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0.95068359375}, {"start": 182.22, "end": 182.48, "word": " of", "probability": 0.9814453125}, {"start": 182.48, "end": 182.92, "word": " infinite", "probability": 0.92529296875}, {"start": 182.92, "end": 183.44, "word": " series", "probability": 0.90380859375}, {"start": 183.44, "end": 184.08, "word": " يعني", "probability": 0.71533203125}, {"start": 184.08, "end": 184.24, "word": " لو", "probability": 0.91943359375}, {"start": 184.24, "end": 184.6, "word": " كانت", "probability": 0.95361328125}, {"start": 184.6, "end": 185.24, "word": " الـSK", "probability": 0.6307373046875}, {"start": 185.24, "end": 185.7, "word": " عندي", "probability": 0.7294921875}, {"start": 185.7, "end": 186.16, "word": " هذه", "probability": 0.46337890625}, {"start": 186.16, "end": 187.32, "word": " converges", "probability": 0.7374267578125}, {"start": 187.32, "end": 187.6, "word": " to", "probability": 0.939453125}, {"start": 187.6, "end": 188.06, "word": " some", "probability": 0.7958984375}, {"start": 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"word": " وهذه", "probability": 0.769287109375}, {"start": 207.76, "end": 208.04, "word": " S", "probability": 0.87158203125}, {"start": 208.04, "end": 208.32, "word": " N", "probability": 0.81591796875}, {"start": 208.32, "end": 208.84, "word": " وهذه", "probability": 0.907958984375}, {"start": 208.84, "end": 209.22, "word": " S", "probability": 0.96337890625}, {"start": 209.22, "end": 209.52, "word": " N", "probability": 0.83349609375}, {"start": 209.52, "end": 209.78, "word": " كل", "probability": 0.168701171875}, {"start": 209.78, "end": 210.04, "word": " برج", "probability": 0.467041015625}, {"start": 210.04, "end": 210.42, "word": " للاس", "probability": 0.5524088541666666}], "temperature": 1.0}, {"id": 12, "seek": 22748, "start": 210.58, "end": 227.48, "text": "هذه اللي بنسميها الـ infinite series اللي هي في حالة ال convergence أو ال limit هذه exist تبع ال sequence of partial sums بنسميها اللي هي limit exist بنسميها S لأن ال elements XN are called the terms", "tokens": [3224, 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"probability": 0.615234375}, {"start": 217.64, "end": 217.9, "word": " sequence", "probability": 0.8466796875}, {"start": 217.9, "end": 218.06, "word": " of", "probability": 0.61279296875}, {"start": 218.06, "end": 218.3, "word": " partial", "probability": 0.787109375}, {"start": 218.3, "end": 218.72, "word": " sums", "probability": 0.9501953125}, {"start": 218.72, "end": 219.98, "word": " بنسميها", "probability": 0.916259765625}, {"start": 219.98, "end": 220.32, "word": " اللي", "probability": 0.9091796875}, {"start": 220.32, "end": 220.52, "word": " هي", "probability": 0.94287109375}, {"start": 220.52, "end": 220.8, "word": " limit", "probability": 0.611328125}, {"start": 220.8, "end": 221.18, "word": " exist", "probability": 0.73779296875}, {"start": 221.18, "end": 221.92, "word": " بنسميها", "probability": 0.805419921875}, {"start": 221.92, "end": 222.4, "word": " S", "probability": 0.83642578125}, {"start": 222.4, "end": 223.3, "word": " لأن", "probability": 0.819091796875}, {"start": 223.3, "end": 223.5, "word": " ال", "probability": 0.62255859375}, {"start": 223.5, "end": 224.2, "word": " elements", "probability": 0.7578125}, {"start": 224.2, "end": 225.04, "word": " XN", "probability": 0.37164306640625}, {"start": 225.04, "end": 225.88, "word": " are", "probability": 0.38232421875}, {"start": 225.88, "end": 226.48, "word": " called", "probability": 0.9140625}, {"start": 226.48, "end": 226.82, "word": " the", "probability": 0.87744140625}, {"start": 226.82, "end": 227.48, "word": " terms", "probability": 0.90576171875}], "temperature": 1.0}, {"id": 13, "seek": 25573, "start": 228.27, "end": 255.73, "text": "and S and are called the partial sums of this infinite series يعني هدولة اللي هي ال .. ال xk's بنسميها اللي هي ال terms تبعة ال infinite series و ال S and أو ال Sk بنسميها اللي هي عبارة عن أيش ال sequence of partial sums أو بنسميهم are partial sums of this infinite series نيجي الآن بما أنه اللي هو في النهاية ال series اللي عندنا هذه", "tokens": [474, 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{"start": 248.25, "end": 248.85, "word": " of", "probability": 0.9814453125}, {"start": 248.85, "end": 249.25, "word": " this", "probability": 0.9365234375}, {"start": 249.25, "end": 249.73, "word": " infinite", "probability": 0.953125}, {"start": 249.73, "end": 250.33, "word": " series", "probability": 0.9013671875}, {"start": 250.33, "end": 251.11, "word": " نيجي", "probability": 0.8955078125}, {"start": 251.11, "end": 251.41, "word": " الآن", "probability": 0.74072265625}, {"start": 251.41, "end": 251.77, "word": " بما", "probability": 0.869140625}, {"start": 251.77, "end": 252.19, "word": " أنه", "probability": 0.5772705078125}, {"start": 252.19, "end": 252.41, "word": " اللي", "probability": 0.988037109375}, {"start": 252.41, "end": 252.71, "word": " هو", "probability": 0.99609375}, {"start": 252.71, "end": 252.89, "word": " في", "probability": 0.94921875}, {"start": 252.89, "end": 253.67, "word": " النهاية", "probability": 0.9482421875}, {"start": 253.67, "end": 254.27, "word": " ال", "probability": 0.8173828125}, {"start": 254.27, "end": 254.65, "word": " series", "probability": 0.96484375}, {"start": 254.65, "end": 254.95, "word": " اللي", "probability": 0.985595703125}, {"start": 254.95, "end": 255.35, "word": " عندنا", "probability": 0.946533203125}, {"start": 255.35, "end": 255.73, "word": " هذه", "probability": 0.54052734375}], "temperature": 1.0}, {"id": 14, "seek": 27752, "start": 256.16, "end": 277.52, "text": "عبارة عن limit في حالة ال convergence هو عبارة عن limit of a sequence إذا تنطبق عليها قوانين ال sequences اللي أخدناها في chapter 3 إذا متوقع إنه احنا نستخدم ما تحدثنا فيه في chapter 3 أو نتائجها للحصول على النظريات اللي احنا بدنا نبرهنها", "tokens": [3615, 3555, 9640, 3660, 18871, 4948, 8978, 11331, 6027, 3660, 2423, 32181, 31439, 6225, 3555, 9640, 3660, 18871, 4948, 295, 257, 8310, 11933, 15730, 6055, 1863, 9566, 3555, 4587, 25894, 11296, 12174, 2407, 7649, 9957, 2423, 22978, 13672, 1829, 5551, 9778, 3215, 8315, 11296, 8978, 7187, 805, 11933, 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تحدثنا", "probability": 0.975830078125}, {"start": 270.76, "end": 270.96, "word": " فيه", "probability": 0.978515625}, {"start": 270.96, "end": 271.08, "word": " في", "probability": 0.8759765625}, {"start": 271.08, "end": 271.36, "word": " chapter", "probability": 0.85107421875}, {"start": 271.36, "end": 271.88, "word": " 3", "probability": 0.95654296875}, {"start": 271.88, "end": 272.14, "word": " أو", "probability": 0.837890625}, {"start": 272.14, "end": 273.46, "word": " نتائجها", "probability": 0.9212890625}, {"start": 273.46, "end": 274.66, "word": " للحصول", "probability": 0.966796875}, {"start": 274.66, "end": 275.02, "word": " على", "probability": 0.93408203125}, {"start": 275.02, "end": 276.1, "word": " النظريات", "probability": 0.926025390625}, {"start": 276.1, "end": 276.42, "word": " اللي", "probability": 0.973876953125}, {"start": 276.42, "end": 276.7, "word": " احنا", "probability": 0.9300130208333334}, {"start": 276.7, "end": 277.0, "word": " بدنا", "probability": 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"word": " the", "probability": 0.82275390625}, {"start": 284.35, "end": 284.71, "word": " series", "probability": 0.88037109375}, {"start": 284.71, "end": 285.11, "word": " summation", "probability": 0.67529296875}, {"start": 285.11, "end": 285.73, "word": " xn", "probability": 0.6251220703125}, {"start": 285.73, "end": 286.19, "word": " and", "probability": 0.8876953125}, {"start": 286.19, "end": 286.81, "word": " summation", "probability": 0.859375}, {"start": 286.81, "end": 287.29, "word": " yn", "probability": 0.8984375}, {"start": 287.29, "end": 288.25, "word": " converge", "probability": 0.623046875}, {"start": 288.25, "end": 288.61, "word": " يعني", "probability": 0.749755859375}, {"start": 288.61, "end": 289.43, "word": " السيريز", "probability": 0.73919677734375}, {"start": 289.43, "end": 289.77, "word": " هذه", "probability": 0.513671875}, {"start": 289.77, "end": 289.95, "word": " من", "probability": 0.80419921875}, {"start": 289.95, "end": 290.17, "word": " n", 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{"start": 293.25, "end": 293.91, "word": " موجود", "probability": 0.9847005208333334}, {"start": 293.91, "end": 294.33, "word": " و", "probability": 0.44970703125}, {"start": 294.33, "end": 294.59, "word": " هذا", "probability": 0.88037109375}, {"start": 294.59, "end": 294.75, "word": " ال", "probability": 0.96533203125}, {"start": 294.75, "end": 294.95, "word": " sum", "probability": 0.9599609375}, {"start": 294.95, "end": 295.39, "word": " موجود", "probability": 0.9905598958333334}, {"start": 295.39, "end": 295.67, "word": " يعني", "probability": 0.916259765625}, {"start": 295.67, "end": 297.63, "word": " السيريز", "probability": 0.818359375}, {"start": 297.63, "end": 298.05, "word": " هذه", "probability": 0.693359375}, {"start": 298.05, "end": 298.69, "word": " اللي", "probability": 0.748291015625}, {"start": 298.69, "end": 298.81, "word": " هي", "probability": 0.90380859375}, {"start": 298.81, "end": 299.17, "word": " sequence", "probability": 0.40625}, {"start": 299.17, "end": 299.43, "word": " of", "probability": 0.8662109375}, {"start": 299.43, "end": 299.67, "word": " partial", "probability": 0.95849609375}, {"start": 299.67, "end": 300.01, "word": " sums", "probability": 0.96630859375}, {"start": 300.01, "end": 300.67, "word": " سبعتها", "probability": 0.9091796875}, {"start": 300.67, "end": 301.25, "word": " ال", "probability": 0.57421875}, {"start": 301.25, "end": 301.49, "word": " limit", "probability": 0.845703125}, {"start": 301.49, "end": 301.69, "word": " لها", "probability": 0.625732421875}, {"start": 301.69, "end": 302.45, "word": " موجودة", "probability": 0.98779296875}, {"start": 302.45, "end": 302.81, "word": " و", "probability": 0.8310546875}, {"start": 302.81, "end": 302.93, "word": " ال", "probability": 0.428466796875}, {"start": 302.93, "end": 303.37, "word": " summation", "probability": 0.95703125}, {"start": 303.37, "end": 303.85, "word": " yn", "probability": 0.7333984375}, {"start": 303.85, "end": 304.59, "word": " converge", "probability": 0.6630859375}, {"start": 304.59, "end": 305.05, "word": " يعني", "probability": 0.973876953125}, {"start": 305.05, "end": 305.53, "word": " السيريز", "probability": 0.8880615234375}], "temperature": 1.0}, {"id": 16, "seek": 32419, "start": 305.57, "end": 324.19, "text": "سيكوانس الـ partial sums السبعية ده برضه موجودة limit لها then the series summation xn زائد yn برضه converges ومش هيك كمان وقيمة السيكوه السيريز الجديدة summation xn زائد yn بساوي السيريز الأولى زائد السيريز الثانية", "tokens": [3794, 1829, 4117, 2407, 7649, 3794, 2423, 39184, 14641, 34499, 21136, 3555, 3615, 10632, 11778, 3224, 4724, 43042, 3224, 3714, 29245, 23328, 3660, 4948, 5296, 11296, 550, 264, 2638, 28811, 2031, 77, 30767, 16373, 3215, 17861, 4724, 43042, 3224, 9652, 2880, 4032, 2304, 8592, 39896, 4117, 9122, 2304, 7649, 4032, 4587, 32640, 3660, 21136, 1829, 4117, 2407, 3224, 21136, 13546, 1829, 11622, 25724, 16254, 41891, 28811, 2031, 77, 30767, 16373, 3215, 17861, 4724, 3794, 995, 45865, 21136, 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{"start": 308.73, "end": 309.23, "word": " لها", "probability": 0.741943359375}, {"start": 309.23, "end": 310.11, "word": " then", "probability": 0.390869140625}, {"start": 310.11, "end": 310.39, "word": " the", "probability": 0.494873046875}, {"start": 310.39, "end": 310.79, "word": " series", "probability": 0.8505859375}, {"start": 310.79, "end": 311.45, "word": " summation", "probability": 0.31689453125}, {"start": 311.45, "end": 312.23, "word": " xn", "probability": 0.5301513671875}, {"start": 312.23, "end": 312.71, "word": " زائد", "probability": 0.77197265625}, {"start": 312.71, "end": 313.23, "word": " yn", "probability": 0.9453125}, {"start": 313.23, "end": 314.21, "word": " برضه", "probability": 0.9514973958333334}, {"start": 314.21, "end": 315.07, "word": " converges", "probability": 0.6170654296875}, {"start": 315.07, "end": 315.49, "word": " ومش", "probability": 0.95361328125}, {"start": 315.49, "end": 315.75, "word": " هيك", "probability": 0.91748046875}, {"start": 315.75, "end": 316.19, "word": " كمان", "probability": 0.9894205729166666}, {"start": 316.19, "end": 317.21, "word": " وقيمة", "probability": 0.948486328125}, {"start": 317.21, "end": 318.09, "word": " السيكوه", "probability": 0.6875244140625}, {"start": 318.09, "end": 318.63, "word": " السيريز", "probability": 0.8099365234375}, {"start": 318.63, "end": 319.13, "word": " الجديدة", "probability": 0.8702799479166666}, {"start": 319.13, "end": 319.43, "word": " summation", "probability": 0.81298828125}, {"start": 319.43, "end": 319.87, "word": " xn", "probability": 0.967529296875}, {"start": 319.87, "end": 320.11, "word": " زائد", "probability": 0.8868815104166666}, {"start": 320.11, "end": 320.51, "word": " yn", "probability": 0.97705078125}, {"start": 320.51, "end": 321.35, "word": " بساوي", "probability": 0.82208251953125}, {"start": 321.35, "end": 321.87, "word": " السيريز", "probability": 0.916015625}, {"start": 321.87, "end": 322.47, "word": " الأولى", "probability": 0.9708658854166666}, 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774.81, "word": " بنكون", "probability": 0.85107421875}, {"start": 774.81, "end": 775.17, "word": " منها", "probability": 0.985595703125}, {"start": 775.17, "end": 775.49, "word": " sequence", "probability": 0.80712890625}, {"start": 775.49, "end": 775.69, "word": " of", "probability": 0.7841796875}, {"start": 775.69, "end": 775.91, "word": " partial", "probability": 0.94580078125}, {"start": 775.91, "end": 776.35, "word": " sums", "probability": 0.9296875}, {"start": 776.35, "end": 777.25, "word": " لازم", "probability": 0.9817708333333334}, {"start": 777.25, "end": 777.51, "word": " limit", "probability": 0.489990234375}, {"start": 777.51, "end": 777.83, "word": " هيش", "probability": 0.3597412109375}, {"start": 777.83, "end": 778.31, "word": " يساوي", "probability": 0.9276123046875}], "temperature": 1.0}, {"id": 37, "seek": 80416, "start": 779.64, "end": 804.16, "text": "يساوي سفر وبناء عليه لو كانت ال limit لها تساوي سفر على طول بنحكم على summation لل Xn إيش ماله diverse وكنا نقول هذا test of divergence مش test of convergence لأن ممكن ال limit تساوي سفر لكن ال summation لل Xn يكون diverse والمثال اللي انتوا مشهور اللي هو summation 1 على n هذا اللي هو limit", "tokens": [1829, 3794, 995, 45865, 8608, 5172, 2288, 46599, 1863, 16606, 47356, 45164, 25961, 2655, 2423, 4948, 5296, 11296, 6055, 3794, 995, 45865, 8608, 5172, 2288, 15844, 23032, 12610, 44945, 5016, 24793, 15844, 28811, 24976, 1783, 77, 11933, 1829, 8592, 3714, 6027, 3224, 9521, 4032, 4117, 8315, 8717, 39648, 23758, 1500, 295, 47387, 37893, 1500, 295, 32181, 5296, 33456, 3714, 43020, 2423, 4948, 6055, 3794, 995, 45865, 8608, 5172, 2288, 44381, 2423, 28811, 24976, 1783, 77, 7251, 30544, 9521, 4032, 45340, 12984, 6027, 13672, 1829, 16472, 2655, 14407, 37893, 3224, 13063, 13672, 1829, 31439, 28811, 502, 15844, 297, 23758, 13672, 1829, 31439, 4948], "avg_logprob": -0.28686285481869594, "compression_ratio": 1.9026548672566372, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 779.64, "end": 780.2, 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"probability": 0.9130859375}, {"start": 790.56, "end": 790.9, "word": " of", "probability": 0.970703125}, {"start": 790.9, "end": 791.68, "word": " divergence", "probability": 0.96044921875}, {"start": 791.68, "end": 792.24, "word": " مش", "probability": 0.802734375}, {"start": 792.24, "end": 792.58, "word": " test", "probability": 0.60107421875}, {"start": 792.58, "end": 792.76, "word": " of", "probability": 0.966796875}, {"start": 792.76, "end": 793.42, "word": " convergence", "probability": 0.96142578125}, {"start": 793.42, "end": 794.34, "word": " لأن", "probability": 0.80859375}, {"start": 794.34, "end": 794.72, "word": " ممكن", "probability": 0.8173828125}, {"start": 794.72, "end": 794.88, "word": " ال", "probability": 0.437744140625}, {"start": 794.88, "end": 795.06, "word": " limit", "probability": 0.96728515625}, {"start": 795.06, "end": 795.5, "word": " تساوي", "probability": 0.98046875}, {"start": 795.5, "end": 795.84, "word": " سفر", "probability": 0.97216796875}, {"start": 795.84, "end": 796.16, "word": " لكن", "probability": 0.892578125}, {"start": 796.16, "end": 796.36, "word": " ال", "probability": 0.8095703125}, {"start": 796.36, "end": 796.74, "word": " summation", "probability": 0.9541015625}, {"start": 796.74, "end": 796.98, "word": " لل", "probability": 0.74658203125}, {"start": 796.98, "end": 797.48, "word": " Xn", "probability": 0.944580078125}, {"start": 797.48, "end": 797.96, "word": " يكون", "probability": 0.951171875}, {"start": 797.96, "end": 798.82, "word": " diverse", "probability": 0.462158203125}, {"start": 798.82, "end": 799.52, "word": " والمثال", "probability": 0.8084716796875}, {"start": 799.52, "end": 799.66, "word": " اللي", "probability": 0.94384765625}, {"start": 799.66, "end": 799.96, "word": " انتوا", "probability": 0.6985677083333334}, {"start": 799.96, "end": 800.52, "word": " مشهور", "probability": 0.98828125}, {"start": 800.52, "end": 800.96, "word": " اللي", "probability": 0.833251953125}, {"start": 800.96, "end": 801.1, "word": " هو", "probability": 0.9716796875}, {"start": 801.1, "end": 801.54, "word": " summation", "probability": 0.8505859375}, {"start": 801.54, "end": 801.84, "word": " 1", "probability": 0.72021484375}, {"start": 801.84, "end": 802.16, "word": " على", "probability": 0.673828125}, {"start": 802.16, "end": 802.48, "word": " n", "probability": 0.4658203125}, {"start": 802.48, "end": 803.22, "word": " هذا", "probability": 0.88232421875}, {"start": 803.22, "end": 803.48, "word": " اللي", "probability": 0.968994140625}, {"start": 803.48, "end": 803.68, "word": " هو", "probability": 0.98974609375}, {"start": 803.68, "end": 804.16, "word": " limit", "probability": 0.97265625}], "temperature": 1.0}, {"id": 38, "seek": 82114, "start": 804.68, "end": 821.14, "text": "الواحد على ان بيساوي سفر but this series diverges زي ما هنشوف بعد شوية و زي ما احنا اصلا عارفين ولكن احنا هنثبته اثبات الان كنا اللي هو اخدناها معلومة في تفاضل بام طيب", "tokens": [6027, 14407, 24401, 15844, 16472, 4724, 1829, 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0.86376953125}, {"start": 807.76, "end": 808.1, "word": " but", "probability": 0.322509765625}, {"start": 808.1, "end": 808.6, "word": " this", "probability": 0.771484375}, {"start": 808.6, "end": 809.16, "word": " series", "probability": 0.8662109375}, {"start": 809.16, "end": 809.9, "word": " diverges", "probability": 0.5975341796875}, {"start": 809.9, "end": 810.08, "word": " زي", "probability": 0.759765625}, {"start": 810.08, "end": 810.16, "word": " ما", "probability": 0.94482421875}, {"start": 810.16, "end": 810.78, "word": " هنشوف", "probability": 0.8851318359375}, {"start": 810.78, "end": 811.3, "word": " بعد", "probability": 0.87841796875}, {"start": 811.3, "end": 811.8, "word": " شوية", "probability": 0.9326171875}, {"start": 811.8, "end": 811.94, "word": " و", "probability": 0.828125}, {"start": 811.94, "end": 812.1, "word": " زي", "probability": 0.793701171875}, {"start": 812.1, "end": 812.2, "word": " ما", "probability": 0.9423828125}, {"start": 812.2, "end": 812.36, "word": " احنا", "probability": 0.91455078125}, {"start": 812.36, "end": 812.72, "word": " اصلا", "probability": 0.8665364583333334}, {"start": 812.72, "end": 813.28, "word": " عارفين", "probability": 0.98876953125}, {"start": 813.28, "end": 813.86, "word": " ولكن", "probability": 0.854248046875}, {"start": 813.86, "end": 814.12, "word": " احنا", "probability": 0.9869791666666666}, {"start": 814.12, "end": 814.8, "word": " هنثبته", "probability": 0.8087890625}, {"start": 814.8, "end": 815.36, "word": " اثبات", "probability": 0.9464111328125}, {"start": 815.36, "end": 815.78, "word": " الان", "probability": 0.6429443359375}, {"start": 815.78, "end": 816.68, "word": " كنا", "probability": 0.84423828125}, {"start": 816.68, "end": 817.58, "word": " اللي", "probability": 0.808349609375}, {"start": 817.58, "end": 817.76, "word": " هو", "probability": 0.94482421875}, {"start": 817.76, "end": 818.26, "word": " اخدناها", "probability": 0.83798828125}, {"start": 818.26, "end": 818.78, "word": " معلومة", "probability": 0.9759521484375}, {"start": 818.78, "end": 819.04, "word": " في", "probability": 0.84814453125}, {"start": 819.04, "end": 820.36, "word": " تفاضل", "probability": 0.9290771484375}, {"start": 820.36, "end": 820.74, "word": " بام", "probability": 0.562255859375}, {"start": 820.74, "end": 821.14, "word": " طيب", "probability": 0.93798828125}], "temperature": 1.0}, {"id": 39, "seek": 84937, "start": 822.45, "end": 849.37, "text": "صلى النبي عليه الصلاة والسلام الان by definition the convergence of summation xn means that limit ال sk شماله exist ايش ال sk عارفين ايش ال sk ال sk هو عبارة عن x واحد زاد x اتنين لما اصل عند xk الان بما انه اللي هو limit sk بساوي اللي هو ال summation لل xn", "tokens": [9381, 23942, 28239, 21292, 47356, 31767, 15040, 3660, 16070, 3794, 37440, 2423, 7649, 538, 7123, 264, 32181, 295, 28811, 2031, 77, 1355, 300, 4948, 2423, 1110, 13412, 2304, 6027, 3224, 2514, 1975, 1829, 8592, 2423, 1110, 6225, 9640, 5172, 9957, 1975, 1829, 8592, 2423, 1110, 2423, 1110, 31439, 6225, 3555, 9640, 3660, 18871, 2031, 36764, 24401, 30767, 18513, 2031, 1975, 2655, 1863, 9957, 5296, 15042, 1975, 36520, 43242, 2031, 74, 2423, 7649, 4724, 15042, 16472, 3224, 13672, 1829, 31439, 4948, 1110, 4724, 3794, 995, 45865, 13672, 1829, 31439, 2423, 28811, 24976, 2031, 77], "avg_logprob": -0.23553856034228143, "compression_ratio": 1.7064220183486238, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 822.45, "end": 822.87, "word": "صلى", "probability": 0.74560546875}, {"start": 822.87, "end": 823.13, "word": " النبي", "probability": 0.6500244140625}, {"start": 823.13, "end": 823.39, "word": " عليه", "probability": 0.86767578125}, {"start": 823.39, "end": 823.81, "word": " الصلاة", "probability": 0.9754231770833334}, {"start": 823.81, "end": 824.31, "word": " والسلام", "probability": 0.9597981770833334}, {"start": 824.31, "end": 824.89, "word": " الان", "probability": 0.6302490234375}, {"start": 824.89, "end": 825.09, "word": " by", "probability": 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{"start": 832.55, "end": 833.33, "word": " exist", "probability": 0.791015625}, {"start": 833.33, "end": 834.03, "word": " ايش", "probability": 0.7303873697916666}, {"start": 834.03, "end": 834.13, "word": " ال", "probability": 0.9599609375}, {"start": 834.13, "end": 834.43, "word": " sk", "probability": 0.92578125}, {"start": 834.43, "end": 834.87, "word": " عارفين", "probability": 0.877685546875}, {"start": 834.87, "end": 835.07, "word": " ايش", "probability": 0.9475911458333334}, {"start": 835.07, "end": 835.21, "word": " ال", "probability": 0.9560546875}, {"start": 835.21, "end": 835.71, "word": " sk", "probability": 0.94091796875}, {"start": 835.71, "end": 836.27, "word": " ال", "probability": 0.71923828125}, {"start": 836.27, "end": 836.73, "word": " sk", "probability": 0.93798828125}, {"start": 836.73, "end": 837.77, "word": " هو", "probability": 0.98046875}, {"start": 837.77, "end": 838.01, "word": " عبارة", "probability": 0.7703857421875}, {"start": 838.01, "end": 838.15, 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احنا", "probability": 0.9322916666666666}, {"start": 910.69, "end": 911.11, "word": " بنعرف", "probability": 0.8409830729166666}, {"start": 911.11, "end": 911.39, "word": " limit", "probability": 0.9150390625}, {"start": 911.39, "end": 911.59, "word": " ال", "probability": 0.84716796875}, {"start": 911.59, "end": 911.95, "word": " sequence", "probability": 0.93408203125}, {"start": 911.95, "end": 912.15, "word": " و", "probability": 0.70556640625}, {"start": 912.15, "end": 912.23, "word": " ال", "probability": 0.544921875}, {"start": 912.23, "end": 912.41, "word": " tail", "probability": 0.66015625}, {"start": 912.41, "end": 912.71, "word": " لها", "probability": 0.56884765625}, {"start": 912.71, "end": 912.89, "word": " زي", "probability": 0.946044921875}, {"start": 912.89, "end": 913.13, "word": " بعض", "probability": 0.991943359375}, {"start": 913.13, "end": 913.29, "word": " ما", "probability": 0.361083984375}, {"start": 913.29, "end": 913.75, "word": " دامت", "probability": 0.7117513020833334}, {"start": 913.75, "end": 913.87, "word": " ال", "probability": 0.88916015625}, {"start": 913.87, "end": 914.19, "word": " limit", "probability": 0.95556640625}, {"start": 914.19, "end": 914.77, "word": " exist", "probability": 0.63232421875}, {"start": 914.77, "end": 915.67, "word": " لذن", "probability": 0.44140625}, {"start": 915.67, "end": 916.01, "word": " هدولة", "probability": 0.73016357421875}, {"start": 916.01, "end": 916.25, "word": " هذه", "probability": 0.53466796875}, {"start": 916.25, "end": 916.73, "word": " ناقصت", "probability": 0.75673828125}, {"start": 916.73, "end": 916.89, "word": " ايش", "probability": 0.8294270833333334}, {"start": 916.89, "end": 917.37, "word": " هيطلع", "probability": 0.9410400390625}, {"start": 917.37, "end": 917.83, "word": " سفر", "probability": 0.8074544270833334}, {"start": 917.83, "end": 918.33, "word": " لذن", "probability": 0.7740885416666666}, {"start": 918.33, "end": 918.55, "word": " صار", "probability": 0.917236328125}, {"start": 918.55, "end": 918.73, "word": " limit", "probability": 0.83349609375}, {"start": 918.73, "end": 918.87, "word": " ال", "probability": 0.79248046875}, {"start": 918.87, "end": 919.19, "word": " اكسان", "probability": 0.790496826171875}, {"start": 919.19, "end": 919.43, "word": " ايش", "probability": 0.9039713541666666}, {"start": 919.43, "end": 920.01, "word": " بساوي", "probability": 0.7760009765625}, {"start": 920.01, "end": 921.01, "word": " بساوي", "probability": 0.8035888671875}, {"start": 921.01, "end": 921.59, "word": " سفر", "probability": 0.9474283854166666}], "temperature": 1.0}, {"id": 43, "seek": 94204, "start": 922.42, "end": 942.04, "text": "بكون عندنا الي هو وصلنا ل theorem 914 اللي هي خلينا نشوف ايش هذه ال theorem بتقول ركزوا معانا بس اذكركم بشغلة", "tokens": [3555, 30544, 43242, 8315, 45595, 31439, 4032, 36520, 8315, 5296, 20904, 1722, 7271, 13672, 1829, 39896, 16490, 1211, 9957, 995, 8717, 8592, 38688, 1975, 1829, 8592, 29538, 2423, 20904, 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"end": 927.48, "word": " هي", "probability": 0.9267578125}, {"start": 927.48, "end": 927.88, "word": " خلينا", "probability": 0.722900390625}, {"start": 927.88, "end": 928.36, "word": " نشوف", "probability": 0.9921875}, {"start": 928.36, "end": 928.72, "word": " ايش", "probability": 0.7696940104166666}, {"start": 928.72, "end": 929.06, "word": " هذه", "probability": 0.429443359375}, {"start": 929.06, "end": 929.4, "word": " ال", "probability": 0.896484375}, {"start": 929.4, "end": 932.28, "word": " theorem", "probability": 0.71240234375}, {"start": 932.28, "end": 933.02, "word": " بتقول", "probability": 0.975830078125}, {"start": 933.02, "end": 935.24, "word": " ركزوا", "probability": 0.8604736328125}, {"start": 935.24, "end": 936.32, "word": " معانا", "probability": 0.9178059895833334}, {"start": 936.32, "end": 939.68, "word": " بس", "probability": 0.943603515625}, {"start": 939.68, "end": 940.8, "word": " اذكركم", "probability": 0.92919921875}, {"start": 940.8, "end": 942.04, "word": " بشغلة", "probability": 0.7896728515625}], "temperature": 1.0}, {"id": 44, "seek": 96076, "start": 943.36, "end": 960.76, "text": "إنه إحنا في الـ monotone convergence theorem في تحليل حقيقي واحد كنا نقول إنه إذا كانت ال sequence increasing أو decreasing يعني لو كانت monotone then the sequence converge if and only if it is bounded", "tokens": [28814, 1863, 3224, 11933, 5016, 8315, 8978, 2423, 39184, 1108, 310, 546, 32181, 20904, 8978, 6055, 5016, 20292, 1211, 11331, 38436, 38436, 36764, 24401, 9122, 8315, 8717, 39648, 36145, 3224, 11933, 15730, 25961, 2655, 2423, 8310, 5662, 34051, 23223, 37495, 22653, 45164, 25961, 2655, 1108, 310, 546, 550, 264, 8310, 41881, 498, 293, 787, 498, 309, 307, 37498], "avg_logprob": -0.1818061369960591, "compression_ratio": 1.5028901734104045, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 943.36, "end": 943.96, "word": "إنه", "probability": 0.536865234375}, {"start": 943.96, "end": 944.44, "word": " إحنا", "probability": 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956.62, "end": 957.44, "word": " the", "probability": 0.66552734375}, {"start": 957.44, "end": 957.92, "word": " sequence", "probability": 0.97705078125}, {"start": 957.92, "end": 958.62, "word": " converge", "probability": 0.497314453125}, {"start": 958.62, "end": 958.88, "word": " if", "probability": 0.931640625}, {"start": 958.88, "end": 959.16, "word": " and", "probability": 0.96044921875}, {"start": 959.16, "end": 959.44, "word": " only", "probability": 0.81787109375}, {"start": 959.44, "end": 959.78, "word": " if", "probability": 0.9677734375}, {"start": 959.78, "end": 960.0, "word": " it", "probability": 0.96630859375}, {"start": 960.0, "end": 960.3, "word": " is", "probability": 0.89697265625}, {"start": 960.3, "end": 960.76, "word": " bounded", "probability": 0.939453125}], "temperature": 1.0}, {"id": 45, "seek": 98522, "start": 962.06, "end": 985.22, "text": "هذه اللي هو في حالة مين الـ monotone functions لكن in general كنا نقول إن الـ sequence is convergent على طول اللي بيعطينا then it is bounded but it may be bounded بط إي شمالها is not convergent وكنا نقول ناخد مثال ناقص واحد على أن ال sequence هذه أو ناقص واحد أس أن ناقص واحد أس أن", "tokens": [3224, 24192, 13672, 1829, 31439, 8978, 11331, 6027, 3660, 3714, 9957, 2423, 39184, 1108, 310, 546, 6828, 44381, 294, 2674, 9122, 8315, 8717, 39648, 36145, 2423, 39184, 8310, 307, 9652, 6930, 15844, 23032, 12610, 13672, 1829, 4724, 40228, 9566, 1829, 8315, 550, 309, 307, 37498, 457, 309, 815, 312, 37498, 4724, 9566, 11933, 1829, 13412, 2304, 6027, 11296, 307, 406, 9652, 6930, 4032, 4117, 8315, 8717, 39648, 8717, 47283, 3215, 50113, 6027, 8717, 995, 4587, 9381, 36764, 24401, 15844, 14739, 2423, 8310, 29538, 34051, 8717, 995, 4587, 9381, 36764, 24401, 5551, 3794, 14739, 8717, 995, 4587, 9381, 36764, 24401, 5551, 3794, 14739], "avg_logprob": -0.27017598013276034, "compression_ratio": 1.7797356828193833, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 962.06, "end": 962.42, "word": "هذه", 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{"start": 982.58, "end": 982.98, "word": " ناقص", "probability": 0.9827880859375}, {"start": 982.98, "end": 983.3, "word": " واحد", "probability": 0.9794921875}, {"start": 983.3, "end": 983.56, "word": " أس", "probability": 0.642578125}, {"start": 983.56, "end": 983.82, "word": " أن", "probability": 0.7392578125}, {"start": 983.82, "end": 984.42, "word": " ناقص", "probability": 0.9093017578125}, {"start": 984.42, "end": 984.72, "word": " واحد", "probability": 0.98486328125}, {"start": 984.72, "end": 984.98, "word": " أس", "probability": 0.970458984375}, {"start": 984.98, "end": 985.22, "word": " أن", "probability": 0.94482421875}], "temperature": 1.0}, {"id": 46, "seek": 101420, "start": 985.8, "end": 1014.2, "text": "نقص واحد وثاني هذه الـ sequence bounded لأن قيمتها الـ absolute value لها واحد but اللي هو ال limit اللي لها does not exist لكن في حالة الـ monotone function لأ ال boundedness يكافئ ال convergence لأن هذا بدنا اللي هو الآن نطبق على ال monotone convergence theorem أو نستخدمها في إثبات نظريتنا اللي هي 914 theorem لت XN be a sequence of non-negative real numbers", "tokens": [1863, 4587, 9381, 36764, 24401, 4032, 12984, 7649, 1829, 29538, 2423, 39184, 8310, 37498, 5296, 33456, 12174, 32640, 2655, 11296, 2423, 39184, 8236, 2158, 5296, 11296, 36764, 24401, 457, 13672, 1829, 31439, 2423, 4948, 13672, 1829, 5296, 11296, 775, 406, 2514, 44381, 8978, 11331, 6027, 3660, 2423, 39184, 1108, 310, 546, 2445, 5296, 10721, 2423, 37498, 1287, 7251, 4117, 31845, 19986, 2423, 32181, 5296, 33456, 23758, 47525, 8315, 13672, 1829, 31439, 6024, 48506, 8717, 9566, 3555, 4587, 15844, 2423, 1108, 310, 546, 32181, 20904, 34051, 8717, 14851, 9778, 40448, 11296, 8978, 11933, 12984, 3555, 9307, 8717, 19913, 16572, 2655, 8315, 13672, 1829, 39896, 1722, 7271, 20904, 5296, 2655, 1783, 45, 312, 257, 8310, 295, 2107, 12, 28561, 1166, 957, 3547], "avg_logprob": -0.289514449017107, "compression_ratio": 1.679054054054054, "no_speech_prob": 0.0, "words": [{"start": 985.8, "end": 986.2, 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"word": " هذا", "probability": 0.97216796875}, {"start": 1000.76, "end": 1001.24, "word": " بدنا", "probability": 0.855224609375}, {"start": 1001.24, "end": 1001.44, "word": " اللي", "probability": 0.95751953125}, {"start": 1001.44, "end": 1001.64, "word": " هو", "probability": 0.99365234375}, {"start": 1001.64, "end": 1002.1, "word": " الآن", "probability": 0.758056640625}, {"start": 1002.1, "end": 1003.1, "word": " نطبق", "probability": 0.8916015625}, {"start": 1003.1, "end": 1003.34, "word": " على", "probability": 0.708984375}, {"start": 1003.34, "end": 1003.52, "word": " ال", "probability": 0.955078125}, {"start": 1003.52, "end": 1003.88, "word": " monotone", "probability": 0.8041178385416666}, {"start": 1003.88, "end": 1004.34, "word": " convergence", "probability": 0.962890625}, {"start": 1004.34, "end": 1004.94, "word": " theorem", "probability": 0.92578125}, {"start": 1004.94, "end": 1005.56, "word": " أو", "probability": 0.8349609375}, {"start": 1005.56, "end": 1006.48, "word": " نستخدمها", "probability": 0.99326171875}, {"start": 1006.48, "end": 1007.14, "word": " في", "probability": 0.9677734375}, {"start": 1007.14, "end": 1007.82, "word": " إثبات", "probability": 0.87939453125}, {"start": 1007.82, "end": 1008.76, "word": " نظريتنا", "probability": 0.98271484375}, {"start": 1008.76, "end": 1009.24, "word": " اللي", "probability": 0.58514404296875}, {"start": 1009.24, "end": 1009.36, "word": " هي", "probability": 0.373046875}, {"start": 1009.36, "end": 1009.98, "word": " 914", "probability": 0.4560546875}, {"start": 1009.98, "end": 1010.6, "word": " theorem", "probability": 0.7646484375}, {"start": 1010.6, "end": 1010.98, "word": " لت", "probability": 0.729736328125}, {"start": 1010.98, "end": 1011.48, "word": " XN", "probability": 0.305908203125}, {"start": 1011.48, "end": 1011.7, "word": " be", "probability": 0.46240234375}, {"start": 1011.7, "end": 1011.9, "word": " a", "probability": 0.9677734375}, {"start": 1011.9, "end": 1012.42, "word": " sequence", "probability": 0.9794921875}, {"start": 1012.42, "end": 1012.7, "word": " of", "probability": 0.9755859375}, {"start": 1012.7, "end": 1012.98, "word": " non", "probability": 0.93896484375}, {"start": 1012.98, "end": 1013.44, "word": "-negative", "probability": 0.7276204427083334}, {"start": 1013.44, "end": 1013.72, "word": " real", "probability": 0.95654296875}, {"start": 1013.72, "end": 1014.2, "word": " numbers", "probability": 0.89990234375}], "temperature": 1.0}, {"id": 47, "seek": 102482, "start": 1014.56, "end": 1024.82, "text": "إذا حكينا عن مين عن sequence xn عنصرها إيش ما لها non negative real numbers يعني أكبر أو تساوي سفر", "tokens": [28814, 15730, 11331, 4117, 1829, 8315, 18871, 3714, 9957, 18871, 8310, 2031, 77, 18871, 9381, 2288, 11296, 11933, 1829, 8592, 19446, 5296, 11296, 2107, 3671, 957, 3547, 37495, 22653, 5551, 4117, 26890, 34051, 6055, 3794, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.3243140185751566, "compression_ratio": 1.1885245901639345, 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case ال summation لـ xn بسوى limit لSk بسوى سبريمان لSk يعني الآن و كأنه بيقوللي إنه limit", "tokens": [12984, 2304, 2423, 39184, 28811, 5296, 39184, 2031, 77, 9154, 21136, 13546, 1829, 11622, 6055, 3555, 34268, 11296, 38874, 498, 293, 787, 498, 264, 8310, 318, 39894, 3794, 2407, 7578, 7324, 295, 14641, 34499, 307, 37498, 37495, 22653, 6024, 48506, 21136, 13546, 1829, 11622, 2423, 28811, 2031, 77, 13672, 1829, 39896, 8032, 2655, 30544, 38874, 11933, 15730, 4032, 6156, 47432, 11933, 15730, 2423, 7324, 11933, 8592, 2304, 6027, 11296, 307, 37498, 294, 341, 1389, 2423, 28811, 5296, 39184, 2031, 77, 4724, 3794, 2407, 7578, 4948, 5296, 50, 74, 4724, 3794, 2407, 7578, 8608, 3555, 16572, 2304, 7649, 5296, 50, 74, 37495, 22653, 6024, 48506, 4032, 9122, 33456, 3224, 4724, 1829, 39648, 20292, 36145, 3224, 4948], "avg_logprob": -0.3981681001083604, "compression_ratio": 1.7469387755102042, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1026.49, "end": 1026.99, "word": "ثم", "probability": 0.57550048828125}, {"start": 1026.99, "end": 1027.33, "word": " الـ", "probability": 0.30133056640625}, {"start": 1027.33, "end": 1027.77, "word": " summation", "probability": 0.568359375}, {"start": 1027.77, "end": 1028.07, "word": " لـ", "probability": 0.6090087890625}, {"start": 1028.07, "end": 1028.39, "word": " xn", "probability": 0.31298828125}, {"start": 1028.39, "end": 1028.63, "word": " من", "probability": 0.294189453125}, {"start": 1028.63, "end": 1028.89, "word": " السيريز", "probability": 0.74530029296875}, {"start": 1028.89, "end": 1029.69, "word": " تبعتها", "probability": 0.687408447265625}, {"start": 1029.69, "end": 1030.63, "word": " converts", "probability": 0.346923828125}, {"start": 1030.63, "end": 1031.17, "word": " if", "probability": 0.85595703125}, {"start": 1031.17, "end": 1031.43, "word": " and", "probability": 0.90869140625}, {"start": 1031.43, "end": 1031.69, "word": " only", "probability": 0.818359375}, {"start": 1031.69, "end": 1031.89, 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إذا", "probability": 0.99072265625}, {"start": 1042.81, "end": 1043.27, "word": " ال", "probability": 0.818359375}, {"start": 1043.27, "end": 1043.63, "word": " Sk", "probability": 0.45263671875}, {"start": 1043.63, "end": 1044.43, "word": " إشمالها", "probability": 0.8212890625}, {"start": 1044.43, "end": 1045.07, "word": " is", "probability": 0.91357421875}, {"start": 1045.07, "end": 1045.69, "word": " bounded", "probability": 0.93017578125}, {"start": 1045.69, "end": 1046.47, "word": " in", "probability": 0.787109375}, {"start": 1046.47, "end": 1046.81, "word": " this", "probability": 0.9658203125}, {"start": 1046.81, "end": 1047.43, "word": " case", "probability": 0.9306640625}, {"start": 1047.43, "end": 1047.95, "word": " ال", "probability": 0.42529296875}, {"start": 1047.95, "end": 1048.41, "word": " summation", "probability": 0.9189453125}, {"start": 1048.41, "end": 1048.69, "word": " لـ", "probability": 0.505859375}, {"start": 1048.69, "end": 1048.97, "word": " xn", "probability": 0.855224609375}, {"start": 1048.97, "end": 1049.29, "word": " بسوى", "probability": 0.655029296875}, {"start": 1049.29, "end": 1049.51, "word": " limit", "probability": 0.81103515625}, {"start": 1049.51, "end": 1050.25, "word": " لSk", "probability": 0.700439453125}, {"start": 1050.25, "end": 1050.97, "word": " بسوى", "probability": 0.8037109375}, {"start": 1050.97, "end": 1051.73, "word": " سبريمان", "probability": 0.676171875}, {"start": 1051.73, "end": 1052.89, "word": " لSk", "probability": 0.606689453125}, {"start": 1052.89, "end": 1053.35, "word": " يعني", "probability": 0.969970703125}, {"start": 1053.35, "end": 1053.65, "word": " الآن", "probability": 0.6865234375}, {"start": 1053.65, "end": 1053.81, "word": " و", "probability": 0.4990234375}, {"start": 1053.81, "end": 1054.11, "word": " كأنه", "probability": 0.531494140625}, {"start": 1054.11, "end": 1054.71, "word": " بيقوللي", "probability": 0.71673583984375}, {"start": 1054.71, "end": 1055.11, "word": " إنه", "probability": 0.4486083984375}, {"start": 1055.11, "end": 1055.65, "word": " limit", "probability": 0.83056640625}], "temperature": 1.0}, {"id": 49, "seek": 107299, "start": 1056.63, "end": 1072.99, "text": "الـ SK exists if and only if SK is bounded هذه الـ SK هي الـ sequence of partial sums تبع السيريز limit الـ SK هي السيريز نفسها الـ x and n من واحد إلى مانع نهاية", "tokens": [6027, 39184, 21483, 2514, 82, 498, 293, 787, 498, 21483, 307, 37498, 29538, 2423, 39184, 21483, 39896, 2423, 39184, 8310, 295, 14641, 34499, 6055, 3555, 3615, 21136, 13546, 1829, 11622, 4948, 2423, 39184, 21483, 39896, 21136, 13546, 1829, 11622, 8717, 36178, 11296, 2423, 39184, 2031, 293, 297, 9154, 36764, 24401, 30731, 3714, 7649, 3615, 8717, 11296, 10632], "avg_logprob": -0.4692887895066163, "compression_ratio": 1.4, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 1056.63, "end": 1056.99, "word": "الـ", "probability": 0.71337890625}, {"start": 1056.99, "end": 1057.37, "word": " SK", "probability": 0.2391357421875}, {"start": 1057.37, "end": 1059.57, "word": " exists", "probability": 0.32232666015625}, {"start": 1059.57, "end": 1059.83, "word": " if", "probability": 0.8818359375}, {"start": 1059.83, "end": 1060.09, "word": " and", "probability": 0.8955078125}, {"start": 1060.09, "end": 1060.35, "word": " only", "probability": 0.92822265625}, {"start": 1060.35, "end": 1060.73, "word": " if", "probability": 0.9794921875}, {"start": 1060.73, "end": 1061.31, "word": " SK", "probability": 0.93798828125}, {"start": 1061.31, "end": 1062.75, "word": " is", "probability": 0.9296875}, {"start": 1062.75, "end": 1063.35, "word": " bounded", "probability": 0.93212890625}, {"start": 1063.35, "end": 1064.37, "word": " هذه", "probability": 0.232421875}, {"start": 1064.37, "end": 1064.81, "word": " الـ", "probability": 0.6343994140625}, {"start": 1064.81, "end": 1065.13, "word": " SK", "probability": 0.365478515625}, {"start": 1065.13, "end": 1065.49, "word": " هي", "probability": 0.6552734375}, {"start": 1065.49, "end": 1065.67, "word": " الـ", "probability": 0.5018310546875}, {"start": 1065.67, "end": 1065.89, "word": " sequence", "probability": 0.75390625}, {"start": 1065.89, "end": 1066.07, "word": " of", "probability": 0.31982421875}, {"start": 1066.07, "end": 1066.31, "word": " partial", "probability": 0.84765625}, {"start": 1066.31, "end": 1066.71, "word": " sums", "probability": 0.9677734375}, {"start": 1066.71, "end": 1067.03, "word": " تبع", "probability": 0.7205403645833334}, {"start": 1067.03, "end": 1067.75, "word": " السيريز", "probability": 0.786865234375}, {"start": 1067.75, "end": 1068.41, "word": " limit", "probability": 0.07867431640625}, {"start": 1068.41, "end": 1068.63, "word": " الـ", "probability": 0.4246826171875}, {"start": 1068.63, "end": 1068.93, "word": " SK", "probability": 0.9658203125}, {"start": 1068.93, "end": 1069.23, "word": " هي", "probability": 0.87060546875}, {"start": 1069.23, "end": 1069.73, "word": " السيريز", "probability": 0.9285888671875}, {"start": 1069.73, "end": 1070.23, "word": " نفسها", "probability": 0.9833984375}, {"start": 1070.23, "end": 1070.45, "word": " الـ", "probability": 0.5147705078125}, {"start": 1070.45, "end": 1070.63, "word": " x", "probability": 0.435546875}, {"start": 1070.63, "end": 1070.91, "word": " and", "probability": 0.076904296875}, {"start": 1070.91, "end": 1071.09, "word": " n", "probability": 0.74755859375}, {"start": 1071.09, "end": 1071.25, "word": " من", "probability": 0.93212890625}, {"start": 1071.25, "end": 1071.79, "word": " واحد", "probability": 0.662109375}, {"start": 1071.79, "end": 1072.09, "word": " إلى", "probability": 0.9091796875}, {"start": 1072.09, "end": 1072.53, "word": " مانع", "probability": 0.5465494791666666}, {"start": 1072.53, "end": 1072.99, "word": " نهاية", "probability": 0.8190104166666666}], "temperature": 1.0}, {"id": 50, "seek": 109369, "start": 1073.57, "end": 1093.69, "text": "الآن باختصار اللي هو هنقوله أنه أصلا هذه ال SQL sequence of partial sums is an increasing sequence مدام increasing يعني بمعنى آخر monotone أو بالظبط اللي هو خلّيني أقول واحدة من ال monotone هي increasing ت increasing هي increasing علنا الآن مدام increasing", "tokens": [6027, 148, 48506, 4724, 47283, 2655, 9381, 9640, 13672, 1829, 31439, 8032, 1863, 39648, 3224, 14739, 3224, 5551, 9381, 15040, 29538, 2423, 19200, 8310, 295, 14641, 34499, 307, 364, 5662, 8310, 3714, 3215, 10943, 5662, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 19753, 34740, 1108, 310, 546, 34051, 20666, 19913, 3555, 9566, 13672, 1829, 31439, 16490, 1211, 11703, 9957, 1829, 5551, 39648, 36764, 24401, 3660, 9154, 2423, 1108, 310, 546, 39896, 5662, 6055, 5662, 39896, 5662, 11203, 8315, 6024, 48506, 3714, 3215, 10943, 5662], "avg_logprob": -0.29577206443337833, "compression_ratio": 1.708133971291866, "no_speech_prob": 0.0, "words": [{"start": 1073.57, "end": 1074.05, "word": "الآن", "probability": 0.5706380208333334}, {"start": 1074.05, "end": 1074.89, "word": " باختصار", "probability": 0.941015625}, {"start": 1074.89, "end": 1075.41, "word": " اللي", "probability": 0.627197265625}, {"start": 1075.41, "end": 1075.55, "word": " هو", "probability": 0.5498046875}, {"start": 1075.55, "end": 1076.87, "word": " هنقوله", "probability": 0.713134765625}, {"start": 1076.87, "end": 1077.17, "word": " أنه", "probability": 0.662353515625}, {"start": 1077.17, "end": 1077.59, "word": " أصلا", "probability": 0.8981119791666666}, {"start": 1077.59, "end": 1078.11, "word": " هذه", "probability": 0.6103515625}, {"start": 1078.11, "end": 1078.73, "word": " ال", "probability": 0.767578125}, {"start": 1078.73, "end": 1079.15, "word": " SQL", "probability": 0.0755615234375}, {"start": 1079.15, "end": 1079.67, "word": " sequence", "probability": 0.5615234375}, {"start": 1079.67, "end": 1079.83, "word": " of", "probability": 0.88427734375}, {"start": 1079.83, "end": 1080.13, "word": " partial", "probability": 0.91845703125}, {"start": 1080.13, "end": 1080.57, "word": " sums", "probability": 0.95703125}, {"start": 1080.57, "end": 1080.91, "word": " is", "probability": 0.78466796875}, {"start": 1080.91, "end": 1081.21, "word": " an", "probability": 0.91650390625}, {"start": 1081.21, "end": 1081.81, "word": " increasing", "probability": 0.93408203125}, {"start": 1081.81, "end": 1082.65, "word": " sequence", "probability": 0.966796875}, {"start": 1082.65, "end": 1083.31, "word": " مدام", "probability": 0.7654622395833334}, {"start": 1083.31, "end": 1083.83, "word": " increasing", "probability": 0.837890625}, {"start": 1083.83, "end": 1084.55, "word": " يعني", "probability": 0.946044921875}, {"start": 1084.55, "end": 1084.91, "word": " بمعنى", "probability": 0.98056640625}, {"start": 1084.91, "end": 1085.25, "word": " آخر", "probability": 0.77783203125}, {"start": 1085.25, "end": 1085.95, "word": " monotone", "probability": 0.698486328125}, {"start": 1085.95, "end": 1086.81, "word": " أو", "probability": 0.853515625}, {"start": 1086.81, "end": 1087.43, "word": " بالظبط", "probability": 0.9671630859375}, {"start": 1087.43, "end": 1087.63, "word": " اللي", "probability": 0.96875}, {"start": 1087.63, "end": 1087.85, "word": " هو", "probability": 0.9853515625}, {"start": 1087.85, "end": 1088.27, "word": " خلّيني", "probability": 0.657763671875}, {"start": 1088.27, "end": 1088.59, "word": " أقول", "probability": 0.93505859375}, {"start": 1088.59, "end": 1089.49, "word": " واحدة", "probability": 0.7728678385416666}, {"start": 1089.49, "end": 1089.59, "word": " من", "probability": 0.99560546875}, {"start": 1089.59, "end": 1089.71, "word": " ال", "probability": 0.69140625}, {"start": 1089.71, "end": 1090.09, "word": " monotone", "probability": 0.7713216145833334}, {"start": 1090.09, "end": 1090.21, "word": " هي", "probability": 0.201171875}, {"start": 1090.21, "end": 1090.49, "word": " increasing", "probability": 0.9736328125}, {"start": 1090.49, "end": 1090.71, "word": " ت", "probability": 0.236328125}, {"start": 1090.71, "end": 1091.13, "word": " increasing", "probability": 0.85498046875}, {"start": 1091.13, "end": 1091.35, "word": " هي", "probability": 0.8798828125}, {"start": 1091.35, "end": 1091.73, "word": " increasing", "probability": 0.990234375}, {"start": 1091.73, "end": 1092.09, "word": " علنا", "probability": 0.738037109375}, {"start": 1092.09, "end": 1092.53, "word": " الآن", "probability": 0.799072265625}, {"start": 1092.53, "end": 1093.13, "word": " مدام", "probability": 0.8893229166666666}, {"start": 1093.13, "end": 1093.69, "word": " increasing", "probability": 0.98681640625}], "temperature": 1.0}, {"id": 51, "seek": 111607, "start": 1094.51, "end": 1116.07, "text": "هيكون عنده الـ Existence limit يكافي الـ Boundedness ويكون خلصنا برهان النظرية حسب الـ Newton convergence theorem ومش هيك وهيكون limit هاش ما لمدام increasing السبريمام لعنصرها هذه الـ Newton convergence theorem خليني نشوف هذا الكلام بالتفصيل اللي حكيته", "tokens": [3224, 1829, 30544, 43242, 3224, 2423, 39184, 2111, 468, 655, 4948, 7251, 4117, 31845, 1829, 2423, 39184, 363, 37706, 1287, 4032, 1829, 30544, 16490, 1211, 9381, 8315, 4724, 2288, 3224, 7649, 28239, 19913, 2288, 10632, 11331, 35457, 2423, 39184, 19541, 32181, 20904, 4032, 2304, 8592, 39896, 4117, 4032, 3224, 1829, 30544, 4948, 8032, 33599, 19446, 32767, 3215, 10943, 5662, 21136, 3555, 16572, 2304, 10943, 5296, 3615, 1863, 9381, 2288, 11296, 29538, 2423, 39184, 19541, 32181, 20904, 16490, 1211, 9957, 1829, 8717, 8592, 38688, 23758, 2423, 28820, 10943, 20666, 2655, 5172, 9381, 26895, 13672, 1829, 11331, 4117, 36081, 3224], "avg_logprob": -0.39930554953488434, "compression_ratio": 1.645021645021645, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1094.51, "end": 1095.03, "word": "هيكون", "probability": 0.5684407552083334}, {"start": 1095.03, "end": 1095.53, "word": " عنده", "probability": 0.34619140625}, {"start": 1095.53, "end": 1096.05, "word": " الـ", "probability": 0.59326171875}, {"start": 1096.05, "end": 1097.05, "word": " Existence", "probability": 0.7740885416666666}, {"start": 1097.05, "end": 1097.49, "word": " limit", "probability": 0.473388671875}, {"start": 1097.49, "end": 1098.25, "word": " يكافي", "probability": 0.7447509765625}, {"start": 1098.25, "end": 1098.49, "word": " الـ", "probability": 0.5753173828125}, {"start": 1098.49, "end": 1099.13, "word": " Boundedness", "probability": 0.7371419270833334}, {"start": 1099.13, "end": 1099.39, "word": " ويكون", "probability": 0.5062662760416666}, {"start": 1099.39, "end": 1099.89, "word": " خلصنا", "probability": 0.796142578125}, {"start": 1099.89, "end": 1100.33, "word": " برهان", "probability": 0.831787109375}, {"start": 1100.33, "end": 1101.33, "word": " النظرية", "probability": 0.9210205078125}, {"start": 1101.33, "end": 1101.79, "word": " حسب", "probability": 0.75732421875}, {"start": 1101.79, "end": 1101.93, "word": " الـ", "probability": 0.526123046875}, {"start": 1101.93, "end": 1102.03, "word": " Newton", "probability": 0.83740234375}, {"start": 1102.03, "end": 1102.53, "word": " convergence", "probability": 0.50341796875}, {"start": 1102.53, "end": 1102.99, "word": " theorem", "probability": 0.91796875}, {"start": 1102.99, "end": 1103.63, "word": " ومش", "probability": 0.6509195963541666}, {"start": 1103.63, "end": 1103.85, "word": " هيك", "probability": 0.942626953125}, {"start": 1103.85, "end": 1104.31, "word": " وهيكون", "probability": 0.71734619140625}, {"start": 1104.31, "end": 1104.65, "word": " limit", "probability": 0.6240234375}, {"start": 1104.65, "end": 1105.19, "word": " هاش", "probability": 0.343994140625}, {"start": 1105.19, "end": 1105.37, "word": " ما", "probability": 0.52685546875}, {"start": 1105.37, "end": 1105.89, "word": " لمدام", "probability": 0.8102213541666666}, {"start": 1105.89, "end": 1106.63, "word": " increasing", "probability": 0.76708984375}, {"start": 1106.63, "end": 1108.49, "word": " السبريمام", "probability": 0.644873046875}, {"start": 1108.49, "end": 1110.77, "word": " لعنصرها", "probability": 0.8000691731770834}, {"start": 1110.77, "end": 1111.75, "word": " هذه", "probability": 0.30712890625}, {"start": 1111.75, "end": 1112.05, "word": " الـ", "probability": 0.35601806640625}, {"start": 1112.05, "end": 1112.27, "word": " Newton", "probability": 0.8564453125}, {"start": 1112.27, "end": 1112.87, "word": " convergence", "probability": 0.95166015625}, {"start": 1112.87, "end": 1113.27, "word": " theorem", "probability": 0.90234375}, {"start": 1113.27, "end": 1113.89, "word": " خليني", "probability": 0.77880859375}, {"start": 1113.89, "end": 1114.19, "word": " نشوف", "probability": 0.8074544270833334}, {"start": 1114.19, "end": 1114.41, "word": " هذا", "probability": 0.2275390625}, {"start": 1114.41, "end": 1114.77, "word": " الكلام", "probability": 0.92333984375}, {"start": 1114.77, "end": 1115.39, "word": " بالتفصيل", "probability": 0.9501953125}, {"start": 1115.39, "end": 1115.51, "word": " اللي", "probability": 0.9365234375}, {"start": 1115.51, "end": 1116.07, "word": " حكيته", "probability": 0.9854736328125}], "temperature": 1.0}, {"id": 52, "seek": 113785, "start": 1117.12, "end": 1137.86, "text": "بما أن xn أكبر يساوي 0 الـ xn أكبر يساوي 0 then the sequence of partial sums is monotone increasing function ليش؟ لأن S1 عبارة عن x1 S1 عبارة عن x1 أكيد أصغر من x1 زاد x2 التي هي مين؟ S2", "tokens": [3555, 15042, 14739, 2031, 77, 5551, 4117, 26890, 7251, 3794, 995, 45865, 1958, 2423, 39184, 2031, 77, 5551, 4117, 26890, 7251, 3794, 995, 45865, 1958, 550, 264, 8310, 295, 14641, 34499, 307, 1108, 310, 546, 5662, 2445, 32239, 8592, 22807, 5296, 33456, 318, 16, 6225, 3555, 9640, 3660, 18871, 2031, 16, 318, 16, 6225, 3555, 9640, 3660, 18871, 2031, 16, 5551, 4117, 25708, 5551, 9381, 17082, 2288, 9154, 2031, 16, 30767, 18513, 2031, 17, 38392, 39896, 3714, 9957, 22807, 318, 17], "avg_logprob": -0.26086126667697257, "compression_ratio": 1.4545454545454546, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1117.12, "end": 1117.54, "word": "بما", "probability": 0.96484375}, {"start": 1117.54, "end": 1117.8, "word": " أن", "probability": 0.49169921875}, {"start": 1117.8, "end": 1118.34, "word": " xn", "probability": 0.4720458984375}, {"start": 1118.34, "end": 1118.74, "word": " أكبر", "probability": 0.796630859375}, {"start": 1118.74, "end": 1119.22, "word": " يساوي", "probability": 0.67279052734375}, {"start": 1119.22, "end": 1119.68, "word": " 0", "probability": 0.456298828125}, {"start": 1119.68, "end": 1120.34, "word": " الـ", "probability": 0.368560791015625}, {"start": 1120.34, "end": 1120.6, "word": " xn", "probability": 0.742431640625}, {"start": 1120.6, "end": 1120.86, "word": " أكبر", "probability": 0.97509765625}, {"start": 1120.86, "end": 1121.08, "word": " يساوي", "probability": 0.9627685546875}, {"start": 1121.08, "end": 1121.48, "word": " 0", "probability": 0.76904296875}, {"start": 1121.48, "end": 1122.14, "word": " then", "probability": 0.258544921875}, {"start": 1122.14, "end": 1122.36, "word": " the", "probability": 0.8193359375}, {"start": 1122.36, "end": 1122.76, "word": " sequence", "probability": 0.970703125}, {"start": 1122.76, "end": 1122.96, "word": " of", "probability": 0.96533203125}, {"start": 1122.96, "end": 1123.3, "word": " partial", "probability": 0.89892578125}, {"start": 1123.3, "end": 1123.86, "word": " sums", "probability": 0.97216796875}, {"start": 1123.86, "end": 1124.56, "word": " is", "probability": 0.931640625}, {"start": 1124.56, "end": 1125.2, "word": " monotone", "probability": 0.8395182291666666}, {"start": 1125.2, "end": 1125.8, "word": " increasing", "probability": 0.4248046875}, {"start": 1125.8, "end": 1126.42, "word": " function", "probability": 0.955078125}, {"start": 1126.42, "end": 1127.36, "word": " ليش؟", "probability": 0.6770833333333334}, {"start": 1127.36, "end": 1127.68, "word": " لأن", "probability": 0.9404296875}, {"start": 1127.68, "end": 1128.54, "word": " S1", "probability": 0.6044921875}, {"start": 1128.54, "end": 1129.2, "word": " 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1212.17, "word": " و", "probability": 0.81103515625}, {"start": 1212.17, "end": 1212.41, "word": " هو", "probability": 0.89208984375}, {"start": 1212.41, "end": 1213.33, "word": " المطلوب", "probability": 0.9779052734375}, {"start": 1213.33, "end": 1214.27, "word": " طيب", "probability": 0.9469401041666666}, {"start": 1214.27, "end": 1216.33, "word": " هذا", "probability": 0.560546875}, {"start": 1216.33, "end": 1217.11, "word": " لما", "probability": 0.78125}, {"start": 1217.11, "end": 1217.39, "word": " يكون", "probability": 0.9775390625}, {"start": 1217.39, "end": 1217.53, "word": " ال", "probability": 0.93994140625}, {"start": 1217.53, "end": 1217.77, "word": " terms", "probability": 0.6875}, {"start": 1217.77, "end": 1218.17, "word": " سبعات", "probability": 0.6793212890625}, {"start": 1218.17, "end": 1218.27, "word": " ال", "probability": 0.92578125}, {"start": 1218.27, "end": 1218.61, "word": " sequence", "probability": 0.9677734375}, {"start": 1218.61, "end": 1219.33, "word": " يشملها", "probability": 0.77850341796875}, {"start": 1219.33, "end": 1220.47, "word": " موجبات", "probability": 0.9552001953125}, {"start": 1220.47, "end": 1220.65, "word": " أو", "probability": 0.8095703125}, {"start": 1220.65, "end": 1221.25, "word": " non", "probability": 0.44970703125}, {"start": 1221.25, "end": 1221.63, "word": " negative", "probability": 0.6416015625}], "temperature": 1.0}, {"id": 57, "seek": 124660, "start": 1222.71, "end": 1246.61, "text": "الانكوشي criterion for اللي هو series احنا زي ما كنا نقول في التحليل الحقيقي واحد احيانا ما بنقدرش نعرف ايش ال limit لكن بنكون عارفين ان ال sequence نفسها converts فبدنا نعبر عن ال convergence لل sequence بطريقة اللي هي ال terms تبعتها مش عن طريقة اللي هي معرفة ال limit", "tokens": [6027, 7649, 4117, 2407, 8592, 1829, 46691, 337, 13672, 1829, 31439, 2638, 1975, 5016, 8315, 30767, 1829, 19446, 9122, 8315, 8717, 39648, 8978, 16712, 5016, 20292, 1211, 21542, 38436, 38436, 36764, 24401, 1975, 5016, 1829, 7649, 995, 19446, 44945, 28543, 2288, 8592, 8717, 3615, 28480, 1975, 1829, 8592, 2423, 4948, 44381, 44945, 30544, 6225, 9640, 5172, 9957, 16472, 2423, 8310, 8717, 36178, 11296, 38874, 6156, 44510, 8315, 8717, 3615, 26890, 18871, 2423, 32181, 24976, 8310, 4724, 9566, 16572, 28671, 13672, 1829, 39896, 2423, 2115, 6055, 3555, 34268, 11296, 37893, 18871, 23032, 16572, 28671, 13672, 1829, 39896, 20449, 28480, 3660, 2423, 4948], "avg_logprob": -0.18290441074207717, "compression_ratio": 1.7957446808510638, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1222.71, "end": 1223.51, "word": "الانكوشي", "probability": 0.5163370768229166}, {"start": 1223.51, "end": 1224.07, "word": " criterion", "probability": 0.181396484375}, {"start": 1224.07, "end": 1224.87, "word": " for", "probability": 0.533203125}, {"start": 1224.87, "end": 1225.27, "word": " اللي", "probability": 0.76123046875}, {"start": 1225.27, "end": 1225.67, "word": " هو", "probability": 0.98583984375}, {"start": 1225.67, "end": 1226.35, "word": " series", "probability": 0.64013671875}, {"start": 1226.35, "end": 1227.59, "word": " احنا", "probability": 0.8208821614583334}, {"start": 1227.59, "end": 1228.93, "word": " زي", "probability": 0.967041015625}, {"start": 1228.93, "end": 1229.03, "word": " ما", "probability": 0.98583984375}, {"start": 1229.03, "end": 1229.29, "word": " كنا", "probability": 0.9716796875}, {"start": 1229.29, "end": 1229.61, "word": " نقول", "probability": 0.97265625}, {"start": 1229.61, "end": 1229.81, "word": " في", "probability": 0.93701171875}, {"start": 1229.81, "end": 1230.69, "word": " التحليل", "probability": 0.922607421875}, {"start": 1230.69, "end": 1231.11, "word": " الحقيقي", "probability": 0.966796875}, {"start": 1231.11, "end": 1231.43, "word": " واحد", "probability": 0.96923828125}, {"start": 1231.43, "end": 1231.87, "word": " احيانا", "probability": 0.86220703125}, {"start": 1231.87, "end": 1231.99, "word": " ما", "probability": 0.6943359375}, {"start": 1231.99, "end": 1232.53, "word": " بنقدرش", "probability": 0.8765869140625}, {"start": 1232.53, "end": 1232.91, "word": " نعرف", "probability": 0.9694010416666666}, {"start": 1232.91, "end": 1233.13, "word": " ايش", "probability": 0.7906901041666666}, {"start": 1233.13, "end": 1233.27, "word": " ال", "probability": 0.8134765625}, {"start": 1233.27, "end": 1233.59, "word": " limit", "probability": 0.8876953125}, {"start": 1233.59, "end": 1234.51, "word": " لكن", "probability": 0.80859375}, {"start": 1234.51, "end": 1235.11, "word": " بنكون", "probability": 0.646728515625}, {"start": 1235.11, "end": 1236.61, "word": " عارفين", "probability": 0.9918212890625}, {"start": 1236.61, "end": 1236.77, "word": " ان", "probability": 0.78271484375}, {"start": 1236.77, "end": 1236.93, "word": " ال", "probability": 0.86865234375}, {"start": 1236.93, "end": 1237.31, "word": " sequence", "probability": 0.9482421875}, {"start": 1237.31, "end": 1237.99, "word": " نفسها", "probability": 0.9939778645833334}, {"start": 1237.99, "end": 1238.87, "word": " converts", "probability": 0.458740234375}, {"start": 1238.87, "end": 1239.51, "word": " فبدنا", "probability": 0.7928059895833334}, {"start": 1239.51, "end": 1239.91, "word": " نعبر", "probability": 0.85302734375}, {"start": 1239.91, "end": 1240.21, "word": " عن", "probability": 0.99072265625}, {"start": 1240.21, "end": 1240.75, "word": " ال", "probability": 0.9169921875}, {"start": 1240.75, "end": 1241.27, "word": " convergence", "probability": 0.9873046875}, {"start": 1241.27, "end": 1241.61, "word": " لل", "probability": 0.7978515625}, {"start": 1241.61, "end": 1242.19, "word": " sequence", "probability": 0.9716796875}, {"start": 1242.19, "end": 1242.87, "word": " بطريقة", "probability": 0.9432373046875}, {"start": 1242.87, "end": 1243.03, "word": " اللي", "probability": 0.948486328125}, {"start": 1243.03, "end": 1243.29, "word": " هي", "probability": 0.939453125}, {"start": 1243.29, "end": 1243.53, "word": " ال", "probability": 0.8623046875}, {"start": 1243.53, "end": 1243.93, "word": " terms", "probability": 0.9365234375}, {"start": 1243.93, "end": 1244.55, "word": " تبعتها", "probability": 0.866455078125}, {"start": 1244.55, "end": 1244.73, "word": " مش", "probability": 0.955078125}, {"start": 1244.73, "end": 1244.95, "word": " عن", "probability": 0.95654296875}, {"start": 1244.95, "end": 1245.43, "word": " طريقة", "probability": 0.9567057291666666}, {"start": 1245.43, "end": 1245.59, "word": " اللي", "probability": 0.9267578125}, {"start": 1245.59, "end": 1245.77, "word": " هي", "probability": 0.888671875}, {"start": 1245.77, "end": 1246.21, "word": " معرفة", "probability": 0.9894205729166666}, {"start": 1246.21, "end": 1246.35, "word": " ال", "probability": 0.91943359375}, {"start": 1246.35, "end": 1246.61, "word": " limit", "probability": 0.97998046875}], "temperature": 1.0}, {"id": 58, "seek": 127405, "start": 1247.01, "end": 1274.05, "text": "فكنا نقول إن الـ xn مثلاً is a Cauchy sequence if and only if for every y أكبر من 0 there exists k element in N such that for every n و m أكبر من k يكون الـ absolute value للـ xn ناقص xm أصغر من إبسلول نحن نجيب اللي هو Cauchy criterion مشابه إليها بس لمين لحالة السيريز ما هي هذه السيريز زي ما قلنا هي عبارة عن في النهاية sequence of partial sums", "tokens": [5172, 4117, 8315, 8717, 39648, 36145, 2423, 39184, 2031, 77, 50113, 15040, 14111, 307, 257, 7544, 625, 88, 8310, 498, 293, 787, 498, 337, 633, 288, 5551, 4117, 26890, 9154, 1958, 456, 8198, 350, 4478, 294, 426, 1270, 300, 337, 633, 297, 4032, 275, 5551, 4117, 26890, 9154, 350, 7251, 30544, 2423, 39184, 8236, 2158, 24976, 39184, 2031, 77, 8717, 995, 4587, 9381, 2031, 76, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 1211, 12610, 8717, 5016, 1863, 8717, 7435, 1829, 3555, 13672, 1829, 31439, 7544, 625, 88, 46691, 37893, 16758, 3224, 11933, 20292, 11296, 4724, 3794, 32767, 9957, 5296, 5016, 6027, 3660, 21136, 13546, 1829, 11622, 19446, 39896, 29538, 21136, 13546, 1829, 11622, 30767, 1829, 19446, 12174, 1211, 8315, 39896, 6225, 3555, 9640, 3660, 18871, 8978, 28239, 11296, 10632, 8310, 295, 14641, 34499], "avg_logprob": -0.268981467794489, "compression_ratio": 1.5973597359735974, "no_speech_prob": 0.0, "words": [{"start": 1247.01, "end": 1247.49, "word": "فكنا", "probability": 0.504150390625}, {"start": 1247.49, "end": 1247.81, "word": " نقول", "probability": 0.925048828125}, {"start": 1247.81, "end": 1248.27, "word": " إن", "probability": 0.41015625}, {"start": 1248.27, "end": 1248.67, "word": " الـ", "probability": 0.6719970703125}, {"start": 1248.67, "end": 1249.05, "word": " xn", "probability": 0.23223876953125}, {"start": 1249.05, "end": 1249.91, "word": " مثلاً", "probability": 0.720458984375}, {"start": 1249.91, "end": 1250.21, "word": " is", "probability": 0.453369140625}, {"start": 1250.21, "end": 1250.45, "word": " a", "probability": 0.78125}, {"start": 1250.45, "end": 1250.69, "word": " Cauchy", "probability": 0.9505208333333334}, {"start": 1250.69, "end": 1251.19, "word": " sequence", "probability": 0.724609375}, {"start": 1251.19, "end": 1251.37, "word": " if", "probability": 0.728515625}, {"start": 1251.37, "end": 1251.57, "word": " and", "probability": 0.95068359375}, {"start": 1251.57, "end": 1251.79, "word": " only", "probability": 0.9267578125}, {"start": 1251.79, "end": 1251.95, "word": " if", "probability": 0.9111328125}, {"start": 1251.95, "end": 1252.09, "word": " for", "probability": 0.8818359375}, {"start": 1252.09, "end": 1252.25, "word": " every", "probability": 0.82275390625}, {"start": 1252.25, "end": 1252.45, "word": " y", "probability": 0.38037109375}, {"start": 1252.45, "end": 1252.73, "word": " أكبر", "probability": 0.94775390625}, {"start": 1252.73, "end": 1252.85, "word": " من", "probability": 0.9912109375}, {"start": 1252.85, "end": 1253.01, "word": " 0", "probability": 0.85009765625}, {"start": 1253.01, "end": 1253.29, "word": " there", "probability": 0.63916015625}, {"start": 1253.29, "end": 1253.73, "word": " exists", "probability": 0.8271484375}, {"start": 1253.73, "end": 1254.07, "word": " k", "probability": 0.51416015625}, {"start": 1254.07, "end": 1254.43, "word": " element", "probability": 0.8603515625}, {"start": 1254.43, "end": 1254.69, "word": " in", "probability": 0.9482421875}, {"start": 1254.69, "end": 1254.93, "word": " N", "probability": 0.68896484375}, {"start": 1254.93, "end": 1255.45, "word": " such", "probability": 0.6875}, {"start": 1255.45, "end": 1255.73, "word": " that", "probability": 0.9521484375}, {"start": 1255.73, "end": 1255.93, "word": " for", "probability": 0.96630859375}, {"start": 1255.93, "end": 1256.19, "word": " every", "probability": 0.837890625}, {"start": 1256.19, "end": 1256.47, "word": " n", "probability": 0.443359375}, {"start": 1256.47, "end": 1256.63, "word": " و", "probability": 0.8828125}, {"start": 1256.63, "end": 1256.93, "word": " m", "probability": 0.474853515625}, {"start": 1256.93, "end": 1257.39, "word": " أكبر", "probability": 0.984375}, {"start": 1257.39, "end": 1257.57, "word": " من", "probability": 0.99072265625}, {"start": 1257.57, "end": 1257.91, "word": " k", "probability": 0.873046875}, {"start": 1257.91, "end": 1258.59, "word": " يكون", "probability": 0.510498046875}, {"start": 1258.59, "end": 1258.75, "word": " الـ", "probability": 0.24774169921875}, {"start": 1258.75, "end": 1258.95, "word": " absolute", "probability": 0.8154296875}, {"start": 1258.95, "end": 1259.35, "word": " value", "probability": 0.98046875}, {"start": 1259.35, "end": 1259.65, "word": " للـ", "probability": 0.63037109375}, {"start": 1259.65, "end": 1260.29, "word": " xn", "probability": 0.895263671875}, {"start": 1260.29, "end": 1260.75, "word": " ناقص", "probability": 0.9326171875}, {"start": 1260.75, "end": 1261.19, "word": " xm", "probability": 0.885986328125}, {"start": 1261.19, "end": 1261.73, "word": " أصغر", "probability": 0.990478515625}, {"start": 1261.73, "end": 1261.95, "word": " من", "probability": 0.99072265625}, {"start": 1261.95, "end": 1262.39, "word": " إبسلول", "probability": 0.7229736328125}, {"start": 1262.39, "end": 1263.03, "word": " نحن", "probability": 0.662109375}, {"start": 1263.03, "end": 1263.35, "word": " نجيب", "probability": 0.700439453125}, {"start": 1263.35, "end": 1263.47, "word": " اللي", "probability": 0.73046875}, {"start": 1263.47, "end": 1263.63, "word": " هو", "probability": 0.95849609375}, {"start": 1263.63, "end": 1263.99, "word": " Cauchy", "probability": 0.8606770833333334}, {"start": 1263.99, "end": 1264.55, "word": " criterion", "probability": 0.85693359375}, {"start": 1264.55, "end": 1265.17, "word": " مشابه", "probability": 0.9754231770833334}, {"start": 1265.17, "end": 1265.49, "word": " إليها", "probability": 0.6400553385416666}, {"start": 1265.49, "end": 1265.73, "word": " بس", "probability": 0.846435546875}, {"start": 1265.73, "end": 1266.17, "word": " لمين", "probability": 0.685302734375}, {"start": 1266.17, "end": 1266.97, "word": " لحالة", "probability": 0.9500732421875}, {"start": 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1270.51, "end": 1271.17, "word": " النهاية", "probability": 0.9357096354166666}, {"start": 1271.17, "end": 1272.01, "word": " sequence", "probability": 0.90283203125}, {"start": 1272.01, "end": 1272.57, "word": " of", "probability": 0.98046875}, {"start": 1272.57, "end": 1273.23, "word": " partial", "probability": 0.96728515625}, {"start": 1273.23, "end": 1274.05, "word": " sums", "probability": 0.94677734375}], "temperature": 1.0}, {"id": 59, "seek": 129831, "start": 1275.51, "end": 1298.31, "text": "طيب يا جماعة نيجي لكوشيك ال 915 اللي هي quotient criterion for series the series summation xn in R converts if and only if for every ي أكبر من سفر there is a natural number M such that if M و N أكبر أو سوى M of Y هكون الأسئلة ماقصة أسئلة M اللي هو بسوى xn زائد 1", "tokens": [9566, 1829, 3555, 35186, 10874, 15042, 27884, 8717, 1829, 7435, 1829, 5296, 4117, 2407, 8592, 1829, 4117, 2423, 1722, 5211, 13672, 1829, 39896, 9641, 1196, 46691, 337, 2638, 264, 2638, 28811, 2031, 77, 294, 497, 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1477.66, "word": " the", "probability": 0.828125}, {"start": 1477.66, "end": 1478.32, "word": " series", "probability": 0.90673828125}, {"start": 1478.32, "end": 1479.68, "word": " سماشي", "probability": 0.511566162109375}, {"start": 1479.68, "end": 1480.16, "word": " xn", "probability": 0.91162109375}, {"start": 1480.16, "end": 1480.38, "word": " is", "probability": 0.9375}, {"start": 1480.38, "end": 1481.02, "word": " absolutely", "probability": 0.767578125}, {"start": 1481.02, "end": 1482.18, "word": " convergent", "probability": 0.979736328125}], "temperature": 1.0}, {"id": 68, "seek": 149247, "start": 1484.65, "end": 1492.47, "text": "إذا كانت سلسلة أبسط قيم XN مرتبطة بالـ R", "tokens": [28814, 15730, 25961, 2655, 8608, 1211, 3794, 37977, 5551, 3555, 3794, 9566, 12174, 32640, 1783, 45, 3714, 43500, 3555, 9566, 3660, 20666, 39184, 497], "avg_logprob": -0.8162500190734864, "compression_ratio": 0.9583333333333334, "no_speech_prob": 0.0, "words": [{"start": 1484.6499999999999, "end": 1486.05, "word": "إذا", "probability": 0.488037109375}, {"start": 1486.05, "end": 1486.63, "word": " كانت", "probability": 0.6663818359375}, {"start": 1486.63, "end": 1487.41, "word": " سلسلة", "probability": 0.650390625}, {"start": 1487.41, "end": 1488.61, "word": " أبسط", "probability": 0.421600341796875}, {"start": 1488.61, "end": 1489.05, "word": " قيم", "probability": 0.786376953125}, {"start": 1489.05, "end": 1490.21, "word": " XN", "probability": 0.364990234375}, {"start": 1490.21, "end": 1491.99, "word": " مرتبطة", "probability": 0.64351806640625}, {"start": 1491.99, "end": 1492.11, "word": " بالـ", "probability": 0.5003662109375}, {"start": 1492.11, "end": 1492.47, "word": " R", "probability": 0.611328125}], "temperature": 1.0}, {"id": 69, "seek": 151882, "start": 1497.86, "end": 1518.82, "text": "if it is convergent but not إيش ما لها absolutely convergent يعني في series في الدنيا أكيد بتكون convergent لكن مش absolutely convergent هذه ال series اللي من هالنوع اللي بتكون convergent لكن مش absolutely convergent بنسميه إيش ما لها conditionally convergent", "tokens": [351, 309, 307, 9652, 6930, 457, 406, 11933, 1829, 8592, 19446, 5296, 11296, 3122, 9652, 6930, 37495, 22653, 8978, 2638, 8978, 32748, 22653, 995, 5551, 4117, 25708, 39894, 30544, 9652, 6930, 44381, 37893, 3122, 9652, 6930, 29538, 2423, 2638, 13672, 1829, 9154, 8032, 6027, 1863, 45367, 13672, 1829, 39894, 30544, 9652, 6930, 44381, 37893, 3122, 9652, 6930, 44945, 38251, 1829, 3224, 11933, 1829, 8592, 19446, 5296, 11296, 4188, 379, 9652, 6930], "avg_logprob": -0.23480902053415775, "compression_ratio": 1.9883040935672514, "no_speech_prob": 0.0, "words": [{"start": 1497.86, "end": 1498.3, "word": "if", "probability": 0.1131591796875}, {"start": 1498.3, "end": 1498.76, "word": " it", "probability": 0.9619140625}, {"start": 1498.76, "end": 1499.08, "word": " is", "probability": 0.88916015625}, {"start": 1499.08, "end": 1499.78, "word": " convergent", "probability": 0.977783203125}, {"start": 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1504.68, "end": 1505.1, "word": " أكيد", "probability": 0.9265950520833334}, {"start": 1505.1, "end": 1505.62, "word": " بتكون", "probability": 0.968994140625}, {"start": 1505.62, "end": 1506.76, "word": " convergent", "probability": 0.887939453125}, {"start": 1506.76, "end": 1507.06, "word": " لكن", "probability": 0.91455078125}, {"start": 1507.06, "end": 1507.4, "word": " مش", "probability": 0.98974609375}, {"start": 1507.4, "end": 1508.26, "word": " absolutely", "probability": 0.63671875}, {"start": 1508.26, "end": 1509.7, "word": " convergent", "probability": 0.9072265625}, {"start": 1509.7, "end": 1510.84, "word": " هذه", "probability": 0.384765625}, {"start": 1510.84, "end": 1511.1, "word": " ال", "probability": 0.93701171875}, {"start": 1511.1, "end": 1511.44, "word": " series", "probability": 0.7919921875}, {"start": 1511.44, "end": 1511.64, "word": " اللي", "probability": 0.668701171875}, {"start": 1511.64, "end": 1511.76, "word": " من", "probability": 0.9111328125}, {"start": 1511.76, "end": 1512.14, "word": " هالنوع", "probability": 0.8095703125}, {"start": 1512.14, "end": 1512.28, "word": " اللي", "probability": 0.974365234375}, {"start": 1512.28, "end": 1512.56, "word": " بتكون", "probability": 0.9697265625}, {"start": 1512.56, "end": 1513.12, "word": " convergent", "probability": 0.885498046875}, {"start": 1513.12, "end": 1513.38, "word": " لكن", "probability": 0.93603515625}, {"start": 1513.38, "end": 1513.62, "word": " مش", "probability": 0.99169921875}, {"start": 1513.62, "end": 1514.08, "word": " absolutely", "probability": 0.63427734375}, {"start": 1514.08, "end": 1514.8, "word": " convergent", "probability": 0.967529296875}, {"start": 1514.8, "end": 1515.4, "word": " بنسميه", "probability": 0.78167724609375}, {"start": 1515.4, "end": 1515.68, "word": " إيش", "probability": 0.9384765625}, {"start": 1515.68, "end": 1515.82, "word": " ما", "probability": 0.95166015625}, {"start": 1515.82, "end": 1516.22, "word": " لها", "probability": 0.94189453125}, {"start": 1516.22, "end": 1517.6, "word": " conditionally", "probability": 0.885009765625}, {"start": 1517.6, "end": 1518.82, "word": " convergent", "probability": 0.9716796875}], "temperature": 1.0}, {"id": 70, "seek": 153782, "start": 1520.92, "end": 1537.82, "text": "لكن بعد شوية هنقول ان any absolutely convergent هتكون ايش ما لها is convergent طيب الان نيجي طبعا هذا في R كل الشغل في ال real numbers تسعة واحد سبعة theorem", "tokens": [1211, 19452, 39182, 13412, 2407, 10632, 8032, 1863, 39648, 16472, 604, 3122, 9652, 6930, 8032, 2655, 30544, 1975, 1829, 8592, 19446, 5296, 11296, 307, 9652, 6930, 23032, 1829, 3555, 2423, 7649, 8717, 1829, 7435, 1829, 23032, 3555, 3615, 995, 23758, 8978, 497, 28242, 25124, 17082, 1211, 8978, 2423, 957, 3547, 6055, 3794, 27884, 36764, 24401, 8608, 3555, 27884, 20904], "avg_logprob": -0.2703124910593033, "compression_ratio": 1.345029239766082, "no_speech_prob": 6.556510925292969e-07, "words": [{"start": 1520.92, "end": 1521.34, "word": "لكن", "probability": 0.821044921875}, {"start": 1521.34, "end": 1521.68, "word": " بعد", "probability": 0.79833984375}, {"start": 1521.68, "end": 1521.98, "word": " شوية", "probability": 0.8479817708333334}, {"start": 1521.98, "end": 1522.34, "word": " هنقول", "probability": 0.767822265625}, {"start": 1522.34, "end": 1522.54, "word": " ان", "probability": 0.57763671875}, {"start": 1522.54, "end": 1522.86, "word": " any", "probability": 0.14208984375}, {"start": 1522.86, "end": 1523.54, "word": " absolutely", "probability": 0.5537109375}, {"start": 1523.54, "end": 1524.24, "word": " convergent", "probability": 0.95166015625}, {"start": 1524.24, "end": 1524.66, "word": " هتكون", "probability": 0.8258463541666666}, {"start": 1524.66, "end": 1524.92, "word": " ايش", "probability": 0.6602376302083334}, {"start": 1524.92, "end": 1525.1, "word": " ما", "probability": 0.873046875}, {"start": 1525.1, "end": 1525.54, "word": " لها", "probability": 0.72509765625}, {"start": 1525.54, "end": 1526.42, "word": " is", "probability": 0.90576171875}, {"start": 1526.42, "end": 1527.92, "word": " convergent", "probability": 0.968505859375}, {"start": 1527.92, "end": 1529.46, "word": " طيب", "probability": 0.8806966145833334}, {"start": 1529.46, "end": 1530.84, "word": " الان", "probability": 0.6649169921875}, {"start": 1530.84, "end": 1532.86, "word": " نيجي", "probability": 0.9007568359375}, {"start": 1532.86, "end": 1533.24, "word": " طبعا", "probability": 0.87158203125}, {"start": 1533.24, "end": 1533.38, "word": " هذا", "probability": 0.6513671875}, {"start": 1533.38, "end": 1533.54, "word": " في", "probability": 0.88671875}, {"start": 1533.54, "end": 1533.74, "word": " R", "probability": 0.6884765625}, {"start": 1533.74, "end": 1533.98, "word": " كل", "probability": 0.97900390625}, {"start": 1533.98, "end": 1534.36, "word": " الشغل", "probability": 0.9903971354166666}, {"start": 1534.36, "end": 1535.08, "word": " في", "probability": 0.30224609375}, {"start": 1535.08, "end": 1535.28, "word": " ال", "probability": 0.85107421875}, {"start": 1535.28, "end": 1535.46, "word": " real", "probability": 0.6357421875}, {"start": 1535.46, "end": 1535.86, "word": " numbers", "probability": 0.7763671875}, {"start": 1535.86, "end": 1536.68, "word": " تسعة", "probability": 0.7831217447916666}, {"start": 1536.68, "end": 1537.04, "word": " واحد", "probability": 0.811767578125}, {"start": 1537.04, "end": 1537.42, "word": " سبعة", "probability": 0.9552408854166666}, {"start": 1537.42, "end": 1537.82, "word": " theorem", "probability": 0.76220703125}], "temperature": 1.0}, {"id": 71, "seek": 155643, "start": 1538.95, "end": 1556.43, "text": "إذا كانت سلسلة مرتبطة بالكامل فهي مرتبطة بالكامل أيضًا، فهي مرتبطة بالكامل أيضًا، فهي مرتبطة بالكامل أيضًا، فهي مرتبطة بالكامل أيضًا", "tokens": [28814, 15730, 25961, 2655, 8608, 1211, 3794, 37977, 3714, 43500, 3555, 9566, 3660, 20666, 4117, 10943, 1211, 6156, 3224, 1829, 3714, 43500, 3555, 9566, 3660, 20666, 4117, 10943, 1211, 36632, 11242, 14111, 995, 12399, 6156, 3224, 1829, 3714, 43500, 3555, 9566, 3660, 20666, 4117, 10943, 1211, 36632, 11242, 14111, 995, 12399, 6156, 3224, 1829, 3714, 43500, 3555, 9566, 3660, 20666, 4117, 10943, 1211, 36632, 11242, 14111, 995, 12399, 6156, 3224, 1829, 3714, 43500, 3555, 9566, 3660, 20666, 4117, 10943, 1211, 36632, 11242, 14111, 995], "avg_logprob": -0.3733455924426808, "compression_ratio": 3.168831168831169, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1538.95, "end": 1539.43, "word": "إذا", "probability": 0.6387939453125}, {"start": 1539.43, "end": 1540.03, "word": " كانت", "probability": 0.7841796875}, {"start": 1540.03, "end": 1540.59, "word": " سلسلة", "probability": 0.709625244140625}, {"start": 1540.59, "end": 1540.99, "word": " مرتبطة", "probability": 0.60257568359375}, {"start": 1540.99, "end": 1541.95, "word": " بالكامل", "probability": 0.679962158203125}, {"start": 1541.95, "end": 1542.65, "word": " فهي", "probability": 0.666015625}, {"start": 1542.65, "end": 1543.27, "word": " مرتبطة", "probability": 0.83251953125}, {"start": 1543.27, "end": 1543.27, "word": " بالكامل", "probability": 0.886962890625}, {"start": 1543.27, "end": 1543.61, "word": " أيضًا،", "probability": 0.52958984375}, {"start": 1543.61, "end": 1544.73, "word": " فهي", "probability": 0.7312825520833334}, {"start": 1544.73, "end": 1545.53, "word": " مرتبطة", "probability": 0.9505859375}, {"start": 1545.53, "end": 1545.53, "word": " بالكامل", "probability": 0.926513671875}, {"start": 1545.53, "end": 1545.53, "word": " أيضًا،", "probability": 0.67310791015625}, {"start": 1545.53, "end": 1545.99, "word": " فهي", "probability": 0.715576171875}, {"start": 1545.99, "end": 1546.67, "word": " مرتبطة", "probability": 0.98662109375}, {"start": 1546.67, "end": 1547.09, "word": " بالكامل", "probability": 0.9881591796875}, {"start": 1547.09, "end": 1549.05, "word": " أيضًا،", "probability": 0.83095703125}, {"start": 1549.05, "end": 1550.63, "word": " فهي", "probability": 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دي", "probability": 0.890380859375}, {"start": 1987.51, "end": 1987.81, "word": " اللي", "probability": 0.953857421875}, {"start": 1987.81, "end": 1988.17, "word": " هو", "probability": 0.9873046875}], "temperature": 1.0}, {"id": 90, "seek": 200875, "start": 1988.53, "end": 2008.75, "text": "الـ S M نقص S N أصغر من إبسلون هيكون اللي هو في هذه الحالة أثبتت أنه اللي هو الـ S N by Cauchy criterion is convergent اللي هو صار عندي الصممش إلى الآن convergence طيب الديجلة اللي هو المثال اللي بعده المثال المشهور", "tokens": [6027, 39184, 318, 376, 8717, 4587, 9381, 318, 426, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 1211, 11536, 39896, 30544, 13672, 1829, 31439, 8978, 29538, 21542, 6027, 3660, 5551, 12984, 3555, 2655, 2655, 14739, 3224, 13672, 1829, 31439, 2423, 39184, 318, 426, 538, 7544, 625, 88, 46691, 307, 9652, 6930, 13672, 1829, 31439, 20328, 9640, 18871, 16254, 31767, 2304, 2304, 8592, 30731, 6024, 48506, 32181, 23032, 1829, 3555, 2423, 16254, 7435, 37977, 13672, 1829, 31439, 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that summation للواحد and diverse هذه الـ sequence، هذه الـ series اللي هي series مشهورة اللي كنا نسميها الـ B series الـ B بيساوي واحد في هذه الحالة هذه الـ summation يليها واحد and إيش ماله؟ diverse تنشوف", "tokens": [6027, 20292, 31439, 4724, 39184, 707, 857, 855, 300, 2408, 76, 399, 24976, 14407, 24401, 293, 9521, 29538, 2423, 39184, 8310, 12399, 29538, 2423, 39184, 2638, 13672, 1829, 39896, 2638, 37893, 3224, 13063, 3660, 13672, 1829, 9122, 8315, 8717, 38251, 1829, 11296, 2423, 39184, 363, 2638, 2423, 39184, 363, 4724, 1829, 3794, 995, 45865, 36764, 24401, 8978, 29538, 21542, 6027, 3660, 29538, 2423, 39184, 28811, 7251, 20292, 11296, 36764, 24401, 293, 11933, 1829, 8592, 3714, 6027, 3224, 22807, 9521, 6055, 1863, 8592, 38688], "avg_logprob": -0.41294643389327185, "compression_ratio": 1.780104712041885, "no_speech_prob": 1.7285346984863281e-06, "words": [{"start": 2009.34, "end": 2009.7, "word": "اللي", "probability": 0.433837890625}, {"start": 2009.7, "end": 2009.84, "word": " 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{"start": 3032.61, "end": 3032.77, "word": " ال", "probability": 0.86474609375}, {"start": 3032.77, "end": 3034.17, "word": " subsequence", "probability": 0.69775390625}, {"start": 3034.17, "end": 3035.05, "word": " SKR", "probability": 0.6680908203125}], "temperature": 1.0}, {"id": 136, "seek": 304842, "start": 3035.46, "end": 3048.42, "text": "هذه الـ subsequence وضحى انها اكبر او يساوى 1 على ارضها او اتنين يعني as R goes to infinity هذا المقدار بروح لما لنهاية يعني هذه ال sequence is unbounded اذا صار عندى اللي هو", "tokens": [3224, 24192, 2423, 39184, 13924, 655, 4032, 11242, 5016, 7578, 16472, 11296, 1975, 4117, 26890, 1975, 2407, 7251, 3794, 995, 2407, 7578, 502, 15844, 1975, 43042, 11296, 1975, 2407, 1975, 2655, 1863, 9957, 37495, 22653, 382, 497, 1709, 281, 13202, 23758, 9673, 28543, 9640, 4724, 32887, 5016, 5296, 15042, 5296, 1863, 11296, 10632, 37495, 22653, 29538, 2423, 8310, 307, 517, 18767, 292, 1975, 15730, 20328, 9640, 43242, 7578, 13672, 1829, 31439], "avg_logprob": 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0.8251953125}, {"start": 3864.28, "end": 3864.8, "word": " series", "probability": 0.90673828125}, {"start": 3864.8, "end": 3865.16, "word": " is", "probability": 0.83154296875}, {"start": 3865.16, "end": 3865.56, "word": " another", "probability": 0.93505859375}, {"start": 3865.56, "end": 3866.04, "word": " series", "probability": 0.9052734375}, {"start": 3866.04, "end": 3866.22, "word": " هي", "probability": 0.7998046875}, {"start": 3866.22, "end": 3866.46, "word": " في", "probability": 0.391357421875}, {"start": 3866.46, "end": 3866.78, "word": " ريز", "probability": 0.77685546875}, {"start": 3866.78, "end": 3867.1, "word": " أخر", "probability": 0.935546875}, {"start": 3867.1, "end": 3867.66, "word": " هتكون", "probability": 0.821533203125}], "temperature": 1.0}, {"id": 172, "seek": 388760, "start": 3868.34, "end": 3887.6, "text": "which is obtained from the given one يعني بناخدها من من من الأصلية by using all of the terms exactly one once يعني بإننا نستخدم عناصر ال series مرة واحدة فقط لازم نستخدمها و بنستخدمها بمرة واحدة", "tokens": [13690, 307, 14879, 490, 264, 2212, 472, 37495, 22653, 44945, 47283, 3215, 11296, 9154, 9154, 9154, 16247, 36520, 10632, 538, 1228, 439, 295, 264, 2115, 2293, 472, 1564, 37495, 22653, 4724, 28814, 1863, 8315, 8717, 14851, 9778, 40448, 18871, 33546, 2288, 2423, 2638, 3714, 25720, 36764, 24401, 3660, 6156, 47432, 5296, 31377, 2304, 8717, 14851, 9778, 40448, 11296, 4032, 44945, 14851, 9778, 40448, 11296, 4724, 2304, 25720, 36764, 24401, 3660], "avg_logprob": -0.14018486503144384, "compression_ratio": 1.5494505494505495, "no_speech_prob": 5.7220458984375e-06, "words": [{"start": 3868.34, "end": 3868.82, "word": "which", "probability": 0.399169921875}, {"start": 3868.82, "end": 3869.14, "word": " is", "probability": 0.9482421875}, {"start": 3869.14, "end": 3869.7, "word": " obtained", "probability": 0.90478515625}, {"start": 3869.7, "end": 3870.18, "word": " from", "probability": 0.9296875}, {"start": 3870.18, "end": 3870.5, "word": " the", "probability": 0.8955078125}, {"start": 3870.5, "end": 3870.84, "word": " given", "probability": 0.89306640625}, {"start": 3870.84, "end": 3871.12, "word": " one", "probability": 0.9248046875}, {"start": 3871.12, "end": 3871.42, "word": " يعني", "probability": 0.56976318359375}, {"start": 3871.42, "end": 3871.92, "word": " بناخدها", "probability": 0.9410400390625}, {"start": 3871.92, "end": 3872.1, "word": " من", "probability": 0.9921875}, {"start": 3872.1, "end": 3872.32, "word": " من", "probability": 0.487060546875}, {"start": 3872.32, "end": 3872.54, "word": " من", "probability": 0.448486328125}, {"start": 3872.54, "end": 3873.32, "word": " الأصلية", "probability": 0.7530110677083334}, {"start": 3873.32, "end": 3874.36, "word": " by", "probability": 0.837890625}, {"start": 3874.36, "end": 3875.08, "word": " using", "probability": 0.95751953125}, {"start": 3875.08, "end": 3875.64, "word": " all", "probability": 0.9404296875}, {"start": 3875.64, "end": 3875.9, "word": " of", "probability": 0.96533203125}, {"start": 3875.9, "end": 3876.1, "word": " the", "probability": 0.9140625}, {"start": 3876.1, "end": 3876.54, "word": " terms", "probability": 0.8359375}, {"start": 3876.54, "end": 3877.18, "word": " exactly", "probability": 0.9208984375}, {"start": 3877.18, "end": 3877.62, "word": " one", "probability": 0.475341796875}, {"start": 3877.62, "end": 3878.66, "word": " once", "probability": 0.80908203125}, {"start": 3878.66, "end": 3879.56, "word": " يعني", "probability": 0.904296875}, {"start": 3879.56, "end": 3880.1, "word": " بإننا", "probability": 0.8184814453125}, {"start": 3880.1, "end": 3880.7, "word": " نستخدم", "probability": 0.9896240234375}, {"start": 3880.7, "end": 3881.26, "word": " عناصر", "probability": 0.99169921875}, {"start": 3881.26, "end": 3881.42, "word": " ال", "probability": 0.900390625}, {"start": 3881.42, "end": 3881.86, "word": " series", "probability": 0.900390625}, {"start": 3881.86, "end": 3882.62, "word": " مرة", "probability": 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which", "probability": 0.951171875}, {"start": 3892.0, "end": 3892.58, "word": " the", "probability": 0.85107421875}, {"start": 3892.58, "end": 3893.4, "word": " terms", "probability": 0.47314453125}, {"start": 3893.4, "end": 3893.76, "word": " are", "probability": 0.951171875}, {"start": 3893.76, "end": 3894.28, "word": " taken", "probability": 0.82666015625}, {"start": 3894.28, "end": 3895.06, "word": " يعني", "probability": 0.74609375}, {"start": 3895.06, "end": 3895.46, "word": " بس", "probability": 0.906494140625}, {"start": 3895.46, "end": 3895.72, "word": " إيش", "probability": 0.74609375}, {"start": 3895.72, "end": 3896.38, "word": " بنسوي،", "probability": 0.7421875}, {"start": 3896.38, "end": 3897.0, "word": " بنعيد", "probability": 0.9334309895833334}, {"start": 3897.0, "end": 3897.94, "word": " ترتيب", "probability": 0.80419921875}, {"start": 3897.94, "end": 3898.4, "word": " اللي", "probability": 0.77490234375}, {"start": 3898.4, "end": 3898.7, "word": " هي", "probability": 0.8330078125}, {"start": 3898.7, "end": 3899.36, "word": " أماكن", "probability": 0.9441731770833334}, {"start": 3899.36, "end": 3899.62, "word": " اللي", "probability": 0.8984375}, {"start": 3899.62, "end": 3900.02, "word": " هي", "probability": 0.8671875}, {"start": 3900.02, "end": 3900.42, "word": " S", "probability": 0.41845703125}, {"start": 3900.42, "end": 3900.82, "word": " series", "probability": 0.5048828125}, {"start": 3900.82, "end": 3902.06, "word": " الآن", "probability": 0.732421875}, {"start": 3902.06, "end": 3902.32, "word": " يعني", "probability": 0.93505859375}, {"start": 3902.32, "end": 3902.44, "word": " ال", "probability": 0.397705078125}, {"start": 3902.44, "end": 3902.72, "word": " summation", "probability": 0.7900390625}, {"start": 3902.72, "end": 3903.64, "word": " XN", "probability": 0.37677001953125}, {"start": 3903.64, "end": 3905.36, "word": " summation", "probability": 0.2474365234375}, {"start": 3905.36, "end": 3905.88, "word": " XN", "probability": 0.900634765625}, {"start": 3905.88, "end": 3906.0, "word": " هي", "probability": 0.8369140625}, {"start": 3906.0, "end": 3906.54, "word": " series", "probability": 0.58642578125}, {"start": 3906.54, "end": 3907.44, "word": " قعدنا", "probability": 0.797119140625}, {"start": 3907.44, "end": 3908.16, "word": " ترتيبها", "probability": 0.97392578125}, {"start": 3908.16, "end": 3908.48, "word": " اللي", "probability": 0.73583984375}, {"start": 3908.48, "end": 3908.64, "word": " هي", "probability": 0.89453125}, {"start": 3908.64, "end": 3909.1, "word": " summation", "probability": 0.76318359375}, {"start": 3909.1, "end": 3909.8, "word": " YN", "probability": 0.9296875}], "temperature": 1.0}, {"id": 174, "seek": 392787, "start": 3910.81, "end": 3927.87, "text": "الأن الـ XL و الـ YN لو جينا حاطناها في مجموعتين هنقول أكيد أكيد الـ X1 لعند الـ XN لعند المالة النهائية هي نفسها Y1 لعند Y2 لعند الـ Y", "tokens": [6027, 33456, 2423, 39184, 37210, 4032, 2423, 39184, 398, 45, 45164, 10874, 1829, 8315, 11331, 41193, 8315, 11296, 8978, 3714, 7435, 2304, 45367, 2655, 9957, 8032, 1863, 39648, 5551, 4117, 25708, 5551, 4117, 25708, 2423, 39184, 1783, 16, 5296, 3615, 41260, 2423, 39184, 1783, 45, 5296, 3615, 41260, 9673, 6027, 3660, 28239, 3224, 16373, 10632, 39896, 8717, 36178, 11296, 398, 16, 5296, 3615, 41260, 398, 17, 5296, 3615, 41260, 2423, 39184, 398], "avg_logprob": -0.2487157599566734, "compression_ratio": 1.6888888888888889, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 3910.81, "end": 3911.31, "word": "الأن", "probability": 0.3634033203125}, {"start": 3911.31, "end": 3911.87, "word": " الـ", "probability": 0.709228515625}, {"start": 3911.87, "end": 3912.15, "word": " XL", "probability": 0.5048828125}, {"start": 3912.15, "end": 3912.95, "word": " و", "probability": 0.6953125}, {"start": 3912.95, "end": 3913.17, "word": " الـ", "probability": 0.697265625}, {"start": 3913.17, "end": 3913.59, "word": " YN", "probability": 0.820556640625}, {"start": 3913.59, "end": 3913.91, "word": " لو", "probability": 0.9404296875}, {"start": 3913.91, "end": 3914.25, "word": " جينا", "probability": 0.82666015625}, {"start": 3914.25, "end": 3914.85, "word": " حاطناها", "probability": 0.56805419921875}, {"start": 3914.85, "end": 3915.03, "word": " في", "probability": 0.87939453125}, {"start": 3915.03, "end": 3916.03, "word": " مجموعتين", "probability": 0.8758951822916666}, {"start": 3916.03, "end": 3917.39, "word": " هنقول", "probability": 0.8310546875}, {"start": 3917.39, "end": 3918.25, "word": " أكيد", "probability": 0.8990885416666666}, {"start": 3918.25, "end": 3918.77, "word": " أكيد", "probability": 0.7647298177083334}, {"start": 3918.77, "end": 3919.07, "word": " الـ", "probability": 0.7939453125}, {"start": 3919.07, "end": 3919.83, "word": " X1", "probability": 0.7470703125}, {"start": 3919.83, "end": 3920.41, "word": " لعند", "probability": 0.9078776041666666}, {"start": 3920.41, "end": 3920.71, "word": " الـ", "probability": 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"probability": 0.81005859375}], "temperature": 1.0}, {"id": 175, "seek": 395812, "start": 3928.4, "end": 3958.12, "text": "أن إلى ما لا نهاية لكن الـ X1 مش شرط الـ Y1 الـ X2 مش شرط الـ Y2 أما هذه كمجموعة هي نفس المجموعة و بنستخدمش ال term الجديد إلا .. بنستخدمش اللي هنا إلا غير مرة واحدة في اللي هي هنا يعني كل اللي هنا موجودة هنا ولكن بكرتيب آخر فبتكون هذه rearrangement of the original series ال summation لـ X", "tokens": [10721, 1863, 30731, 19446, 20193, 8717, 11296, 10632, 44381, 2423, 39184, 1783, 16, 37893, 13412, 2288, 9566, 2423, 39184, 398, 16, 2423, 39184, 1783, 17, 37893, 13412, 2288, 9566, 2423, 39184, 398, 17, 5551, 15042, 29538, 9122, 2304, 7435, 2304, 2407, 27884, 39896, 8717, 36178, 9673, 7435, 2304, 2407, 27884, 4032, 44945, 14851, 9778, 40448, 8592, 2423, 1433, 25724, 16254, 3215, 11933, 15040, 4386, 44945, 14851, 9778, 40448, 8592, 13672, 1829, 34105, 11933, 15040, 32771, 13546, 3714, 25720, 36764, 24401, 3660, 8978, 13672, 1829, 39896, 34105, 37495, 22653, 28242, 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{"start": 4128.65, "end": 4128.65, "word": " Y2", "probability": 0.903564453125}, {"start": 4128.65, "end": 4128.65, "word": " XF", "probability": 0.98828125}], "temperature": 1.0}, {"id": 184, "seek": 415631, "start": 4128.75, "end": 4156.31, "text": "ما تأثير الـ Rearrangements على السيريز الأصلية بقولك لو كانت السيريز absolutely convergent وده اللي هنتطرقله بس لو كانت السيريز absolutely convergent ترتب زي ما بدك مش هتفرج معانا اللي هو إيه ال convergence يعني let summation xn be an absolutely convergent series in R then any rearrangement of summation xn", "tokens": [15042, 6055, 10721, 12984, 13546, 2423, 39184, 1300, 2284, 933, 1117, 15844, 21136, 13546, 1829, 11622, 16247, 36520, 10632, 4724, 39648, 4117, 45164, 25961, 2655, 21136, 13546, 1829, 11622, 3122, 9652, 6930, 4032, 3215, 3224, 13672, 1829, 8032, 29399, 9566, 2288, 4587, 43761, 4724, 3794, 45164, 25961, 2655, 21136, 13546, 1829, 11622, 3122, 9652, 6930, 6055, 43500, 3555, 30767, 1829, 19446, 47525, 4117, 37893, 8032, 2655, 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الجديدة Summation Yn اللي هي الـ Rearrangement شوف كده لأن Now let M limited M be such that all of the terms X1 لعند الـ Xm are contained as a sum and in T M Y1 لعند ال Ym إيش اللي بيقولوا هذا؟ وهذا الكلام اللي هو اللي إحنا بدنا نتهيئله و هو اللي بيفتحنا الطريق أمام البرهان", "tokens": [10721, 5016, 8315, 32239, 8592, 47525, 8315, 4386, 47525, 8315, 2423, 39184, 13934, 25724, 16254, 41891, 2746, 2174, 399, 398, 77, 13672, 1829, 39896, 2423, 39184, 1300, 2284, 933, 518, 13412, 38688, 9122, 3215, 3224, 5296, 33456, 823, 718, 376, 5567, 376, 312, 1270, 300, 439, 295, 264, 2115, 1783, 16, 5296, 3615, 41260, 2423, 39184, 1783, 76, 366, 16212, 382, 257, 2408, 293, 294, 314, 376, 398, 16, 5296, 3615, 41260, 2423, 398, 76, 11933, 1829, 8592, 13672, 1829, 4724, 1829, 39648, 14407, 23758, 22807, 37037, 15730, 2423, 28820, 10943, 13672, 1829, 31439, 13672, 1829, 11933, 5016, 8315, 47525, 8315, 8717, 47395, 1829, 19986, 43761, 4032, 31439, 13672, 1829, 4724, 1829, 5172, 2655, 5016, 8315, 41950, 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4491.34, "end": 4492.68, "word": " إيش", "probability": 0.76171875}, {"start": 4492.68, "end": 4492.82, "word": " اللي", "probability": 0.9892578125}, {"start": 4492.82, "end": 4493.28, "word": " بيقولوا", "probability": 0.8372802734375}, {"start": 4493.28, "end": 4493.62, "word": " هذا؟", "probability": 0.650634765625}, {"start": 4493.62, "end": 4493.88, "word": " وهذا", "probability": 0.63720703125}, {"start": 4493.88, "end": 4494.46, "word": " الكلام", "probability": 0.94873046875}, {"start": 4494.46, "end": 4494.72, "word": " اللي", "probability": 0.985107421875}, {"start": 4494.72, "end": 4495.1, "word": " هو", "probability": 0.97314453125}, {"start": 4495.1, "end": 4495.54, "word": " اللي", "probability": 0.95166015625}, {"start": 4495.54, "end": 4495.82, "word": " إحنا", "probability": 0.80224609375}, {"start": 4495.82, "end": 4496.14, "word": " بدنا", "probability": 0.888916015625}, {"start": 4496.14, "end": 4496.86, "word": " نتهيئله", "probability": 0.786572265625}, {"start": 4496.86, "end": 4497.36, "word": " و", "probability": 0.4716796875}, {"start": 4497.36, "end": 4497.54, "word": " هو", "probability": 0.8427734375}, {"start": 4497.54, "end": 4497.7, "word": " اللي", "probability": 0.98779296875}, {"start": 4497.7, "end": 4498.32, "word": " بيفتحنا", "probability": 0.7858072916666666}, {"start": 4498.32, "end": 4498.82, "word": " الطريق", "probability": 0.97607421875}, {"start": 4498.82, "end": 4499.2, "word": " أمام", "probability": 0.93359375}, {"start": 4499.2, "end": 4499.76, "word": " البرهان", "probability": 0.8734130859375}], "temperature": 1.0}, {"id": 200, "seek": 452432, "start": 4501.4, "end": 4524.32, "text": "جالي بيحكيلي انه خلّينا نختار M في الـN ابحث الـTM هذه اللي هي الـSequence of partial sums لمين للـYN اللي هي Y1 زائد Y2 زائد YM بقوللي أنا بدأ اختار الـM هذه على أساس", "tokens": [7435, 6027, 1829, 4724, 1829, 5016, 4117, 1829, 20292, 16472, 3224, 16490, 1211, 11703, 1829, 8315, 8717, 46456, 9640, 376, 8978, 2423, 39184, 45, 48127, 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" في", "probability": 0.8544921875}, {"start": 4505.8, "end": 4506.26, "word": " الـN", "probability": 0.6119791666666666}, {"start": 4506.26, "end": 4507.66, "word": " ابحث", "probability": 0.9173177083333334}, {"start": 4507.66, "end": 4509.36, "word": " الـTM", "probability": 0.8390299479166666}, {"start": 4509.36, "end": 4510.1, "word": " هذه", "probability": 0.59814453125}, {"start": 4510.1, "end": 4511.26, "word": " اللي", "probability": 0.907470703125}, {"start": 4511.26, "end": 4511.54, "word": " هي", "probability": 0.95068359375}, {"start": 4511.54, "end": 4512.12, "word": " الـSequence", "probability": 0.7490234375}, {"start": 4512.12, "end": 4512.28, "word": " of", "probability": 0.86328125}, {"start": 4512.28, "end": 4512.62, "word": " partial", "probability": 0.72607421875}, {"start": 4512.62, "end": 4512.94, "word": " sums", "probability": 0.916015625}, {"start": 4512.94, "end": 4513.54, "word": " لمين", "probability": 0.5135498046875}, {"start": 4513.54, "end": 4514.74, 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{"start": 4813.68, "end": 4813.92, "word": " SN", "probability": 0.232666015625}, {"start": 4813.92, "end": 4814.24, "word": " زي", "probability": 0.798583984375}, {"start": 4814.24, "end": 4814.56, "word": " SN", "probability": 0.44775390625}, {"start": 4814.56, "end": 4814.98, "word": " ناقص", "probability": 0.98193359375}, {"start": 4814.98, "end": 4815.12, "word": " EH", "probability": 0.22900390625}, {"start": 4815.12, "end": 4815.6, "word": " ناقص", "probability": 0.992919921875}, {"start": 4815.6, "end": 4815.86, "word": " X", "probability": 0.98876953125}, {"start": 4815.86, "end": 4816.64, "word": " هذا", "probability": 0.31103515625}, {"start": 4816.64, "end": 4816.84, "word": " يقول", "probability": 0.890869140625}, {"start": 4816.84, "end": 4816.96, "word": " إنه", "probability": 0.4107666015625}, {"start": 4816.96, "end": 4817.24, "word": " أصغر", "probability": 0.9893798828125}, {"start": 4817.24, "end": 4817.38, "word": " من", "probability": 0.9873046875}, {"start": 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