.13, "word": " Cauchy", "probability": 0.7532552083333334}, {"start": 2358.13, "end": 2360.03, "word": " تمام", "probability": 0.878173828125}, {"start": 2360.03, "end": 2361.43, "word": " but", "probability": 0.5556640625}, {"start": 2361.43, "end": 2364.29, "word": " صورة", "probability": 0.9798177083333334}, {"start": 2364.29, "end": 2364.45, "word": " ال", "probability": 0.947265625}, {"start": 2364.45, "end": 2365.13, "word": " xn", "probability": 0.945556640625}], "temperature": 1.0}, {"id": 86, "seek": 239421, "start": 2368.66, "end": 2394.22, "text": "أيش بتطلع؟ صورة الواحد على ان تطلع ال sequence in صح؟ و ال sequence هذه properly divergent to infinity، اذا I'm divergent، اذا I'm not Cauchy تمام؟", "tokens": [10721, 1829, 8592, 39894, 9566, 1211, 3615, 22807, 20328, 13063, 3660, 2423, 14407, 24401, 15844, 16472, 6055, 9566, 1211, 3615, 2423, 8310, 294, 20328, 5016, 22807, 4032, 2423, 8310, 29538, 6108, 18558, 6930, 281, 13202, 12399, 1975, 15730, 286, 478, 18558, 6930, 12399, 1975, 15730, 286, 478, 406, 7544, 625, 88, 46811, 10943, 22807], "avg_logprob": -0.3125000075860457, "compression_ratio": 1.3092105263157894, "no_speech_prob": 0.0, "words": [{"start": 2368.66, "end": 2368.98, "word": "أيش", "probability": 0.625732421875}, {"start": 2368.98, "end": 2370.5, "word": " بتطلع؟", "probability": 0.88203125}, {"start": 2370.5, "end": 2372.42, "word": " صورة", "probability": 0.8702799479166666}, {"start": 2372.42, "end": 2373.06, "word": " الواحد", "probability": 0.9353841145833334}, {"start": 2373.06, "end": 2373.3, "word": " على", "probability": 0.71728515625}, {"start": 2373.3, "end": 2373.66, "word": " ان", "probability": 0.1959228515625}, {"start": 2373.66, "end": 2376.4, "word": " تطلع", "probability": 0.85247802734375}, {"start": 2376.4, "end": 2376.56, "word": " ال", "probability": 0.93603515625}, {"start": 2376.56, "end": 2377.08, "word": " sequence", "probability": 0.8798828125}, {"start": 2377.08, "end": 2377.46, "word": " in", "probability": 0.69140625}, {"start": 2377.46, "end": 2379.72, "word": " صح؟", "probability": 0.85009765625}, {"start": 2379.72, "end": 2379.88, "word": " و", "probability": 0.56884765625}, {"start": 2379.88, "end": 2380.0, "word": " ال", "probability": 0.76708984375}, {"start": 2380.0, "end": 2380.42, "word": " sequence", "probability": 0.97900390625}, {"start": 2380.42, "end": 2380.92, "word": " هذه", "probability": 0.51416015625}, {"start": 2380.92, "end": 2382.58, "word": " properly", "probability": 0.888671875}, {"start": 2382.58, "end": 2383.42, "word": " divergent", "probability": 0.8203125}, {"start": 2383.42, "end": 2383.62, "word": " to", "probability": 0.931640625}, {"start": 2383.62, "end": 2385.36, "word": " infinity،", "probability": 0.538818359375}, {"start": 2385.36, "end": 2385.52, "word": " اذا", "probability": 0.604248046875}, {"start": 2385.52, "end": 2385.68, "word": " I'm", "probability": 0.683837890625}, {"start": 2385.68, "end": 2387.22, "word": " divergent،", "probability": 0.8802083333333334}, {"start": 2387.22, "end": 2387.88, "word": " اذا", "probability": 0.884521484375}, {"start": 2387.88, "end": 2388.06, "word": " I'm", "probability": 0.976318359375}, {"start": 2388.06, "end": 2388.36, "word": " not", "probability": 0.9658203125}, {"start": 2388.36, "end": 2389.76, "word": " Cauchy", "probability": 0.7501627604166666}, {"start": 2389.76, "end": 2394.22, "word": " تمام؟", "probability": 0.8515625}], "temperature": 1.0}, {"id": 87, "seek": 241905, "start": 2397.13, "end": 2419.05, "text": "Okay؟ وبالتالي إذا هاي في عندي .. هاي في عندي .. إذا if لا تحافظ على ال koshi sequences إذا if does not preserve .. preserve koshi", "tokens": [8297, 22807, 46599, 6027, 2655, 6027, 1829, 11933, 15730, 8032, 47302, 8978, 18871, 16254, 4386, 8032, 47302, 8978, 18871, 16254, 4386, 11933, 15730, 498, 20193, 6055, 5016, 31845, 19913, 15844, 2423, 350, 17392, 22978, 11933, 15730, 498, 775, 406, 15665, 4386, 15665, 350, 17392], "avg_logprob": -0.3019097275204129, "compression_ratio": 1.424, "no_speech_prob": 0.0, "words": [{"start": 2397.13, "end": 2398.09, "word": "Okay؟", "probability": 0.373291015625}, {"start": 2398.09, "end": 2398.43, "word": " وبالتالي", "probability": 0.844189453125}, {"start": 2398.43, "end": 2398.59, "word": " إذا", "probability": 0.5555419921875}, {"start": 2398.59, "end": 2398.85, "word": " هاي", "probability": 0.6365966796875}, {"start": 2398.85, "end": 2398.93, "word": " في", "probability": 0.880859375}, {"start": 2398.93, "end": 2399.35, "word": " عندي", "probability": 0.896240234375}, {"start": 2399.35, "end": 2399.89, "word": " ..", "probability": 0.55517578125}, {"start": 2399.89, "end": 2400.67, "word": " هاي", "probability": 0.76171875}, {"start": 2400.67, "end": 2400.79, "word": " في", "probability": 0.98583984375}, {"start": 2400.79, "end": 2401.27, "word": " عندي", "probability": 0.98828125}, {"start": 2401.27, "end": 2401.45, "word": " ..", "probability": 0.521484375}, {"start": 2401.45, "end": 2401.93, "word": " إذا", "probability": 0.937744140625}, {"start": 2401.93, "end": 2402.43, "word": " if", "probability": 0.72265625}, {"start": 2402.43, "end": 2403.23, "word": " لا", "probability": 0.41845703125}, {"start": 2403.23, "end": 2403.97, "word": " تحافظ", "probability": 0.992919921875}, {"start": 2403.97, "end": 2404.13, "word": " على", "probability": 0.8408203125}, {"start": 2404.13, "end": 2404.29, "word": " ال", "probability": 0.85986328125}, {"start": 2404.29, "end": 2404.53, "word": " koshi", "probability": 0.332733154296875}, {"start": 2404.53, "end": 2405.17, "word": " sequences", "probability": 0.89990234375}, {"start": 2405.17, "end": 2406.07, "word": " إذا", "probability": 0.81982421875}, {"start": 2406.07, "end": 2406.53, "word": " if", "probability": 0.92822265625}, {"start": 2406.53, "end": 2408.79, "word": " does", "probability": 0.90087890625}, {"start": 2408.79, "end": 2409.27, "word": " not", "probability": 0.97412109375}, {"start": 2409.27, "end": 2413.21, "word": " preserve", "probability": 0.9443359375}, {"start": 2413.21, "end": 2414.29, "word": " ..", "probability": 0.853515625}, {"start": 2414.29, "end": 2416.61, "word": " preserve", "probability": 0.93994140625}, {"start": 2416.61, "end": 2419.05, "word": " koshi", "probability": 0.860107421875}], "temperature": 1.0}, {"id": 88, "seek": 245141, "start": 2426.33, "end": 2451.41, "text": "sequences وبالتالي حسب النظرية الأخيرة مابتكونش uniformly continuous لأن لو كانت uniformly continuous فالمفروض تاخد كوشي sequence زي هذه تعطينا صورتها كوشي sequence وهذا مستحيل okay تمام واضح في أي سؤال اي استفسار اذا هيك نكتفي بهذا القدر من section خمسة اربعة وزي ما حكينا سابقا", "tokens": [11834, 2667, 46599, 6027, 2655, 6027, 1829, 11331, 35457, 28239, 19913, 2288, 10632, 16247, 9778, 48923, 3714, 16758, 2655, 30544, 8592, 48806, 10957, 5296, 33456, 45164, 25961, 2655, 48806, 10957, 6156, 45340, 5172, 32887, 11242, 6055, 47283, 3215, 9122, 2407, 8592, 1829, 8310, 30767, 1829, 29538, 37279, 9566, 1829, 8315, 20328, 13063, 2655, 11296, 9122, 2407, 8592, 1829, 8310, 37037, 15730, 3714, 14851, 5016, 26895, 1392, 46811, 10943, 4032, 46958, 5016, 8978, 36632, 8608, 33604, 6027, 1975, 1829, 44713, 36178, 9640, 1975, 15730, 39896, 4117, 8717, 4117, 2655, 41185, 39627, 15730, 25062, 3215, 2288, 9154, 3541, 16490, 2304, 3794, 3660, 1975, 25513, 27884, 4032, 11622, 1829, 19446, 11331, 4117, 1829, 8315, 8608, 16758, 4587, 995], "avg_logprob": -0.1654094817309544, "compression_ratio": 1.681992337164751, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2426.3299999999995, "end": 2427.1499999999996, "word": "sequences", "probability": 0.4925537109375}, {"start": 2427.1499999999996, "end": 2427.97, "word": " وبالتالي", "probability": 0.8931640625}, {"start": 2427.97, "end": 2428.27, "word": " حسب", "probability": 0.906494140625}, {"start": 2428.27, "end": 2428.91, "word": " النظرية", "probability": 0.9725341796875}, {"start": 2428.91, "end": 2429.69, "word": " الأخيرة", "probability": 0.9474283854166666}, {"start": 2429.69, "end": 2431.61, "word": " مابتكونش", "probability": 0.831396484375}, {"start": 2431.61, "end": 2432.27, "word": " uniformly", "probability": 0.9287109375}, {"start": 2432.27, "end": 2433.23, "word": " continuous", "probability": 0.84619140625}, {"start": 2433.23, "end": 2433.51, "word": " لأن", "probability": 0.78466796875}, {"start": 2433.51, "end": 2433.69, "word": " لو", "probability": 0.95849609375}, {"start": 2433.69, "end": 2434.09, "word": " كانت", "probability": 0.97900390625}, {"start": 2434.09, "end": 2434.63, "word": " uniformly", "probability": 0.94677734375}, {"start": 2434.63, "end": 2435.37, "word": " continuous", "probability": 0.90966796875}, {"start": 2435.37, "end": 2436.43, "word": " فالمفروض", "probability": 0.88017578125}, {"start": 2436.43, "end": 2436.83, "word": " تاخد", "probability": 0.9694010416666666}, {"start": 2436.83, "end": 2437.23, "word": " كوشي", "probability": 0.79345703125}, {"start": 2437.23, "end": 2437.65, "word": " sequence", "probability": 0.89697265625}, {"start": 2437.65, "end": 2437.97, "word": " زي", "probability": 0.96044921875}, {"start": 2437.97, "end": 2438.37, "word": " هذه", "probability": 0.8779296875}, {"start": 2438.37, "end": 2439.33, "word": " تعطينا", "probability": 0.818115234375}, {"start": 2439.33, "end": 2439.73, "word": " صورتها", "probability": 0.8692626953125}, {"start": 2439.73, "end": 2440.03, "word": " كوشي", "probability": 0.968994140625}, {"start": 2440.03, "end": 2440.39, "word": " sequence", "probability": 0.970703125}, {"start": 2440.39, "end": 2440.67, "word": " وهذا", "probability": 0.8525390625}, {"start": 2440.67, "end": 2441.27, "word": " مستحيل", "probability": 0.98486328125}, {"start": 2441.27, "end": 2442.21, "word": " okay", "probability": 0.5185546875}, {"start": 2442.21, "end": 2442.73, "word": " تمام", "probability": 0.9599609375}, {"start": 2442.73, "end": 2443.67, "word": " واضح", "probability": 0.96435546875}, {"start": 2443.67, "end": 2444.59, "word": " في", "probability": 0.5556640625}, {"start": 2444.59, "end": 2444.75, "word": " أي", "probability": 0.63623046875}, {"start": 2444.75, "end": 2445.09, "word": " سؤال", "probability": 0.9908854166666666}, {"start": 2445.09, "end": 2445.29, "word": " اي", "probability": 0.7254638671875}, {"start": 2445.29, "end": 2445.83, "word": " استفسار", "probability": 0.7311604817708334}, {"start": 2445.83, "end": 2446.79, "word": " اذا", "probability": 0.802490234375}, {"start": 2446.79, "end": 2447.23, "word": " هيك", 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