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ممكن", "probability": 0.987060546875}, {"start": 92.14, "end": 92.52, "word": " تاخد", "probability": 0.9840494791666666}, {"start": 92.52, "end": 92.86, "word": " مودب", "probability": 0.7964680989583334}, {"start": 92.86, "end": 93.04, "word": " أو", "probability": 0.935546875}, {"start": 93.04, "end": 93.5, "word": " سالب", "probability": 0.9755859375}, {"start": 93.5, "end": 94.18, "word": " ولكن", "probability": 0.888916015625}, {"start": 94.18, "end": 94.46, "word": " ال", "probability": 0.40869140625}, {"start": 94.46, "end": 94.68, "word": " set", "probability": 0.734375}, {"start": 94.68, "end": 94.86, "word": " to", "probability": 0.96044921875}, {"start": 94.86, "end": 95.02, "word": " be", "probability": 0.94921875}, {"start": 95.02, "end": 95.66, "word": " alternating", "probability": 0.978515625}, {"start": 95.66, "end": 96.04, "word": " الآن", "probability": 0.56707763671875}, {"start": 96.04, "end": 96.24, "word": " لما", "probability": 0.95263671875}, {"start": 96.24, "end": 96.58, "word": " بنقول", "probability": 0.74267578125}, {"start": 96.58, "end": 96.84, "word": " عنه", "probability": 0.749755859375}, {"start": 96.84, "end": 96.92, "word": " ال", "probability": 0.49951171875}, {"start": 96.92, "end": 97.5, "word": " alternating", "probability": 0.97900390625}, {"start": 97.5, "end": 98.5, "word": " بدنا", "probability": 0.8583984375}, {"start": 98.5, "end": 99.02, "word": " نيجي", "probability": 0.9794921875}, {"start": 99.02, "end": 99.48, "word": " أنه", "probability": 0.4971923828125}, {"start": 99.48, "end": 100.38, "word": " انقيدهم", "probability": 0.8201904296875}, {"start": 100.38, "end": 100.82, "word": " بمعنى", "probability": 0.97099609375}, {"start": 100.82, "end": 101.12, "word": " أخر", "probability": 0.83935546875}, {"start": 101.12, "end": 101.66, "word": " it", "probability": 0.82763671875}, {"start": 101.66, "end": 101.82, "word": " is", "probability": 0.88232421875}, {"start": 101.82, "end": 102.06, "word": " set", "probability": 0.466796875}, {"start": 102.06, "end": 102.18, "word": " to", "probability": 0.98095703125}, {"start": 102.18, "end": 102.34, "word": " be", "probability": 0.9423828125}, {"start": 102.34, "end": 102.96, "word": " alternating", "probability": 0.95458984375}, {"start": 102.96, "end": 103.36, "word": " if", "probability": 0.8076171875}, {"start": 103.36, "end": 103.54, "word": " the", "probability": 0.892578125}, {"start": 103.54, "end": 103.86, "word": " terms", "probability": 0.5830078125}], "temperature": 1.0}, {"id": 5, "seek": 12956, "start": 104.96, "end": 129.56, "text": "نقص واحد أسنان زائد واحد XN are all positive or all negative يعني يا كلنا دولة أيش مجبات يا كلنا أيش سالبات if the sequence X بيسوي XN اللي هي is alternating we say that the series summation اللي هي it generates is an alternating أيش ما لها series", "tokens": [1863, 4587, 9381, 36764, 24401, 5551, 3794, 1863, 7649, 30767, 16373, 3215, 36764, 24401, 1783, 45, 366, 439, 3353, 420, 439, 3671, 37495, 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"end": 107.78, "word": " are", "probability": 0.33251953125}, {"start": 107.78, "end": 108.28, "word": " all", "probability": 0.88330078125}, {"start": 108.28, "end": 109.0, "word": " positive", "probability": 0.8623046875}, {"start": 109.0, "end": 109.46, "word": " or", "probability": 0.82080078125}, {"start": 109.46, "end": 109.76, "word": " all", "probability": 0.84228515625}, {"start": 109.76, "end": 110.14, "word": " negative", "probability": 0.9267578125}, {"start": 110.14, "end": 110.48, "word": " يعني", "probability": 0.813232421875}, {"start": 110.48, "end": 110.64, "word": " يا", "probability": 0.468994140625}, {"start": 110.64, "end": 111.04, "word": " كلنا", "probability": 0.85693359375}, {"start": 111.04, "end": 111.42, "word": " دولة", "probability": 0.686279296875}, {"start": 111.42, "end": 111.68, "word": " أيش", "probability": 0.60577392578125}, {"start": 111.68, "end": 112.64, "word": " مجبات", "probability": 0.838623046875}, {"start": 112.64, "end": 112.8, "word": " يا", "probability": 0.6083984375}, {"start": 112.8, "end": 113.16, "word": " كلنا", "probability": 0.88134765625}, {"start": 113.16, "end": 113.62, "word": " أيش", "probability": 0.794921875}, {"start": 113.62, "end": 114.66, "word": " سالبات", "probability": 0.96435546875}, {"start": 114.66, "end": 115.4, "word": " if", "probability": 0.66357421875}, {"start": 115.4, "end": 115.6, "word": " the", "probability": 0.87109375}, {"start": 115.6, "end": 116.02, "word": " sequence", "probability": 0.97412109375}, {"start": 116.02, "end": 116.24, "word": " X", "probability": 0.92431640625}, {"start": 116.24, "end": 116.6, "word": " بيسوي", "probability": 0.707275390625}, {"start": 116.6, "end": 117.28, "word": " XN", "probability": 0.884521484375}, {"start": 117.28, "end": 118.2, "word": " اللي", "probability": 0.88427734375}, {"start": 118.2, "end": 118.64, "word": " هي", "probability": 0.89990234375}, {"start": 118.64, "end": 119.2, "word": " is", "probability": 0.80078125}, {"start": 119.2, "end": 120.06, "word": " alternating", "probability": 0.9638671875}, {"start": 120.06, "end": 120.46, "word": " we", "probability": 0.59033203125}, {"start": 120.46, "end": 120.74, "word": " say", "probability": 0.931640625}, {"start": 120.74, "end": 121.36, "word": " that", "probability": 0.8603515625}, {"start": 121.36, "end": 122.14, "word": " the", "probability": 0.67236328125}, {"start": 122.14, "end": 122.58, "word": " series", "probability": 0.9072265625}, {"start": 122.58, "end": 123.44, "word": " summation", "probability": 0.744140625}, {"start": 123.44, "end": 124.4, "word": " اللي", "probability": 0.82275390625}, {"start": 124.4, "end": 124.68, "word": " هي", "probability": 0.9150390625}, {"start": 124.68, "end": 125.06, "word": " it", "probability": 0.81591796875}, {"start": 125.06, "end": 125.82, "word": " generates", "probability": 0.8935546875}, {"start": 125.82, "end": 126.16, "word": " is", "probability": 0.86474609375}, {"start": 126.16, "end": 126.44, "word": " an", "probability": 0.7490234375}, {"start": 126.44, "end": 127.52, "word": " alternating", "probability": 0.958984375}, {"start": 127.52, "end": 128.24, "word": " أيش", "probability": 0.802978515625}, {"start": 128.24, "end": 128.86, "word": " ما", "probability": 0.869140625}, {"start": 128.86, "end": 129.18, "word": " لها", "probability": 0.821044921875}, {"start": 129.18, "end": 129.56, "word": " series", "probability": 0.90087890625}], "temperature": 1.0}, {"id": 6, "seek": 15791, "start": 129.82, "end": 157.92, "text": "مدام هذه كلها positive أو كلها negative صارت على بعض و هذه تنساش أنه مرة بتاخد positive و مرة بتاخد negative إذا ال series ال Xn أو ال Xn الأصلي هذه هتكون مرة بتاخد موجب و مرة بتاخد سالب أو مرة بتاخد سالب و مرة بتاخد موجب فعشان هيك بدل ما نكتبها زيك و نقول هذه دايما كلها موجبة بنيجي بنكتبها بصورة ثانية بنقول خلينا نكتب ال series Xn تساوي ناقص واحد زائد واحد في مين في Zn", "tokens": [2304, 3215, 10943, 29538, 28242, 11296, 3353, 34051, 28242, 11296, 3671, 20328, 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1176, 77], "avg_logprob": -0.13272165437770445, "compression_ratio": 2.1808510638297873, "no_speech_prob": 8.940696716308594e-07, "words": [{"start": 129.82, "end": 130.28, "word": "مدام", "probability": 0.7314453125}, {"start": 130.28, "end": 130.5, "word": " هذه", "probability": 0.70751953125}, {"start": 130.5, "end": 130.82, "word": " كلها", "probability": 0.946044921875}, {"start": 130.82, "end": 131.22, "word": " positive", "probability": 0.7646484375}, {"start": 131.22, "end": 131.4, "word": " أو", "probability": 0.814453125}, {"start": 131.4, "end": 131.68, "word": " كلها", "probability": 0.92724609375}, {"start": 131.68, "end": 132.02, "word": " negative", "probability": 0.94384765625}, {"start": 132.02, "end": 132.4, "word": " صارت", "probability": 0.9635416666666666}, {"start": 132.4, "end": 132.58, "word": " على", "probability": 0.82373046875}, {"start": 132.58, "end": 133.02, "word": " بعض", "probability": 0.995361328125}, {"start": 133.02, "end": 133.36, "word": " و", "probability": 0.485107421875}, {"start": 133.36, "end": 133.6, "word": " هذه", "probability": 0.50048828125}, {"start": 133.6, "end": 134.08, "word": " تنساش", "probability": 0.9271240234375}, {"start": 134.08, "end": 134.3, "word": " أنه", "probability": 0.6168212890625}, {"start": 134.3, "end": 134.42, "word": " مرة", "probability": 0.963134765625}, {"start": 134.42, "end": 134.76, "word": " بتاخد", "probability": 0.9345703125}, {"start": 134.76, "end": 135.1, "word": " positive", "probability": 0.92724609375}, {"start": 135.1, "end": 135.26, "word": " و", "probability": 0.97802734375}, {"start": 135.26, "end": 135.36, "word": " مرة", "probability": 0.932373046875}, {"start": 135.36, "end": 135.74, "word": " بتاخد", "probability": 0.9554036458333334}, {"start": 135.74, "end": 136.2, "word": " negative", "probability": 0.97265625}, {"start": 136.2, "end": 136.76, "word": " إذا", "probability": 0.72119140625}, {"start": 136.76, "end": 136.94, "word": " ال", "probability": 0.87255859375}, {"start": 136.94, "end": 137.28, "word": " series", "probability": 0.79638671875}, {"start": 137.28, "end": 137.52, "word": " ال", "probability": 0.54541015625}, {"start": 137.52, "end": 137.94, "word": " Xn", "probability": 0.5247802734375}, {"start": 137.94, "end": 138.2, "word": " أو", "probability": 0.80419921875}, {"start": 138.2, "end": 138.52, "word": " ال", "probability": 0.89990234375}, {"start": 138.52, "end": 138.84, "word": " Xn", "probability": 0.792236328125}, {"start": 138.84, "end": 139.3, "word": " الأصلي", "probability": 0.7740885416666666}, {"start": 139.3, "end": 139.68, "word": " هذه", "probability": 0.693359375}, {"start": 139.68, "end": 140.54, "word": " هتكون", "probability": 0.8709309895833334}, {"start": 140.54, "end": 140.8, "word": " مرة", "probability": 0.991943359375}, {"start": 140.8, "end": 141.18, "word": " بتاخد", "probability": 0.97265625}, {"start": 141.18, "end": 141.52, "word": " موجب", "probability": 0.9716796875}, {"start": 141.52, "end": 141.66, "word": " و", "probability": 0.99072265625}, {"start": 141.66, "end": 141.76, "word": " مرة", "probability": 0.943115234375}, {"start": 141.76, "end": 142.08, "word": " بتاخد", "probability": 0.9402669270833334}, {"start": 142.08, "end": 142.38, "word": " سالب", "probability": 0.9440104166666666}, {"start": 142.38, "end": 142.52, "word": " أو", "probability": 0.8427734375}, {"start": 142.52, "end": 142.72, "word": " مرة", "probability": 0.9892578125}, {"start": 142.72, "end": 143.06, "word": " بتاخد", "probability": 0.96240234375}, {"start": 143.06, "end": 143.42, "word": " سالب", "probability": 0.98779296875}, {"start": 143.42, "end": 143.52, "word": " و", "probability": 0.99267578125}, {"start": 143.52, "end": 143.7, "word": " مرة", "probability": 0.9619140625}, {"start": 143.7, "end": 144.28, "word": " بتاخد", "probability": 0.9674479166666666}, {"start": 144.28, "end": 144.72, "word": " موجب", "probability": 0.9939778645833334}, {"start": 144.72, "end": 145.66, "word": " فعشان", "probability": 0.953125}, {"start": 145.66, "end": 145.82, "word": " هيك", "probability": 0.901611328125}, {"start": 145.82, "end": 146.1, "word": " بدل", "probability": 0.98193359375}, {"start": 146.1, "end": 146.2, "word": " ما", "probability": 0.9130859375}, {"start": 146.2, "end": 146.66, "word": " نكتبها", "probability": 0.9947265625}, {"start": 146.66, "end": 147.0, "word": " زيك", "probability": 0.8782552083333334}, {"start": 147.0, "end": 147.08, "word": " و", "probability": 0.7470703125}, {"start": 147.08, "end": 147.26, "word": " نقول", "probability": 0.972900390625}, {"start": 147.26, "end": 147.52, "word": " هذه", "probability": 0.720703125}, {"start": 147.52, "end": 147.82, "word": " دايما", "probability": 0.8746744791666666}, {"start": 147.82, "end": 148.2, "word": " كلها", "probability": 0.986083984375}, {"start": 148.2, "end": 148.7, "word": " موجبة", "probability": 0.9134114583333334}, {"start": 148.7, "end": 149.66, "word": " بنيجي", "probability": 0.900146484375}, {"start": 149.66, "end": 150.22, "word": " بنكتبها", "probability": 0.91552734375}, {"start": 150.22, "end": 150.72, "word": " بصورة", "probability": 0.9910888671875}, {"start": 150.72, "end": 151.06, "word": " ثانية", "probability": 0.9295247395833334}, {"start": 151.06, "end": 151.4, "word": " بنقول", "probability": 0.871826171875}, {"start": 151.4, "end": 151.92, "word": " خلينا", "probability": 0.7327880859375}, {"start": 151.92, "end": 152.3, "word": " نكتب", "probability": 0.9981689453125}, {"start": 152.3, "end": 152.44, "word": " ال", "probability": 0.9560546875}, {"start": 152.44, "end": 152.86, "word": " series", "probability": 0.94677734375}, {"start": 152.86, "end": 153.9, "word": " Xn", "probability": 0.910888671875}, {"start": 153.9, "end": 154.54, "word": " تساوي", "probability": 0.80780029296875}, {"start": 154.54, "end": 154.92, "word": " ناقص", "probability": 0.762603759765625}, {"start": 154.92, "end": 155.16, "word": " واحد", "probability": 0.87353515625}, {"start": 155.16, "end": 155.68, "word": " زائد", "probability": 0.5301106770833334}, {"start": 155.68, "end": 156.0, "word": " واحد", "probability": 0.96630859375}, {"start": 156.0, "end": 156.14, "word": " في", "probability": 0.9541015625}, {"start": 156.14, "end": 156.52, "word": " مين", "probability": 0.878173828125}, {"start": 156.52, "end": 157.12, "word": " في", "probability": 0.888671875}, {"start": 157.12, "end": 157.92, "word": " Zn", "probability": 0.770751953125}], "temperature": 1.0}, {"id": 7, "seek": 18408, "start": 158.52, "end": 184.08, "text": "و بتصير الان Zn هي اللي دايما positive و هذه هي اللي بتحدد الإشارة عشان هيك اللي لما نحكي عن ال alternating series هنصير نكتبها على الصورة هذه ناقص واحد أس أن زائد واحد أو ناقص واحد أس أن في Zn و Zn دايما تكون موجبة و الناقص واحد أس أن زائد واحد أو ناقص واحد أس أن هتتحدد لي هي", "tokens": [2407, 39894, 9381, 13546, 2423, 7649, 1176, 77, 39896, 13672, 1829, 11778, 47302, 15042, 3353, 4032, 29538, 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{"start": 175.22, "end": 175.7, "word": " في", "probability": 0.82568359375}, {"start": 175.7, "end": 176.16, "word": " Zn", "probability": 0.925537109375}, {"start": 176.16, "end": 176.3, "word": " و", "probability": 0.8955078125}, {"start": 176.3, "end": 176.78, "word": " Zn", "probability": 0.921875}, {"start": 176.78, "end": 177.36, "word": " دايما", "probability": 0.9484049479166666}, {"start": 177.36, "end": 178.14, "word": " تكون", "probability": 0.90185546875}, {"start": 178.14, "end": 178.78, "word": " موجبة", "probability": 0.9900716145833334}, {"start": 178.78, "end": 179.38, "word": " و", "probability": 0.92041015625}, {"start": 179.38, "end": 179.88, "word": " الناقص", "probability": 0.81060791015625}, {"start": 179.88, "end": 180.18, "word": " واحد", "probability": 0.989990234375}, {"start": 180.18, "end": 180.36, "word": " أس", "probability": 0.9736328125}, {"start": 180.36, "end": 180.48, "word": " أن", "probability": 0.93115234375}, {"start": 180.48, "end": 180.8, "word": " زائد", "probability": 0.97265625}, {"start": 180.8, "end": 181.16, "word": " واحد", "probability": 0.990478515625}, {"start": 181.16, "end": 181.32, "word": " أو", "probability": 0.84716796875}, {"start": 181.32, "end": 181.7, "word": " ناقص", "probability": 0.9947509765625}, {"start": 181.7, "end": 182.04, "word": " واحد", "probability": 0.994384765625}, {"start": 182.04, "end": 182.24, "word": " أس", "probability": 0.970947265625}, {"start": 182.24, "end": 182.4, "word": " أن", "probability": 0.89794921875}, {"start": 182.4, "end": 183.52, "word": " هتتحدد", "probability": 0.84951171875}, {"start": 183.52, "end": 183.7, "word": " لي", "probability": 0.65283203125}, {"start": 183.7, "end": 184.08, "word": " هي", "probability": 0.7119140625}], "temperature": 1.0}, {"id": 8, "seek": 20355, "start": 184.53, "end": 203.55, "text": "اللي هو إنها مرة موجبة و مرة سالبة هل هتحدد اللي هو في الأول موجب وبعدين سالب حسب اللي هو الأسئن زائد واحد أو الهاشئن الان نيجي اللي هو بدنا نفحص ال series اللي منها النوع هل هذه ال series", "tokens": [6027, 20292, 31439, 36145, 11296, 3714, 25720, 3714, 29245, 49401, 4032, 3714, 25720, 8608, 6027, 49401, 8032, 1211, 8032, 2655, 24401, 3215, 13672, 1829, 31439, 8978, 16247, 12610, 3714, 29245, 3555, 46599, 22488, 9957, 8608, 6027, 3555, 11331, 35457, 13672, 1829, 31439, 16247, 3794, 19986, 1863, 30767, 16373, 3215, 36764, 24401, 34051, 2423, 3224, 33599, 19986, 1863, 2423, 7649, 8717, 1829, 7435, 1829, 13672, 1829, 31439, 47525, 8315, 8717, 5172, 5016, 9381, 2423, 2638, 13672, 1829, 9154, 11296, 28239, 45367, 8032, 1211, 29538, 2423, 2638], "avg_logprob": -0.1687863391152648, "compression_ratio": 1.8895348837209303, "no_speech_prob": 3.2186508178710938e-06, "words": [{"start": 184.53, "end": 185.01, "word": "اللي", "probability": 0.5989990234375}, {"start": 185.01, "end": 185.41, "word": " هو", "probability": 0.857421875}, {"start": 185.41, "end": 185.91, "word": " إنها", "probability": 0.81005859375}, {"start": 185.91, "end": 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"probability": 0.8250325520833334}, {"start": 191.97, "end": 192.39, "word": " سالب", "probability": 0.9866536458333334}, {"start": 192.39, "end": 192.77, "word": " حسب", "probability": 0.85888671875}, {"start": 192.77, "end": 192.97, "word": " اللي", "probability": 0.984619140625}, {"start": 192.97, "end": 193.15, "word": " هو", "probability": 0.99072265625}, {"start": 193.15, "end": 193.73, "word": " الأسئن", "probability": 0.69775390625}, {"start": 193.73, "end": 194.05, "word": " زائد", "probability": 0.91162109375}, {"start": 194.05, "end": 194.53, "word": " واحد", "probability": 0.984130859375}, {"start": 194.53, "end": 194.91, "word": " أو", "probability": 0.814453125}, {"start": 194.91, "end": 196.01, "word": " الهاشئن", "probability": 0.539990234375}, {"start": 196.01, "end": 196.93, "word": " الان", "probability": 0.6976318359375}, {"start": 196.93, "end": 198.01, "word": " نيجي", "probability": 0.83837890625}, {"start": 198.01, "end": 198.33, "word": " اللي", "probability": 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1.0}, {"id": 9, "seek": 22865, "start": 203.73, "end": 228.65, "text": "اللي هي converge ولا diverge وهذا اللي هو الشيء الجديد عن اللي هو ال section السادق الآن اللي بنقوله alternating series test let Z بتساوي ZN be a decreasing sequence of strictly positive numbers with limit ZN بساوي سفر إذا في عندي شروط الآن لل series اللي أنا بده أفحصها", "tokens": [6027, 20292, 39896, 41881, 49429, 18558, 432, 37037, 15730, 13672, 1829, 31439, 25124, 1829, 38207, 25724, 16254, 3215, 18871, 13672, 1829, 31439, 2423, 3541, 21136, 18513, 4587, 6024, 48506, 13672, 1829, 44945, 39648, 3224, 40062, 2638, 1500, 718, 1176, 4724, 2655, 3794, 995, 45865, 1176, 45, 312, 257, 23223, 8310, 295, 20792, 3353, 3547, 365, 4948, 1176, 45, 4724, 3794, 995, 45865, 8608, 5172, 2288, 11933, 15730, 8978, 18871, 16254, 13412, 32887, 9566, 6024, 48506, 24976, 2638, 13672, 1829, 41850, 47525, 3224, 5551, 5172, 5016, 9381, 11296], "avg_logprob": -0.3213778432797302, "compression_ratio": 1.5857740585774058, "no_speech_prob": 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{"start": 215.27, "end": 215.83, "word": " بتساوي", "probability": 0.673126220703125}, {"start": 215.83, "end": 216.39, "word": " ZN", "probability": 0.6826171875}, {"start": 216.39, "end": 217.01, "word": " be", "probability": 0.357421875}, {"start": 217.01, "end": 217.33, "word": " a", "probability": 0.96484375}, {"start": 217.33, "end": 217.87, "word": " decreasing", "probability": 0.94921875}, {"start": 217.87, "end": 218.61, "word": " sequence", "probability": 0.98095703125}, {"start": 218.61, "end": 218.89, "word": " of", "probability": 0.96435546875}, {"start": 218.89, "end": 219.51, "word": " strictly", "probability": 0.94287109375}, {"start": 219.51, "end": 220.09, "word": " positive", "probability": 0.94970703125}, {"start": 220.09, "end": 220.81, "word": " numbers", "probability": 0.88623046875}, {"start": 220.81, "end": 221.49, "word": " with", "probability": 0.35791015625}, {"start": 221.49, "end": 222.47, "word": " limit", "probability": 0.884765625}, {"start": 222.47, "end": 223.05, "word": " ZN", "probability": 0.945068359375}, {"start": 223.05, "end": 223.87, "word": " بساوي", "probability": 0.59539794921875}, {"start": 223.87, "end": 224.41, "word": " سفر", "probability": 0.79296875}, {"start": 224.41, "end": 225.01, "word": " إذا", "probability": 0.5986328125}, {"start": 225.01, "end": 225.23, "word": " في", "probability": 0.350830078125}, {"start": 225.23, "end": 225.59, "word": " عندي", "probability": 0.6982421875}, {"start": 225.59, "end": 226.05, "word": " شروط", "probability": 0.9671223958333334}, {"start": 226.05, "end": 226.43, "word": " الآن", "probability": 0.6251220703125}, {"start": 226.43, "end": 226.73, "word": " لل", "probability": 0.7626953125}, {"start": 226.73, "end": 227.15, "word": " series", "probability": 0.87939453125}, {"start": 227.15, "end": 227.51, "word": " اللي", "probability": 0.982421875}, {"start": 227.51, "end": 227.71, "word": " أنا", "probability": 0.5771484375}, {"start": 227.71, "end": 228.03, "word": " بده", "probability": 0.4532470703125}, {"start": 228.03, "end": 228.65, "word": " أفحصها", "probability": 0.9095703125}], "temperature": 1.0}, {"id": 10, "seek": 25500, "start": 229.04, "end": 255.0, "text": "أول حاجة بدي أكون عندي Zn عبارة عن decreasing sequence وكل واحدة of strictly positive numbers وكل واحدة إيه شمالها عبارة عن positive number يعني أكبر من 0 strictly و اللي هو لكل N فصار عندى اللي هو شرطين إنها تكون decreasing و limit و الـ Zn أكبر من 0 strictly لكل N و الشرط الثالث", "tokens": [10721, 12610, 11331, 26108, 3660, 4724, 16254, 5551, 30544, 43242, 1829, 1176, 77, 6225, 3555, 9640, 3660, 18871, 23223, 8310, 4032, 28820, 36764, 24401, 3660, 295, 20792, 3353, 3547, 4032, 28820, 36764, 24401, 3660, 11933, 1829, 3224, 13412, 2304, 6027, 11296, 6225, 3555, 9640, 3660, 18871, 3353, 1230, 37495, 22653, 5551, 4117, 26890, 9154, 1958, 20792, 4032, 13672, 1829, 31439, 5296, 28820, 426, 6156, 9381, 9640, 43242, 7578, 13672, 1829, 31439, 13412, 2288, 9566, 9957, 36145, 11296, 6055, 30544, 23223, 4032, 4948, 4032, 2423, 39184, 1176, 77, 5551, 4117, 26890, 9154, 1958, 20792, 5296, 28820, 426, 4032, 25124, 2288, 9566, 6024, 104, 6027, 12984], "avg_logprob": -0.16160713945116315, "compression_ratio": 1.84304932735426, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 229.04, "end": 229.42, "word": "أول", "probability": 0.95166015625}, {"start": 229.42, "end": 229.78, "word": " حاجة", "probability": 0.9842122395833334}, {"start": 229.78, "end": 230.02, "word": " بدي", "probability": 0.44384765625}, {"start": 230.02, "end": 230.32, "word": " أكون", "probability": 0.6129150390625}, {"start": 230.32, "end": 230.74, "word": " عندي", "probability": 0.631591796875}, {"start": 230.74, "end": 231.34, "word": " Zn", "probability": 0.510498046875}, {"start": 231.34, "end": 231.8, "word": " عبارة", "probability": 0.9921875}, {"start": 231.8, "end": 232.0, "word": " عن", "probability": 0.99365234375}, {"start": 232.0, "end": 232.56, "word": " decreasing", 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244.36, "end": 244.62, "word": " N", "probability": 0.390625}, {"start": 244.62, "end": 245.24, "word": " فصار", "probability": 0.9451497395833334}, {"start": 245.24, "end": 245.74, "word": " عندى", "probability": 0.580810546875}, {"start": 245.74, "end": 246.0, "word": " اللي", "probability": 0.91064453125}, {"start": 246.0, "end": 246.32, "word": " هو", "probability": 0.97412109375}, {"start": 246.32, "end": 247.4, "word": " شرطين", "probability": 0.9742431640625}, {"start": 247.4, "end": 247.66, "word": " إنها", "probability": 0.798828125}, {"start": 247.66, "end": 248.0, "word": " تكون", "probability": 0.99267578125}, {"start": 248.0, "end": 248.66, "word": " decreasing", "probability": 0.9541015625}, {"start": 248.66, "end": 249.44, "word": " و", "probability": 0.90771484375}, {"start": 249.44, "end": 249.92, "word": " limit", "probability": 0.8623046875}, {"start": 249.92, "end": 250.52, "word": " و", "probability": 0.7275390625}, {"start": 250.52, "end": 251.1, "word": " الـ", 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alternating series تحقق ثلاث شروط ZN decreasing sequence strictly positive numbers الـ ZN و limit الـ ZN بساوي سفر اللي أنا بقول لذن الان النتيجة ال alternating series الصممش ناقص واحد وزن زاد واحد ZN إشمالها is convergent", "tokens": [6027, 20292, 31439, 4948, 2423, 39184, 1176, 45, 7251, 3794, 995, 45865, 8608, 5172, 2288, 11933, 15730, 20328, 9640, 2655, 2423, 39184, 8310, 13672, 1829, 47525, 3224, 5551, 4117, 2407, 11703, 1863, 9154, 11296, 2423, 40062, 2638, 6055, 5016, 4587, 4587, 38637, 1211, 5718, 104, 13412, 32887, 9566, 1176, 45, 23223, 8310, 20792, 3353, 3547, 2423, 39184, 1176, 45, 4032, 4948, 2423, 39184, 1176, 45, 4724, 3794, 995, 45865, 8608, 5172, 2288, 13672, 1829, 41850, 4724, 39648, 5296, 8848, 1863, 2423, 7649, 28239, 31371, 7435, 3660, 2423, 40062, 2638, 31767, 2304, 2304, 8592, 8717, 995, 4587, 9381, 36764, 24401, 4032, 11622, 1863, 30767, 18513, 36764, 24401, 1176, 45, 11933, 8592, 2304, 6027, 11296, 307, 9652, 6930], "avg_logprob": -0.3231837484571669, 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"probability": 0.890625}, {"start": 272.47, "end": 272.55, "word": " أنا", "probability": 0.64697265625}, {"start": 272.55, "end": 272.85, "word": " بقول", "probability": 0.984375}, {"start": 272.85, "end": 273.29, "word": " لذن", "probability": 0.5343424479166666}, {"start": 273.29, "end": 274.03, "word": " الان", "probability": 0.38482666015625}, {"start": 274.03, "end": 274.61, "word": " النتيجة", "probability": 0.945068359375}, {"start": 274.61, "end": 275.11, "word": " ال", "probability": 0.58447265625}, {"start": 275.11, "end": 275.81, "word": " alternating", "probability": 0.7724609375}, {"start": 275.81, "end": 276.77, "word": " series", "probability": 0.88623046875}, {"start": 276.77, "end": 277.65, "word": " الصممش", "probability": 0.67230224609375}, {"start": 277.65, "end": 278.23, "word": " ناقص", "probability": 0.78515625}, {"start": 278.23, "end": 278.55, "word": " واحد", "probability": 0.71923828125}, {"start": 278.55, "end": 278.79, "word": " وزن", "probability": 0.3234049479166667}, {"start": 278.79, "end": 279.09, "word": " زاد", "probability": 0.6937255859375}, {"start": 279.09, "end": 279.33, "word": " واحد", "probability": 0.97802734375}, {"start": 279.33, "end": 279.73, "word": " ZN", "probability": 0.751220703125}, {"start": 279.73, "end": 280.59, "word": " إشمالها", "probability": 0.70556640625}, {"start": 280.59, "end": 281.49, "word": " is", "probability": 0.853515625}, {"start": 281.49, "end": 283.23, "word": " convergent", "probability": 0.965576171875}], "temperature": 1.0}, {"id": 12, "seek": 31313, "start": 283.45, "end": 313.13, "text": "إيش مالها؟ هتكون Convergent وانت مغمض يعني لو جينا على اللي هو ال series اللي فوق عندي اللي هي اللي تعرضناها في الأول اللي هي ال 1 على n اللي هو نص اللي هو أكبر من تلت أكبر من ربع أكبر يعني decreasing و limitها بساوة سفر وهي alternating وكل واحد ما هو positive ده هذه ال series إيش مالها؟ Converges حسب نظرية", "tokens": [28814, 1829, 8592, 3714, 6027, 11296, 22807, 8032, 2655, 30544, 2656, 331, 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مالها؟", "probability": 0.7215576171875}, {"start": 284.17, "end": 284.63, "word": " هتكون", "probability": 0.921875}, {"start": 284.63, "end": 285.57, "word": " Convergent", "probability": 0.7646484375}, {"start": 285.57, "end": 285.93, "word": " وانت", "probability": 0.8570963541666666}, {"start": 285.93, "end": 286.49, "word": " مغمض", "probability": 0.9608154296875}, {"start": 286.49, "end": 287.17, "word": " يعني", "probability": 0.857177734375}, {"start": 287.17, "end": 287.35, "word": " لو", "probability": 0.931640625}, {"start": 287.35, "end": 287.79, "word": " جينا", "probability": 0.9684244791666666}, {"start": 287.79, "end": 288.13, "word": " على", "probability": 0.88623046875}, {"start": 288.13, "end": 288.41, "word": " اللي", "probability": 0.933837890625}, {"start": 288.41, "end": 288.75, "word": " هو", "probability": 0.99072265625}, {"start": 288.75, "end": 289.05, "word": " ال", "probability": 0.947265625}, {"start": 289.05, "end": 289.39, "word": " series", 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"word": " من", "probability": 0.9951171875}, {"start": 300.49, "end": 300.73, "word": " ربع", "probability": 0.8474934895833334}, {"start": 300.73, "end": 300.97, "word": " أكبر", "probability": 0.9290364583333334}, {"start": 300.97, "end": 301.21, "word": " يعني", "probability": 0.82666015625}, {"start": 301.21, "end": 301.75, "word": " decreasing", "probability": 0.74755859375}, {"start": 301.75, "end": 301.99, "word": " و", "probability": 0.6708984375}, {"start": 301.99, "end": 302.35, "word": " limitها", "probability": 0.651123046875}, {"start": 302.35, "end": 302.77, "word": " بساوة", "probability": 0.7845703125}, {"start": 302.77, "end": 303.21, "word": " سفر", "probability": 0.771728515625}, {"start": 303.21, "end": 304.05, "word": " وهي", "probability": 0.851318359375}, {"start": 304.05, "end": 305.01, "word": " alternating", "probability": 0.475830078125}, {"start": 305.01, "end": 306.09, "word": " وكل", "probability": 0.8994140625}, {"start": 306.09, "end": 306.33, "word": " 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"probability": 0.8173828125}], "temperature": 1.0}, {"id": 13, "seek": 33941, "start": 313.43, "end": 339.41, "text": "طبعا it's not absolutely convergent لأن لو في absolute convergence بترجعلنا للواحد على n series ماشي الحال الآن عندي نشوف اللي عندنا اللي هو برهان النظرية let z بالساوية zn be decreasing of strictly positive numbers with limit zn بساوية 0 then the series summation نقص واحد zn is convergent خلينا نشوف يا جماعة", "tokens": [9566, 3555, 3615, 995, 309, 311, 406, 3122, 9652, 6930, 5296, 33456, 45164, 8978, 8236, 32181, 39894, 47341, 3615, 1211, 8315, 24976, 14407, 24401, 15844, 297, 2638, 3714, 33599, 1829, 21542, 6027, 6024, 48506, 18871, 16254, 8717, 8592, 38688, 13672, 1829, 43242, 8315, 13672, 1829, 31439, 4724, 2288, 3224, 7649, 28239, 19913, 2288, 10632, 718, 710, 20666, 3794, 995, 2407, 10632, 710, 77, 312, 23223, 295, 20792, 3353, 3547, 365, 4948, 710, 77, 4724, 3794, 995, 2407, 10632, 1958, 550, 264, 2638, 28811, 8717, 4587, 9381, 36764, 24401, 710, 77, 307, 9652, 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عبارة عن Z واحد", "tokens": [6027, 7578, 19446, 20193, 8717, 11296, 10632, 38874, 23758, 13672, 7578, 47525, 8315, 8717, 12984, 3555, 47395, 3714, 33599, 1829, 21542, 6027, 16490, 1211, 11703, 9957, 7578, 8717, 8592, 38688, 1975, 1829, 8592, 13672, 7578, 43242, 7578, 28811, 23758, 2423, 7649, 9154, 36764, 24401, 2423, 7578, 19446, 20193, 8717, 11296, 10632, 38874, 8717, 8592, 38688, 1975, 5016, 35457, 42963, 12610, 1975, 1829, 8592, 1975, 1829, 3224, 13672, 7578, 31439, 2423, 14641, 2408, 318, 1975, 2655, 1863, 9957, 16472, 318, 1975, 2655, 1863, 9957, 16472, 1975, 1829, 8592, 39896, 3794, 995, 45865, 6225, 3555, 9640, 3660, 18871, 1176, 36764, 24401], "avg_logprob": -0.25171876072883603, "compression_ratio": 1.855721393034826, "no_speech_prob": 6.437301635742188e-05, "words": [{"start": 359.99, "end": 360.39, "word": "الى", "probability": 0.5899658203125}, {"start": 360.39, "end": 360.51, "word": " ما", "probability": 0.42529296875}, {"start": 360.51, "end": 360.67, "word": " لا", 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"probability": 0.96484375}, {"start": 443.38, "end": 443.76, "word": " partial", "probability": 0.84228515625}, {"start": 443.76, "end": 444.34, "word": " sums", "probability": 0.93212890625}, {"start": 444.34, "end": 446.24, "word": " ليش؟", "probability": 0.8268229166666666}], "temperature": 1.0}, {"id": 19, "seek": 45485, "start": 446.31, "end": 454.85, "text": "الأن it follows that the subsequence S2 of partial sums is increasing ليش increasing؟ خلّينا نشوف عندي لاحظ الآن", "tokens": [6027, 33456, 309, 10002, 300, 264, 13924, 655, 318, 17, 295, 14641, 34499, 307, 5662, 32239, 8592, 5662, 22807, 16490, 1211, 11703, 1829, 8315, 8717, 8592, 38688, 18871, 16254, 20193, 5016, 19913, 6024, 48506], "avg_logprob": -0.35111606972558157, "compression_ratio": 1.083969465648855, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 446.31, "end": 446.75, "word": "الأن", "probability": 0.5672607421875}, {"start": 446.75, "end": 446.89, "word": " it", "probability": 0.1513671875}, {"start": 446.89, "end": 447.17, "word": " follows", "probability": 0.8740234375}, {"start": 447.17, "end": 447.41, "word": " that", "probability": 0.8818359375}, {"start": 447.41, "end": 447.61, "word": " the", "probability": 0.55615234375}, {"start": 447.61, "end": 448.21, "word": " subsequence", "probability": 0.974365234375}, {"start": 448.21, "end": 448.65, "word": " S2", "probability": 0.5509033203125}, {"start": 448.65, "end": 448.81, "word": " of", "probability": 0.7685546875}, {"start": 448.81, "end": 449.09, "word": " partial", "probability": 0.935546875}, {"start": 449.09, "end": 449.45, "word": " sums", "probability": 0.955078125}, {"start": 449.45, "end": 449.73, "word": " is", "probability": 0.94140625}, {"start": 449.73, "end": 450.51, "word": " increasing", "probability": 0.95703125}, {"start": 450.51, "end": 451.35, "word": " ليش", "probability": 0.6790771484375}, {"start": 451.35, "end": 452.15, "word": " increasing؟", "probability": 0.7156982421875}, {"start": 452.15, "end": 452.51, "word": " خلّينا", "probability": 0.788916015625}, {"start": 452.51, "end": 453.07, "word": " نشوف", "probability": 0.9970703125}, {"start": 453.07, "end": 453.97, "word": " عندي", "probability": 0.625}, {"start": 453.97, "end": 454.51, "word": " لاحظ", "probability": 0.8445638020833334}, {"start": 454.51, "end": 454.85, "word": " الآن", "probability": 0.688232421875}], "temperature": 1.0}, {"id": 20, "seek": 48199, "start": 456.15, "end": 481.99, "text": "الأن لو أخدت S2 وS4 وS6 هتلاقي كل مرة إيش مالك بتضيف term هذا ال term اللي بنضاف اللي هو positive إذا حيكون الـS2 as a sequence of partial sums إيش مالها عبارة عن اللي هو increasing sequence ليش؟ خد بشكل أوضح من اللي حكيته فوق خد S2 خد Z1 ناقص Z2 ناقص Z3", "tokens": [6027, 33456, 45164, 5551, 9778, 3215, 2655, 318, 17, 4032, 50, 19, 4032, 50, 21, 8032, 2655, 15040, 38436, 28242, 3714, 25720, 11933, 1829, 8592, 19446, 23275, 39894, 11242, 33911, 1433, 23758, 2423, 1433, 13672, 1829, 44945, 11242, 31845, 13672, 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"word": " هتكون", "probability": 0.9461263020833334}, {"start": 745.46, "end": 745.9, "word": " أصغر", "probability": 0.98876953125}, {"start": 745.9, "end": 746.04, "word": " من", "probability": 0.99560546875}, {"start": 746.04, "end": 746.4, "word": " إبسلون", "probability": 0.978515625}, {"start": 746.4, "end": 746.62, "word": " زي", "probability": 0.990966796875}, {"start": 746.62, "end": 746.74, "word": " اللي", "probability": 0.97119140625}, {"start": 746.74, "end": 747.18, "word": " فاتت", "probability": 0.9947916666666666}], "temperature": 1.0}, {"id": 32, "seek": 75075, "start": 747.31, "end": 750.75, "text": "يعني الان اس اتنين ان زائد واحد ناقص اس اش حساوي", "tokens": [40228, 22653, 2423, 7649, 24525, 1975, 2655, 1863, 9957, 16472, 30767, 16373, 3215, 36764, 24401, 8717, 995, 4587, 9381, 24525, 1975, 8592, 11331, 3794, 995, 45865], "avg_logprob": -0.37673611331869056, "compression_ratio": 1.2463768115942029, "no_speech_prob": 0.0, "words": [{"start": 747.31, "end": 747.89, "word": "يعني", "probability": 0.773193359375}, {"start": 747.89, "end": 748.17, "word": " الان", "probability": 0.607177734375}, {"start": 748.17, "end": 748.41, "word": " اس", "probability": 0.1248779296875}, {"start": 748.41, "end": 748.73, "word": " اتنين", "probability": 0.8631591796875}, {"start": 748.73, "end": 748.83, "word": " ان", "probability": 0.422119140625}, {"start": 748.83, "end": 749.13, "word": " زائد", "probability": 0.7383626302083334}, {"start": 749.13, "end": 749.39, "word": " واحد", "probability": 0.98876953125}, {"start": 749.39, "end": 749.85, "word": " ناقص", "probability": 0.8634033203125}, {"start": 749.85, "end": 749.99, "word": " اس", "probability": 0.85302734375}, {"start": 749.99, "end": 750.19, "word": " اش", "probability": 0.57763671875}, {"start": 750.19, "end": 750.75, "word": " حساوي", "probability": 0.76202392578125}], "temperature": 1.0}, {"id": 33, "seek": 77895, "start": 751.97, "end": 778.95, "text": "اللي هو عبارة عن هذه عبارة عن أس 2n مضيوفة إليها من مين ال term اللي هو z2n زائد 1 z2n زائد 1 إشارته موجبة لإنه الأصل في ال sequence ناقص 1 و أس n زائد 1 ف2n زائد 1 زائد 1 بيصير 2n زائد 2 يعني موجبة يعني فعلاً بتكون هذه عبارة عن ال أس 2n زائد 1 بيساوي أس 2n زائد z2n زائد 1", "tokens": [6027, 20292, 31439, 6225, 3555, 9640, 3660, 18871, 29538, 6225, 3555, 9640, 3660, 18871, 5551, 3794, 568, 77, 3714, 11242, 1829, 38688, 3660, 11933, 20292, 11296, 9154, 3714, 9957, 2423, 1433, 13672, 1829, 31439, 710, 17, 77, 30767, 16373, 3215, 502, 710, 17, 77, 30767, 16373, 3215, 502, 11933, 8592, 9640, 47395, 3714, 29245, 49401, 5296, 28814, 1863, 3224, 16247, 36520, 8978, 2423, 8310, 8717, 995, 4587, 9381, 502, 4032, 5551, 3794, 297, 30767, 16373, 3215, 502, 6156, 17, 77, 30767, 16373, 3215, 502, 30767, 16373, 3215, 502, 4724, 1829, 9381, 13546, 568, 77, 30767, 16373, 3215, 568, 37495, 22653, 3714, 29245, 49401, 37495, 22653, 6156, 3615, 15040, 14111, 39894, 30544, 29538, 6225, 3555, 9640, 3660, 18871, 2423, 5551, 3794, 568, 77, 30767, 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"word": " إبسلون", "probability": 0.93173828125}, {"start": 792.4, "end": 792.98, "word": " إذا", "probability": 0.6304931640625}, {"start": 792.98, "end": 793.32, "word": " صار", "probability": 0.7105712890625}, {"start": 793.32, "end": 793.68, "word": " عندي", "probability": 0.6162109375}, {"start": 793.68, "end": 794.22, "word": " لأي", "probability": 0.9488932291666666}, {"start": 794.22, "end": 794.94, "word": " إبسلون", "probability": 0.94609375}, {"start": 794.94, "end": 795.52, "word": " أكبر", "probability": 0.96875}, {"start": 795.52, "end": 795.8, "word": " من", "probability": 0.99658203125}, {"start": 795.8, "end": 796.36, "word": " سفر", "probability": 0.7271321614583334}, {"start": 796.36, "end": 797.08, "word": " there", "probability": 0.486083984375}, {"start": 797.08, "end": 797.7, "word": " exist", "probability": 0.548828125}, {"start": 797.7, "end": 798.42, "word": " such", "probability": 0.7470703125}, {"start": 798.42, "end": 799.02, "word": " that", "probability": 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176167, "start": 1734.29, "end": 1761.67, "text": "والـ Xn مش convergent بس convergence to monotone يعني يا increasing يا decreasing يعني ماحدش يجي يقول الـ Xn هو convergent و Yn convergent إذا التلتين الـ summation convergent ليس شرطا الان اللي بقوله أنه لو كانت الواحدة convergent والتانية convergent to نتفة يعني convergent النتفة هذه اللي هي تكون increasing أو decreasing يعني monotone", "tokens": [2407, 6027, 39184, 1783, 77, 37893, 9652, 6930, 4724, 3794, 32181, 281, 1108, 310, 546, 37495, 22653, 35186, 5662, 35186, 23223, 37495, 22653, 19446, 24401, 8592, 7251, 7435, 1829, 7251, 39648, 2423, 39184, 1783, 77, 31439, 9652, 6930, 4032, 398, 77, 9652, 6930, 11933, 15730, 2423, 2655, 1211, 2655, 9957, 2423, 39184, 28811, 9652, 6930, 32239, 3794, 13412, 2288, 9566, 995, 2423, 7649, 13672, 1829, 4724, 39648, 3224, 14739, 3224, 45164, 25961, 2655, 2423, 14407, 24401, 3660, 9652, 6930, 16070, 2655, 7649, 10632, 9652, 6930, 281, 8717, 2655, 5172, 3660, 37495, 22653, 9652, 6930, 28239, 2655, 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convergent", "probability": 0.689208984375}, {"start": 1758.05, "end": 1758.61, "word": " النتفة", "probability": 0.9361572265625}, {"start": 1758.61, "end": 1758.79, "word": " هذه", "probability": 0.76416015625}, {"start": 1758.79, "end": 1758.93, "word": " اللي", "probability": 0.9638671875}, {"start": 1758.93, "end": 1759.03, "word": " هي", "probability": 0.9208984375}, {"start": 1759.03, "end": 1759.31, "word": " تكون", "probability": 0.986328125}, {"start": 1759.31, "end": 1759.97, "word": " increasing", "probability": 0.994140625}, {"start": 1759.97, "end": 1760.33, "word": " أو", "probability": 0.798828125}, {"start": 1760.33, "end": 1760.81, "word": " decreasing", "probability": 0.9794921875}, {"start": 1760.81, "end": 1761.21, "word": " يعني", "probability": 0.94287109375}, {"start": 1761.21, "end": 1761.67, "word": " monotone", "probability": 0.7769368489583334}], "temperature": 1.0}, {"id": 77, "seek": 176814, "start": 1762.02, "end": 1768.14, "text": "خلّينا نشوف كيف اللي هو البرهن النظري البرهان سهل و بعتمد على اللي جابلها مباشرة", "tokens": [9778, 1211, 11703, 9957, 995, 8717, 8592, 38688, 9122, 33911, 13672, 1829, 31439, 2423, 26890, 3224, 1863, 28239, 19913, 16572, 29739, 2288, 3224, 7649, 8608, 3224, 1211, 4032, 4724, 34268, 2304, 3215, 15844, 13672, 1829, 10874, 16758, 1211, 11296, 3714, 3555, 33599, 25720], "avg_logprob": -0.21448863670229912, "compression_ratio": 1.4313725490196079, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1762.02, "end": 1762.54, "word": "خلّينا", "probability": 0.85576171875}, {"start": 1762.54, "end": 1762.94, "word": " نشوف", "probability": 0.966796875}, {"start": 1762.94, "end": 1763.26, "word": " كيف", "probability": 0.817626953125}, {"start": 1763.26, "end": 1763.44, "word": " اللي", "probability": 0.5703125}, {"start": 1763.44, "end": 1763.56, "word": " هو", "probability": 0.94091796875}, {"start": 1763.56, "end": 1764.38, "word": " البرهن", "probability": 0.6866455078125}, {"start": 1764.38, "end": 1764.72, "word": " النظري", "probability": 0.8583984375}, {"start": 1764.72, "end": 1765.26, "word": " البرهان", "probability": 0.67352294921875}, {"start": 1765.26, "end": 1766.02, "word": " سهل", "probability": 0.9957682291666666}, {"start": 1766.02, "end": 1766.14, "word": " و", "probability": 0.6591796875}, {"start": 1766.14, "end": 1766.62, "word": " بعتمد", "probability": 0.783935546875}, {"start": 1766.62, "end": 1766.9, "word": " على", "probability": 0.771484375}, {"start": 1766.9, "end": 1767.22, "word": " اللي", "probability": 0.96728515625}, {"start": 1767.22, "end": 1767.56, "word": " جابلها", "probability": 0.9095458984375}, {"start": 1767.56, "end": 1768.14, "word": " مباشرة", "probability": 0.9925537109375}], "temperature": 1.0}, {"id": 78, "seek": 179529, "start": 1768.89, "end": 1795.29, "text": "إذا Xn كانت تتخلص من نقطة X إذا Xn كانت تتخلص من نقطة X إذا Xn كانت تتخلص من نقطة X إذا Xn ناقص X", "tokens": [28814, 15730, 1783, 77, 25961, 2655, 6055, 2655, 9778, 1211, 9381, 9154, 8717, 47432, 3660, 1783, 11933, 15730, 1783, 77, 25961, 2655, 6055, 2655, 9778, 1211, 9381, 9154, 8717, 47432, 3660, 1783, 11933, 15730, 1783, 77, 25961, 2655, 6055, 2655, 9778, 1211, 9381, 9154, 8717, 47432, 3660, 1783, 11933, 15730, 1783, 77, 8717, 995, 4587, 9381, 1783], "avg_logprob": -0.47386854270408896, "compression_ratio": 2.4307692307692306, "no_speech_prob": 2.5033950805664062e-06, "words": [{"start": 1768.89, "end": 1769.29, "word": "إذا", "probability": 0.57373046875}, {"start": 1769.29, "end": 1769.71, "word": " Xn", "probability": 0.31201171875}, {"start": 1769.71, "end": 1769.99, "word": " كانت", "probability": 0.30377197265625}, {"start": 1769.99, "end": 1770.51, "word": " تتخلص", "probability": 0.597900390625}, {"start": 1770.51, "end": 1771.69, "word": " من", "probability": 0.69775390625}, {"start": 1771.69, "end": 1773.03, "word": " نقطة", "probability": 0.41619873046875}, {"start": 1773.03, "end": 1773.17, "word": " X", "probability": 0.7646484375}, {"start": 1773.17, "end": 1774.11, "word": " إذا", "probability": 0.5032196044921875}, {"start": 1774.11, "end": 1782.03, "word": " Xn", "probability": 0.554443359375}, {"start": 1782.03, "end": 1782.15, "word": " كانت", "probability": 0.84814453125}, {"start": 1782.15, "end": 1782.63, "word": " تتخلص", "probability": 0.97421875}, {"start": 1782.63, "end": 1782.93, "word": " من", "probability": 0.97265625}, {"start": 1782.93, "end": 1783.27, "word": " نقطة", "probability": 0.9794921875}, {"start": 1783.27, "end": 1783.93, "word": " X", "probability": 0.97607421875}, {"start": 1783.93, "end": 1784.17, "word": " إذا", "probability": 0.59686279296875}, {"start": 1784.17, "end": 1784.97, "word": " Xn", "probability": 0.879638671875}, {"start": 1784.97, "end": 1785.07, "word": " كانت", "probability": 0.85302734375}, {"start": 1785.07, "end": 1785.71, "word": " تتخلص", "probability": 0.9912109375}, {"start": 1785.71, "end": 1786.25, "word": " من", "probability": 0.978515625}, {"start": 1786.25, "end": 1786.25, "word": " نقطة", "probability": 0.98828125}, {"start": 1786.25, "end": 1787.25, "word": " X", "probability": 0.9853515625}, {"start": 1787.25, "end": 1787.41, "word": " إذا", "probability": 0.6690673828125}, {"start": 1787.41, "end": 1792.13, "word": " Xn", "probability": 0.93505859375}, {"start": 1792.13, "end": 1794.93, "word": " ناقص", "probability": 0.654144287109375}, {"start": 1794.93, "end": 1795.29, "word": " X", "probability": 0.95458984375}], "temperature": 1.0}, {"id": 79, "seek": 182623, "start": 1796.63, "end": 1826.23, "text": "صارت الأن الـ xn ناقص x مدام الـ xn decreasing وده راحنا منها إيش ثابت حتظلها decreasing إذا صارت الـ yn decreasing ومش decreasing كمان و limit الـ yn الـ un بساوي limit الـ xn ناقص الـ x هذه ما هي ثابت يعني limit xn x ناقص x صفر يعني limit الـ un صفر يعني حولت ال sequence اللي عند الـ xn إلى sequence yn تكون decreasing و limitها بساوي صفر", "tokens": [9381, 9640, 2655, 16247, 1863, 2423, 39184, 2031, 77, 8717, 995, 4587, 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"probability": 0.777587890625}, {"start": 1797.15, "end": 1797.49, "word": " الأن", "probability": 0.622802734375}, {"start": 1797.49, "end": 1797.71, "word": " الـ", "probability": 0.841796875}, {"start": 1797.71, "end": 1798.07, "word": " xn", "probability": 0.248291015625}, {"start": 1798.07, "end": 1798.49, "word": " ناقص", "probability": 0.737060546875}, {"start": 1798.49, "end": 1798.83, "word": " x", "probability": 0.91455078125}, {"start": 1798.83, "end": 1799.23, "word": " مدام", "probability": 0.649658203125}, {"start": 1799.23, "end": 1799.37, "word": " الـ", "probability": 0.888427734375}, {"start": 1799.37, "end": 1799.65, "word": " xn", "probability": 0.959716796875}, {"start": 1799.65, "end": 1800.13, "word": " decreasing", "probability": 0.73291015625}, {"start": 1800.13, "end": 1800.65, "word": " وده", "probability": 0.6717122395833334}, {"start": 1800.65, "end": 1800.89, "word": " راحنا", "probability": 0.966796875}, {"start": 1800.89, "end": 1801.15, "word": " منها", "probability": 0.9599609375}, {"start": 1801.15, "end": 1801.31, "word": " إيش", "probability": 0.6400553385416666}, {"start": 1801.31, "end": 1801.83, "word": " ثابت", "probability": 0.9931640625}, {"start": 1801.83, "end": 1802.63, "word": " حتظلها", "probability": 0.71318359375}, {"start": 1802.63, "end": 1803.17, "word": " decreasing", "probability": 0.96923828125}, {"start": 1803.17, "end": 1803.89, "word": " إذا", "probability": 0.80419921875}, {"start": 1803.89, "end": 1804.33, "word": " صارت", "probability": 0.9130859375}, {"start": 1804.33, "end": 1804.53, "word": " الـ", "probability": 0.785400390625}, {"start": 1804.53, "end": 1804.73, "word": " yn", "probability": 0.74462890625}, {"start": 1804.73, "end": 1805.43, "word": " decreasing", "probability": 0.94482421875}, {"start": 1805.43, "end": 1806.25, "word": " ومش", "probability": 0.9723307291666666}, {"start": 1806.25, "end": 1806.73, "word": " decreasing", "probability": 0.9755859375}, {"start": 1806.73, "end": 1807.35, 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"word": " الـ", "probability": 0.93115234375}, {"start": 1811.23, "end": 1811.35, "word": " x", "probability": 0.8134765625}, {"start": 1811.35, "end": 1811.57, "word": " هذه", "probability": 0.464599609375}, {"start": 1811.57, "end": 1811.67, "word": " ما", "probability": 0.81787109375}, {"start": 1811.67, "end": 1811.77, "word": " هي", "probability": 0.90625}, {"start": 1811.77, "end": 1812.25, "word": " ثابت", "probability": 0.9954427083333334}, {"start": 1812.25, "end": 1812.95, "word": " يعني", "probability": 0.94970703125}, {"start": 1812.95, "end": 1813.35, "word": " limit", "probability": 0.93017578125}, {"start": 1813.35, "end": 1813.83, "word": " xn", "probability": 0.97265625}, {"start": 1813.83, "end": 1814.17, "word": " x", "probability": 0.87451171875}, {"start": 1814.17, "end": 1814.63, "word": " ناقص", "probability": 0.9888916015625}, {"start": 1814.63, "end": 1814.85, "word": " x", "probability": 0.9794921875}, {"start": 1814.85, "end": 1815.47, "word": " صفر", "probability": 0.73193359375}, {"start": 1815.47, "end": 1816.11, "word": " يعني", "probability": 0.94921875}, {"start": 1816.11, "end": 1816.51, "word": " limit", "probability": 0.98779296875}, {"start": 1816.51, "end": 1816.87, "word": " الـ", "probability": 0.958740234375}, {"start": 1816.87, "end": 1817.23, "word": " un", "probability": 0.775390625}, {"start": 1817.23, "end": 1817.77, "word": " صفر", "probability": 0.9661458333333334}, {"start": 1817.77, "end": 1817.99, "word": " يعني", "probability": 0.96337890625}, {"start": 1817.99, "end": 1818.71, "word": " حولت", "probability": 0.9508463541666666}, {"start": 1818.71, "end": 1818.87, "word": " ال", "probability": 0.91845703125}, {"start": 1818.87, "end": 1819.35, "word": " sequence", "probability": 0.578125}, {"start": 1819.35, "end": 1819.63, "word": " اللي", "probability": 0.965087890625}, {"start": 1819.63, "end": 1819.93, "word": " عند", "probability": 0.89306640625}, {"start": 1819.93, "end": 1820.21, "word": " الـ", "probability": 0.5604248046875}, {"start": 1820.21, "end": 1820.73, "word": " xn", "probability": 0.9892578125}, {"start": 1820.73, "end": 1821.25, "word": " إلى", "probability": 0.8134765625}, {"start": 1821.25, "end": 1821.83, "word": " sequence", "probability": 0.8798828125}, {"start": 1821.83, "end": 1822.53, "word": " yn", "probability": 0.947265625}, {"start": 1822.53, "end": 1823.43, "word": " تكون", "probability": 0.914794921875}, {"start": 1823.43, "end": 1824.21, "word": " decreasing", "probability": 0.982421875}, {"start": 1824.21, "end": 1824.91, "word": " و", "probability": 0.92578125}, {"start": 1824.91, "end": 1825.39, "word": " limitها", "probability": 0.841552734375}, {"start": 1825.39, "end": 1825.81, "word": " بساوي", "probability": 0.952392578125}, {"start": 1825.81, "end": 1826.23, "word": " صفر", "probability": 0.9085286458333334}], "temperature": 1.0}, {"id": 80, "seek": 184963, "start": 1826.61, "end": 1849.63, "text": "I saw that UN decreases to zero then XN بيساوي X زائد UN ومنه once ال XN في ال YN صارت عندي ال sequence XN في YN بيساوي X في YN زائد UN في YN ماشي الان عندي", "tokens": [40, 1866, 300, 8229, 24108, 281, 4018, 550, 1783, 45, 4724, 1829, 3794, 995, 45865, 1783, 30767, 16373, 3215, 8229, 4032, 27842, 3224, 1564, 2423, 1783, 45, 8978, 2423, 398, 45, 20328, 9640, 2655, 18871, 16254, 2423, 8310, 1783, 45, 8978, 398, 45, 4724, 1829, 3794, 995, 45865, 1783, 8978, 398, 45, 30767, 16373, 3215, 8229, 8978, 398, 45, 3714, 33599, 1829, 2423, 7649, 18871, 16254], "avg_logprob": -0.22516324804789983, "compression_ratio": 1.4758620689655173, "no_speech_prob": 1.800060272216797e-05, "words": [{"start": 1826.61, "end": 1827.27, "word": "I", "probability": 0.30810546875}, {"start": 1827.27, "end": 1828.05, "word": " saw", "probability": 0.8076171875}, {"start": 1828.05, "end": 1828.43, "word": " that", "probability": 0.93505859375}, {"start": 1828.43, "end": 1828.83, "word": " UN", "probability": 0.3720703125}, {"start": 1828.83, "end": 1829.75, "word": " decreases", "probability": 0.810546875}, {"start": 1829.75, "end": 1830.15, "word": " to", "probability": 0.9736328125}, {"start": 1830.15, "end": 1830.61, "word": " zero", "probability": 0.59521484375}, {"start": 1830.61, "end": 1831.45, "word": " then", "probability": 0.379150390625}, {"start": 1831.45, "end": 1831.95, "word": " XN", "probability": 0.57861328125}, {"start": 1831.95, "end": 1832.39, "word": " بيساوي", "probability": 0.700390625}, {"start": 1832.39, "end": 1832.63, "word": " X", "probability": 0.9150390625}, {"start": 1832.63, "end": 1832.93, "word": " زائد", "probability": 0.6822916666666666}, {"start": 1832.93, "end": 1833.37, "word": " UN", "probability": 0.92236328125}, {"start": 1833.37, "end": 1835.13, "word": " ومنه", "probability": 0.8968098958333334}, {"start": 1835.13, "end": 1835.79, "word": " once", "probability": 0.318603515625}, {"start": 1835.79, "end": 1836.47, "word": " ال", "probability": 0.755859375}, {"start": 1836.47, "end": 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" X", "probability": 0.9697265625}, {"start": 1840.95, "end": 1841.09, "word": " في", "probability": 0.98193359375}, {"start": 1841.09, "end": 1841.61, "word": " YN", "probability": 0.923828125}, {"start": 1841.61, "end": 1842.39, "word": " زائد", "probability": 0.9265950520833334}, {"start": 1842.39, "end": 1843.53, "word": " UN", "probability": 0.873046875}, {"start": 1843.53, "end": 1844.11, "word": " في", "probability": 0.98876953125}, {"start": 1844.11, "end": 1844.81, "word": " YN", "probability": 0.973876953125}, {"start": 1844.81, "end": 1845.81, "word": " ماشي", "probability": 0.9080403645833334}, {"start": 1845.81, "end": 1847.51, "word": " الان", "probability": 0.5445556640625}, {"start": 1847.51, "end": 1849.63, "word": " عندي", "probability": 0.858642578125}], "temperature": 1.0}, {"id": 81, "seek": 186995, "start": 1850.65, "end": 1869.95, "text": "الـ Sequence اللي هي الـ y .. from Dirichlet Test الدنيا اللي هي صارت منيحة، ليش؟ لأنه بما أنه اللي هو الـ u .. هذه طبعا ال 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