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+{"segments": [{"id": 1, "seek": 4617, "start": 21.33, "end": 46.17, "text": "اليوم طبعا هنكمل الشرح أو بعض الملاحظات على النظرية اللي أخدناها في المحاضرة السابقة النظرية هذه بتتحدث عن nested interval property أو خاصية الفترات المتداخلة", "tokens": [6027, 1829, 20498, 23032, 3555, 3615, 995, 8032, 1863, 24793, 1211, 25124, 2288, 5016, 34051, 45030, 11242, 9673, 15040, 5016, 19913, 9307, 15844, 28239, 19913, 2288, 10632, 13672, 1829, 5551, 9778, 3215, 8315, 11296, 8978, 9673, 5016, 46958, 25720, 21136, 16758, 28671, 28239, 19913, 2288, 10632, 29538, 39894, 2655, 24401, 12984, 18871, 15646, 292, 15035, 4707, 34051, 16490, 33546, 10632, 27188, 2655, 2288, 9307, 9673, 2655, 28259, 9778, 37977], "avg_logprob": -0.08766741092715945, "compression_ratio": 1.542857142857143, "no_speech_prob": 0.0, "words": [{"start": 21.33, "end": 22.45, "word": "اليوم", "probability": 0.97119140625}, {"start": 22.45, "end": 22.93, "word": " طبعا", "probability": 0.9915771484375}, {"start": 22.93, "end": 23.77, 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"probability": 0.71728515625}, {"start": 138.1, "end": 138.58, "word": " تكونوا", "probability": 0.9269205729166666}, {"start": 138.58, "end": 139.2, "word": " قرأتهوا", "probability": 0.88017578125}, {"start": 139.2, "end": 139.48, "word": " كمان", "probability": 0.8963216145833334}, {"start": 139.48, "end": 139.76, "word": " مرة", "probability": 0.968017578125}, {"start": 139.76, "end": 140.74, "word": " وفهمتهوا", "probability": 0.8712890625}, {"start": 140.74, "end": 141.7, "word": " في", "probability": 0.489501953125}, {"start": 141.7, "end": 142.0, "word": " حد", "probability": 0.98486328125}, {"start": 142.0, "end": 142.26, "word": " عنده", "probability": 0.933349609375}, {"start": 142.26, "end": 142.96, "word": " استفسار", "probability": 0.7740071614583334}, {"start": 142.96, "end": 143.18, "word": " على", "probability": 0.69921875}, {"start": 143.18, "end": 144.9, "word": " المرهانة", "probability": 0.797607421875}, {"start": 144.9, "end": 145.28, "word": " النظرية", "probability": 0.8377685546875}, {"start": 145.28, "end": 145.64, "word": " هذه", "probability": 0.89306640625}, {"start": 145.64, "end": 147.4, "word": " طيب", "probability": 0.95751953125}, {"start": 147.4, "end": 147.86, "word": " الآن", "probability": 0.658935546875}, {"start": 147.86, "end": 148.48, "word": " النظرية", "probability": 0.9752197265625}, {"start": 148.48, "end": 148.9, "word": " هذه", "probability": 0.92138671875}, {"start": 148.9, "end": 149.56, "word": " نرجع", "probability": 0.90966796875}, {"start": 149.56, "end": 150.0, "word": " للنظرية", "probability": 0.87021484375}, {"start": 150.0, "end": 150.34, "word": " كمان", "probability": 0.9775390625}, {"start": 150.34, "end": 150.72, "word": " مرة", "probability": 0.9912109375}, {"start": 150.72, "end": 155.82, "word": " الآن", "probability": 0.6685791015625}, {"start": 155.82, "end": 156.2, "word": " في", "probability": 0.9130859375}, {"start": 156.2, "end": 157.42, "word": " ملاحظة", "probability": 0.9763671875}, {"start": 157.42, "end": 158.58, "word": " بتقول", "probability": 0.970947265625}, {"start": 158.58, "end": 159.06, "word": " انه", "probability": 0.6796875}, {"start": 159.06, "end": 159.28, "word": " لو", "probability": 0.92236328125}, {"start": 159.28, "end": 159.62, "word": " انا", "probability": 0.77001953125}, {"start": 159.62, "end": 159.8, "word": " في", "probability": 0.87744140625}, {"start": 159.8, "end": 160.34, "word": " النظرية", "probability": 0.9862060546875}, {"start": 160.34, "end": 160.7, "word": " هذه", "probability": 0.94677734375}, {"start": 160.7, "end": 161.48, "word": " الفترات", "probability": 0.958740234375}, {"start": 161.48, "end": 162.1, "word": " هذه", "probability": 0.9345703125}], "temperature": 1.0}, {"id": 6, "seek": 18746, "start": 163.94, "end": 187.46, "text": "الفرض ان الفترات in مغلقة closed لو حذفت شيلت الفرض هذا فالنظرية هذه بتبطل تكون صحيحة فالنظرية هذه بتبطل تكون صحيحة وحنشوف counter example يوضح عدم صحتها كذلك", "tokens": [6027, 5172, 43042, 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"طب افرضه ان هذا شرط متحقق في الفترات لكن اللي مش متحقق اللي هو ال boundedness يعني الفترات هذه ليست محدودة ليست bounded برضه في الحالة هذه المظهرية تفشل و في counter example يوضح فشلها okay اذا حنشوف two counter examples خليني نشوفهم مع بعض", "tokens": [9566, 3555, 1975, 5172, 43042, 3224, 16472, 23758, 13412, 2288, 9566, 44650, 5016, 4587, 4587, 8978, 27188, 2655, 2288, 9307, 44381, 13672, 1829, 37893, 44650, 5016, 4587, 4587, 13672, 1829, 31439, 2423, 37498, 1287, 37495, 22653, 27188, 2655, 2288, 9307, 29538, 32239, 14851, 3714, 24401, 23328, 3660, 32239, 14851, 37498, 4724, 43042, 3224, 8978, 21542, 6027, 3660, 29538, 9673, 19913, 3224, 2288, 10632, 6055, 5172, 8592, 1211, 4032, 8978, 5682, 1365, 7251, 2407, 11242, 5016, 6156, 8592, 1211, 11296, 1392, 1975, 15730, 11331, 1863, 8592, 38688, 732, 5682, 5110, 16490, 1211, 9957, 1829, 8717, 8592, 38688, 16095, 20449, 45030, 11242], "avg_logprob": -0.16383044790513446, "compression_ratio": 1.76036866359447, "no_speech_prob": 0.0, 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{"start": 206.62, "end": 207.02, "word": " حنشوف", "probability": 0.7491455078125}, {"start": 207.02, "end": 207.22, "word": " two", "probability": 0.91650390625}, {"start": 207.22, "end": 207.74, "word": " counter", "probability": 0.8515625}, {"start": 207.74, "end": 208.86, "word": " examples", "probability": 0.828125}, {"start": 208.86, "end": 209.64, "word": " خليني", "probability": 0.851806640625}, {"start": 209.64, "end": 210.12, "word": " نشوفهم", "probability": 0.9012451171875}, {"start": 210.12, "end": 210.28, "word": " مع", "probability": 0.98876953125}, {"start": 210.28, "end": 210.64, "word": " بعض", "probability": 0.99169921875}], "temperature": 1.0}, {"id": 8, "seek": 24343, "start": 216.61, "end": 243.43, "text": "إذا هدى ال remark اللى انا اتحدث عنها قلت انه it should be noted يجب ملاحظة ان journal بصورة عامة instant sequence of intervals need not have a common point يعني لو فيه ending sequence من الفترات المتداخلة مش شرط تقاطعهم يكون في في يعني اى نقطة او نقطة مشاركة يعني مش شرط ان التقاطع لها يساوي فيه", "tokens": [28814, 15730, 8032, 3215, 7578, 2423, 7942, 13672, 7578, 1975, 8315, 1975, 2655, 24401, 12984, 18871, 11296, 12174, 1211, 2655, 16472, 3224, 309, 820, 312, 12964, 7251, 7435, 3555, 3714, 15040, 5016, 19913, 3660, 16472, 6708, 4724, 9381, 13063, 3660, 6225, 10943, 3660, 9836, 8310, 295, 26651, 643, 406, 362, 257, 2689, 935, 37495, 22653, 45164, 8978, 3224, 8121, 8310, 9154, 27188, 2655, 2288, 9307, 9673, 2655, 3215, 47283, 37977, 37893, 13412, 2288, 9566, 6055, 4587, 41193, 3615, 16095, 7251, 30544, 8978, 8978, 37495, 22653, 1975, 7578, 8717, 47432, 3660, 1975, 2407, 8717, 47432, 3660, 37893, 9640, 4117, 3660, 37495, 22653, 37893, 13412, 2288, 9566, 16472, 16712, 4587, 41193, 3615, 5296, 11296, 7251, 3794, 995, 45865, 8978, 3224], "avg_logprob": -0.20365020958315425, "compression_ratio": 1.6383763837638377, "no_speech_prob": 0.0, "words": [{"start": 216.61, "end": 216.95, "word": "إذا", "probability": 0.557373046875}, {"start": 216.95, 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"probability": 0.930908203125}, {"start": 241.29, "end": 241.51, "word": " مش", "probability": 0.9873046875}, {"start": 241.51, "end": 241.79, "word": " شرط", "probability": 0.99560546875}, {"start": 241.79, "end": 241.89, "word": " ان", "probability": 0.703125}, {"start": 241.89, "end": 242.45, "word": " التقاطع", "probability": 0.93212890625}, {"start": 242.45, "end": 242.65, "word": " لها", "probability": 0.6429443359375}, {"start": 242.65, "end": 243.03, "word": " يساوي", "probability": 0.9388427734375}, {"start": 243.03, "end": 243.43, "word": " فيه", "probability": 0.76220703125}], "temperature": 1.0}, {"id": 9, "seek": 27166, "start": 244.58, "end": 271.66, "text": "فالأنثى لها دى هدا هى اللى حكينا عنها اول مثال هاى فى المثال الاول الفرض the hypothesis الفرض ان ال intervals I in فى نظرية 22 be closed cannot be dropped يعني لا يمكن حذفه", "tokens": [5172, 6027, 33456, 12984, 7578, 5296, 11296, 11778, 7578, 8032, 28259, 8032, 7578, 13672, 7578, 11331, 4117, 1829, 8315, 18871, 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"word": " عنها", "probability": 0.9931640625}, {"start": 248.9, "end": 251.0, "word": " اول", "probability": 0.767578125}, {"start": 251.0, "end": 252.92, "word": " مثال", "probability": 0.991455078125}, {"start": 252.92, "end": 258.5, "word": " هاى", "probability": 0.5193684895833334}, {"start": 258.5, "end": 258.6, "word": " فى", "probability": 0.77099609375}, {"start": 258.6, "end": 259.04, "word": " المثال", "probability": 0.96337890625}, {"start": 259.04, "end": 259.54, "word": " الاول", "probability": 0.91064453125}, {"start": 259.54, "end": 260.8, "word": " الفرض", "probability": 0.895751953125}, {"start": 260.8, "end": 261.44, "word": " the", "probability": 0.245361328125}, {"start": 261.44, "end": 262.0, "word": " hypothesis", "probability": 0.82275390625}, {"start": 262.0, "end": 262.6, "word": " الفرض", "probability": 0.9189453125}, {"start": 262.6, "end": 262.92, "word": " ان", "probability": 0.89404296875}, {"start": 262.92, "end": 263.08, "word": " ال", "probability": 0.9130859375}, {"start": 263.08, "end": 263.68, "word": " intervals", "probability": 0.8447265625}, {"start": 263.68, "end": 264.1, "word": " I", "probability": 0.63330078125}, {"start": 264.1, "end": 264.48, "word": " in", "probability": 0.46533203125}, {"start": 264.48, "end": 265.28, "word": " فى", "probability": 0.896728515625}, {"start": 265.28, "end": 265.6, "word": " نظرية", "probability": 0.9677734375}, {"start": 265.6, "end": 266.16, "word": " 22", "probability": 0.67041015625}, {"start": 266.16, "end": 266.78, "word": " be", "probability": 0.5703125}, {"start": 266.78, "end": 267.44, "word": " closed", "probability": 0.8984375}, {"start": 267.44, "end": 268.58, "word": " cannot", "probability": 0.52099609375}, {"start": 268.58, "end": 268.94, "word": " be", "probability": 0.95556640625}, {"start": 268.94, "end": 269.46, "word": " dropped", "probability": 0.80126953125}, {"start": 269.46, "end": 269.94, "word": " يعني", "probability": 0.85546875}, {"start": 269.94, "end": 270.1, "word": " لا", "probability": 0.85595703125}, {"start": 270.1, "end": 270.58, "word": " يمكن", "probability": 0.96875}, {"start": 270.58, "end": 271.66, "word": " حذفه", "probability": 0.8817138671875}], "temperature": 1.0}, {"id": 10, "seek": 30210, "start": 273.26, "end": 302.1, "text": "لا يمكن الاستجناء عنه وتبقى النظرية نظرية صحيحة for example على سبيل المثال لو أخدت الفترات I N الفترة I N هي الفترة المفتوحة من 0 ل 1 على N حيث N عدد طبيعي فواضح ان الفترات هدي nested صح؟ لأن الفترة الأولى هتكون الفترة مفتوحة من 0 ل 1", "tokens": [15040, 7251, 43020, 42963, 14851, 7435, 8315, 38207, 18871, 3224, 34683, 3555, 4587, 7578, 28239, 19913, 2288, 10632, 8717, 19913, 2288, 10632, 20328, 5016, 1829, 5016, 3660, 337, 1365, 15844, 8608, 21292, 1211, 9673, 12984, 6027, 45164, 5551, 9778, 3215, 2655, 27188, 2655, 2288, 9307, 286, 426, 27188, 2655, 25720, 286, 426, 39896, 27188, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 9154, 1958, 5296, 502, 15844, 426, 11331, 1829, 12984, 426, 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I", "probability": 0.9775390625}, {"start": 288.26, "end": 288.48, "word": " N", "probability": 0.96533203125}, {"start": 288.48, "end": 288.62, "word": " هي", "probability": 0.9208984375}, {"start": 288.62, "end": 289.12, "word": " الفترة", "probability": 0.9788411458333334}, {"start": 289.12, "end": 289.84, "word": " المفتوحة", "probability": 0.9761555989583334}, {"start": 289.84, "end": 290.0, "word": " من", "probability": 0.9853515625}, {"start": 290.0, "end": 290.24, "word": " 0", "probability": 0.55224609375}, {"start": 290.24, "end": 290.42, "word": " ل", "probability": 0.72216796875}, {"start": 290.42, "end": 290.68, "word": " 1", "probability": 0.63330078125}, {"start": 290.68, "end": 290.94, "word": " على", "probability": 0.779296875}, {"start": 290.94, "end": 291.24, "word": " N", "probability": 0.9228515625}, {"start": 291.24, "end": 292.16, "word": " حيث", "probability": 0.8561197916666666}, {"start": 292.16, "end": 292.4, "word": " N", "probability": 0.44140625}, {"start": 292.4, "end": 292.8, "word": " عدد", "probability": 0.9684244791666666}, {"start": 292.8, "end": 293.4, "word": " طبيعي", "probability": 0.97216796875}, {"start": 293.4, "end": 295.42, "word": " فواضح", "probability": 0.955322265625}, {"start": 295.42, "end": 295.58, "word": " ان", "probability": 0.495849609375}, {"start": 295.58, "end": 296.18, "word": " الفترات", "probability": 0.990966796875}, {"start": 296.18, "end": 296.52, "word": " هدي", "probability": 0.48193359375}, {"start": 296.52, "end": 297.2, "word": " nested", "probability": 0.653076171875}, {"start": 297.2, "end": 298.54, "word": " صح؟", "probability": 0.6971028645833334}, {"start": 298.54, "end": 299.1, "word": " لأن", "probability": 0.84716796875}, {"start": 299.1, "end": 299.6, "word": " الفترة", "probability": 0.98291015625}, {"start": 299.6, "end": 299.96, "word": " الأولى", "probability": 0.9773763020833334}, {"start": 299.96, "end": 300.46, "word": " هتكون", "probability": 0.82763671875}, {"start": 300.46, "end": 300.86, "word": " الفترة", "probability": 0.9423828125}, {"start": 300.86, "end": 301.28, "word": " مفتوحة", "probability": 0.9508463541666666}, {"start": 301.28, "end": 301.4, "word": " من", "probability": 0.99267578125}, {"start": 301.4, "end": 301.64, "word": " 0", "probability": 0.958984375}, {"start": 301.64, "end": 301.84, "word": " ل", "probability": 0.9248046875}, {"start": 301.84, "end": 302.1, "word": " 1", "probability": 0.927734375}], "temperature": 1.0}, {"id": 11, "seek": 32910, "start": 303.04, "end": 329.1, "text": "الفترة التانية الفترة مفتوحة من سفر لنص وهذه محتوى في I واحد و I تلاتة الفترة مفتوحة من سفر لتلت محتوى داخل I اتنين و هكذا لذلك واضح ان ال sequence of open intervals IN is nested sequence كذلك عناصر ال sequence هذه bounded هذه فترات محصورة", "tokens": [6027, 5172, 2655, 25720, 16712, 7649, 10632, 27188, 2655, 25720, 3714, 5172, 2655, 2407, 5016, 3660, 9154, 8608, 5172, 2288, 5296, 1863, 9381, 37037, 24192, 3714, 33753, 2407, 7578, 8978, 286, 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0.740234375}, {"start": 317.1, "end": 317.24, "word": " ال", "probability": 0.685546875}, {"start": 317.24, "end": 317.82, "word": " sequence", "probability": 0.90087890625}, {"start": 317.82, "end": 318.86, "word": " of", "probability": 0.92138671875}, {"start": 318.86, "end": 319.44, "word": " open", "probability": 0.87353515625}, {"start": 319.44, "end": 320.06, "word": " intervals", "probability": 0.87744140625}, {"start": 320.06, "end": 320.72, "word": " IN", "probability": 0.26123046875}, {"start": 320.72, "end": 321.16, "word": " is", "probability": 0.78173828125}, {"start": 321.16, "end": 321.72, "word": " nested", "probability": 0.967529296875}, {"start": 321.72, "end": 322.32, "word": " sequence", "probability": 0.97021484375}, {"start": 322.32, "end": 324.34, "word": " كذلك", "probability": 0.9837239583333334}, {"start": 324.34, "end": 325.24, "word": " عناصر", "probability": 0.9661458333333334}, {"start": 325.24, "end": 325.4, "word": " ال", "probability": 0.9248046875}, 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576.01, "end": 594.97, "text": "and closed مغلقة لكن ماهياش bounded مش محصورة it's not bounded .. هذه كمجموعة is not bounded above، كمجموعة ليس لها supreme، is not bounded above، اذا شرط ال boundedness اختل وبالتالي نتيجة النظرية هتختل", "tokens": [474, 5395, 3714, 17082, 1211, 28671, 44381, 19446, 3224, 1829, 33599, 37498, 37893, 3714, 5016, 9381, 13063, 3660, 309, 311, 406, 37498, 4386, 29538, 9122, 2304, 7435, 2304, 2407, 27884, 307, 406, 37498, 3673, 12399, 9122, 2304, 7435, 2304, 2407, 27884, 32239, 3794, 5296, 11296, 27756, 12399, 307, 406, 37498, 3673, 12399, 1975, 15730, 13412, 2288, 9566, 2423, 37498, 1287, 1975, 46456, 1211, 46599, 6027, 2655, 6027, 1829, 8717, 31371, 7435, 3660, 28239, 19913, 2288, 10632, 8032, 2655, 46456, 1211], "avg_logprob": -0.21334876248865953, "compression_ratio": 1.6, "no_speech_prob": 0.0, "words": [{"start": 576.01, "end": 576.47, "word": "and", "probability": 0.6904296875}, {"start": 576.47, "end": 577.03, "word": " closed", "probability": 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" nested", "probability": 0.85546875}, {"start": 740.15, "end": 740.83, "word": " intervals", "probability": 0.791015625}, {"start": 740.83, "end": 741.39, "word": " theorem", "probability": 0.8212890625}, {"start": 741.39, "end": 742.85, "word": " صحيحة،", "probability": 0.8179931640625}, {"start": 742.85, "end": 745.73, "word": " okay؟", "probability": 0.77734375}, {"start": 745.73, "end": 745.95, "word": " في", "probability": 0.70361328125}, {"start": 745.95, "end": 746.59, "word": " نظرية", "probability": 0.97607421875}, {"start": 746.59, "end": 747.23, "word": " تانية", "probability": 0.99658203125}], "temperature": 1.0}, {"id": 28, "seek": 77515, "start": 748.93, "end": 775.15, "text": "يمكن هذه مرت معاكم في المبادئ لكن اليوم هنعطيلها برهان يعتمد على ال nested intervals theorem او nested intervals property برهان جديد غير اللي أخدته في مبادئ الرياضيات فالنظرية هذه 24 تتحدث عن ال uncountability of the real numbers", "tokens": [32640, 19452, 29538, 3714, 43500, 20449, 995, 24793, 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of all real numbers is uncountable طيب ما معنى أن ال set تكون countable؟ في حد فيكم بتعرف؟ ال set A أو S definition", "tokens": [5172, 3555, 28820, 4724, 3794, 41193, 3660, 28239, 19913, 2288, 10632, 29538, 39894, 39648, 14739, 3714, 7435, 2304, 2407, 27884, 18863, 3215, 18513, 21542, 38436, 4587, 10632, 307, 6219, 792, 712, 264, 992, 497, 295, 439, 957, 3547, 307, 6219, 792, 712, 23032, 1829, 3555, 19446, 20449, 1863, 7578, 14739, 2423, 992, 6055, 30544, 1207, 712, 22807, 8978, 11331, 3215, 8978, 24793, 39894, 3615, 28480, 22807, 2423, 992, 316, 34051, 318, 7123], "avg_logprob": -0.21511129647085112, "compression_ratio": 1.4278350515463918, "no_speech_prob": 0.0, "words": [{"start": 776.4, "end": 777.02, "word": "فبكل", "probability": 0.6334228515625}, {"start": 777.02, "end": 777.58, "word": " بساطة", "probability": 0.9864501953125}, {"start": 777.58, "end": 778.16, "word": " النظرية", "probability": 0.925537109375}, {"start": 778.16, "end": 778.36, "word": " هذه", "probability": 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16572, 5172, 318, 307, 1207, 712, 498, 293, 787, 498, 9122, 2655, 38688, 9673, 3555, 18513, 19986, 2139, 1975, 15042, 318, 307, 19362, 420, 1975, 2407, 318, 307, 1441, 298, 712], "avg_logprob": -0.19900174190600714, "compression_ratio": 1.117117117117117, "no_speech_prob": 0.0, "words": [{"start": 804.24, "end": 805.12, "word": "definition", "probability": 0.8963216145833334}, {"start": 805.12, "end": 806.0, "word": " تعريف", "probability": 0.9700520833333334}, {"start": 806.0, "end": 806.48, "word": " S", "probability": 0.314697265625}, {"start": 806.48, "end": 806.98, "word": " is", "probability": 0.9375}, {"start": 806.98, "end": 807.92, "word": " countable", "probability": 0.97265625}, {"start": 807.92, "end": 811.92, "word": " if", "probability": 0.927734375}, {"start": 811.92, "end": 812.34, "word": " and", "probability": 0.95556640625}, {"start": 812.34, "end": 812.7, "word": " only", "probability": 0.91845703125}, {"start": 812.7, "end": 813.16, "word": " if", "probability": 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{"id": 31, "seek": 86369, "start": 835.63, "end": 863.69, "text": "أو في بيجيكشن one to one correspondence بينها وبين الأعداد الطبيعية يعني هذا معناه is denumerable قابلة للترقيم طيب إذا كانت ال set ماهياش finite", "tokens": [10721, 2407, 8978, 4724, 1829, 7435, 1829, 4117, 8592, 1863, 472, 281, 472, 38135, 49374, 11296, 46599, 9957, 16247, 22488, 18513, 41950, 21292, 3615, 10632, 37495, 22653, 23758, 20449, 8315, 3224, 307, 1441, 15583, 712, 12174, 16758, 37977, 24976, 2655, 2288, 4587, 32640, 23032, 1829, 3555, 11933, 15730, 25961, 2655, 2423, 992, 19446, 3224, 1829, 33599, 19362], "avg_logprob": -0.16540948147403783, "compression_ratio": 1.3703703703703705, "no_speech_prob": 0.0, "words": [{"start": 835.63, "end": 836.09, "word": "أو", "probability": 0.748046875}, {"start": 836.09, "end": 836.39, "word": " في", "probability": 0.90869140625}, {"start": 836.39, "end": 837.43, "word": " بيجيكشن", "probability": 0.7362234933035714}, {"start": 837.43, "end": 838.15, "word": " one", 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"probability": 0.6717122395833334}, {"start": 847.31, "end": 849.69, "word": " قابلة", "probability": 0.8917643229166666}, {"start": 849.69, "end": 851.23, "word": " للترقيم", "probability": 0.96845703125}, {"start": 851.23, "end": 856.97, "word": " طيب", "probability": 0.9710286458333334}, {"start": 856.97, "end": 857.25, "word": " إذا", "probability": 0.908935546875}, {"start": 857.25, "end": 857.89, "word": " كانت", "probability": 0.992919921875}, {"start": 857.89, "end": 859.41, "word": " ال", "probability": 0.9208984375}, {"start": 859.41, "end": 859.81, "word": " set", "probability": 0.88427734375}, {"start": 859.81, "end": 863.33, "word": " ماهياش", "probability": 0.927734375}, {"start": 863.33, "end": 863.69, "word": " finite", "probability": 0.98046875}], "temperature": 1.0}, {"id": 32, "seek": 89239, "start": 865.07, "end": 892.39, "text": "وماهياش in one to one correspondence with the natural numbers او ماهياش denumerable فبنسميها uncountable غير قابلة للعد countable قابلة للعد uncountable غير قابلة للعد طيب ال ..", "tokens": [2407, 15042, 3224, 1829, 33599, 294, 472, 281, 472, 38135, 365, 264, 3303, 3547, 1975, 2407, 19446, 3224, 1829, 33599, 1441, 15583, 712, 6156, 3555, 1863, 38251, 1829, 11296, 6219, 792, 712, 32771, 13546, 12174, 16758, 37977, 24976, 22488, 1207, 712, 12174, 16758, 37977, 24976, 22488, 6219, 792, 712, 32771, 13546, 12174, 16758, 37977, 24976, 22488, 23032, 1829, 3555, 2423, 4386], "avg_logprob": -0.16519657906986052, "compression_ratio": 1.5973154362416107, "no_speech_prob": 0.0, "words": [{"start": 865.0699999999999, "end": 866.03, "word": "وماهياش", "probability": 0.78505859375}, {"start": 866.03, "end": 866.57, "word": " in", "probability": 0.62109375}, {"start": 866.57, "end": 866.85, "word": " one", "probability": 0.91064453125}, {"start": 866.85, "end": 867.15, "word": " to", "probability": 0.85400390625}, {"start": 867.15, "end": 867.37, "word": " one", "probability": 0.95068359375}, {"start": 867.37, "end": 868.29, "word": " 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ان ال interval هذي و ال interval هذي كلا هما uncountable الفترة المفتوحة من سفر لواحد infinite set اول حاجة infinite set و طبعا ممكن تثبت انها uncountable", "tokens": [2304, 3615, 32887, 5172, 8978, 3714, 3555, 18513, 19986, 12602, 1829, 46958, 1829, 9307, 11778, 2288, 3794, 8315, 16472, 2423, 15035, 8032, 8848, 1829, 4032, 2423, 15035, 8032, 8848, 1829, 9122, 15040, 8032, 15042, 6219, 792, 712, 27188, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 9154, 8608, 5172, 2288, 5296, 14407, 24401, 13785, 992, 1975, 12610, 11331, 26108, 3660, 13785, 992, 4032, 23032, 3555, 3615, 995, 3714, 43020, 6055, 12984, 3555, 2655, 16472, 11296, 6219, 792, 712], "avg_logprob": -0.19649921301044995, "compression_ratio": 1.5747126436781609, "no_speech_prob": 0.0, "words": [{"start": 895.18, "end": 896.18, "word": "معروف", "probability": 0.9410400390625}, {"start": 896.18, "end": 897.18, "word": " في", "probability": 0.71435546875}, {"start": 897.18, "end": 897.82, "word": " مبادئ", "probability": 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957.43, "end": 984.87, "text": "الـ احنا عايزين نثبت عشان نثبت ان ال set هذه ال R لاحظوا ان ال R is in one to one correspondence مع الفترة المفتوحة او المغلقة حتى في byjection بينه وبين الفترة", "tokens": [6027, 39184, 1975, 5016, 8315, 6225, 47302, 11622, 9957, 8717, 12984, 3555, 2655, 6225, 8592, 7649, 8717, 12984, 3555, 2655, 16472, 2423, 992, 29538, 2423, 497, 20193, 5016, 19913, 14407, 16472, 2423, 497, 307, 294, 472, 281, 472, 38135, 20449, 27188, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 1975, 2407, 9673, 17082, 1211, 28671, 11331, 49975, 8978, 538, 1020, 313, 49374, 3224, 46599, 9957, 27188, 2655, 25720], "avg_logprob": -0.2290534420289855, "compression_ratio": 1.5121951219512195, "no_speech_prob": 0.0, "words": [{"start": 957.4300000000001, "end": 958.3100000000001, "word": "الـ", "probability": 0.26239013671875}, {"start": 958.3100000000001, "end": 959.19, "word": " احنا", "probability": 0.7806803385416666}, {"start": 959.19, "end": 959.71, "word": " عايزين", 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"probability": 0.84259033203125}, {"start": 1032.58, "end": 1032.84, "word": " هذه", "probability": 0.87060546875}, {"start": 1032.84, "end": 1033.28, "word": " finite", "probability": 0.9873046875}, {"start": 1033.28, "end": 1033.8, "word": " إذا", "probability": 0.78662109375}, {"start": 1033.8, "end": 1034.14, "word": " كانت", "probability": 0.917236328125}, {"start": 1034.14, "end": 1034.14, "word": " هذه", "probability": 0.97998046875}, {"start": 1034.14, "end": 1034.48, "word": " infinite", "probability": 0.69921875}, {"start": 1034.48, "end": 1034.92, "word": " تظهر", "probability": 0.974853515625}, {"start": 1034.92, "end": 1035.14, "word": " هذه", "probability": 0.94580078125}, {"start": 1035.14, "end": 1035.54, "word": " infinite", "probability": 0.97216796875}, {"start": 1035.54, "end": 1037.8, "word": " كل", "probability": 0.6376953125}, {"start": 1037.8, "end": 1038.02, "word": " هذه", "probability": 0.9765625}, {"start": 1038.02, "end": 1038.58, "word": " نظريات", 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"word": " R", "probability": 0.372802734375}, {"start": 1045.93, "end": 1046.73, "word": " uncountable", "probability": 0.7298177083333334}, {"start": 1046.73, "end": 1051.01, "word": " طيب", "probability": 0.79736328125}, {"start": 1051.01, "end": 1051.55, "word": " لإثبات", "probability": 0.841357421875}, {"start": 1051.55, "end": 1052.21, "word": " ذلك", "probability": 0.969482421875}, {"start": 1052.21, "end": 1054.21, "word": " هنا", "probability": 0.09002685546875}, {"start": 1054.21, "end": 1054.79, "word": " عايزين", "probability": 0.9334716796875}, {"start": 1054.79, "end": 1055.75, "word": " نثبت", "probability": 0.9866943359375}, {"start": 1055.75, "end": 1058.45, "word": " إن", "probability": 0.50390625}, {"start": 1058.45, "end": 1059.21, "word": " الفترة", "probability": 0.9822591145833334}, {"start": 1059.21, "end": 1060.73, "word": " هادى", "probability": 0.8961588541666666}, {"start": 1060.73, "end": 1061.91, "word": " نثبت", "probability": 0.77587890625}, {"start": 1061.91, "end": 1062.05, "word": " إن", "probability": 0.49755859375}, {"start": 1062.05, "end": 1062.53, "word": " الفترة", "probability": 0.9781901041666666}, {"start": 1062.53, "end": 1062.97, "word": " هادى", "probability": 0.9654947916666666}, {"start": 1062.97, "end": 1063.83, "word": " uncountable", "probability": 0.8444010416666666}, {"start": 1063.83, "end": 1064.39, "word": " لبرهان", "probability": 0.79754638671875}, {"start": 1064.39, "end": 1064.83, "word": " ذلك", "probability": 0.992919921875}, {"start": 1064.83, "end": 1066.63, "word": " نعمل", "probability": 0.8401692708333334}, {"start": 1066.63, "end": 1067.03, "word": " برهان", "probability": 0.975830078125}, {"start": 1067.03, "end": 1067.77, "word": " بالتناقض", "probability": 0.96455078125}], "temperature": 1.0}, {"id": 39, "seek": 109764, "start": 1077.1, "end": 1097.64, "text": "بنثبت ان الفترة المغلقة هذي uncountable نفرض المقيد ان الفترة هذي countable لاحظوا ان الفترة هذي infinite والان countable اذا بتطلع equipotent او in one to one correspondence with natural numbers", "tokens": [3555, 1863, 12984, 3555, 2655, 16472, 27188, 2655, 25720, 9673, 17082, 1211, 28671, 8032, 8848, 1829, 6219, 792, 712, 8717, 5172, 43042, 9673, 4587, 25708, 16472, 27188, 2655, 25720, 8032, 8848, 1829, 1207, 712, 20193, 5016, 19913, 14407, 16472, 27188, 2655, 25720, 8032, 8848, 1829, 13785, 16070, 7649, 1207, 712, 1975, 15730, 39894, 9566, 1211, 3615, 5037, 310, 317, 1975, 2407, 294, 472, 281, 472, 38135, 365, 3303, 3547], "avg_logprob": -0.315625005534717, "compression_ratio": 1.5941176470588236, "no_speech_prob": 0.0, "words": [{"start": 1077.1, "end": 1077.76, "word": "بنثبت", "probability": 0.652099609375}, {"start": 1077.76, "end": 1077.86, "word": " ان", "probability": 0.3935546875}, {"start": 1077.86, "end": 1078.26, "word": " الفترة", "probability": 0.9762369791666666}, {"start": 1078.26, "end": 1078.72, "word": " المغلقة", "probability": 0.89501953125}, {"start": 1078.72, "end": 1079.02, "word": " هذي", "probability": 0.48583984375}, {"start": 1079.02, "end": 1079.84, "word": " uncountable", "probability": 0.7830403645833334}, {"start": 1079.84, "end": 1081.16, "word": " نفرض", "probability": 0.4908040364583333}, {"start": 1081.16, "end": 1084.94, "word": " المقيد", "probability": 0.713134765625}, {"start": 1084.94, "end": 1085.46, "word": " ان", "probability": 0.4931640625}, {"start": 1085.46, "end": 1085.94, "word": " الفترة", "probability": 0.9840494791666666}, {"start": 1085.94, "end": 1086.28, "word": " هذي", "probability": 0.81689453125}, {"start": 1086.28, "end": 1086.94, "word": " countable", "probability": 0.967041015625}, {"start": 1086.94, "end": 1087.92, "word": " لاحظوا", "probability": 0.793548583984375}, {"start": 1087.92, "end": 1088.02, "word": " ان", "probability": 0.79931640625}, {"start": 1088.02, "end": 1088.44, "word": " الفترة", "probability": 0.98193359375}, {"start": 1088.44, "end": 1088.78, "word": " هذي", "probability": 0.90283203125}, {"start": 1088.78, "end": 1089.32, "word": " infinite", "probability": 0.74560546875}, {"start": 1089.32, "end": 1090.88, "word": " والان", "probability": 0.6458740234375}, {"start": 1090.88, "end": 1091.72, "word": " countable", "probability": 0.955078125}, {"start": 1091.72, "end": 1092.7, "word": " اذا", "probability": 0.5946044921875}, {"start": 1092.7, "end": 1093.26, "word": " بتطلع", "probability": 0.899169921875}, {"start": 1093.26, "end": 1094.26, "word": " equipotent", "probability": 0.7721354166666666}, {"start": 1094.26, "end": 1094.5, "word": " او", "probability": 0.907958984375}, {"start": 1094.5, "end": 1094.68, "word": " in", "probability": 0.7099609375}, {"start": 1094.68, "end": 1094.88, "word": " one", "probability": 0.9287109375}, {"start": 1094.88, "end": 1094.98, "word": " to", "probability": 0.7041015625}, {"start": 1094.98, "end": 1095.1, "word": " one", "probability": 0.94384765625}, {"start": 1095.1, "end": 1095.76, "word": " correspondence", "probability": 0.94921875}, {"start": 1095.76, "end": 1096.34, "word": " with", "probability": 0.92041015625}, {"start": 1096.34, "end": 1096.9, "word": " natural", "probability": 0.51904296875}, {"start": 1096.9, "end": 1097.64, "word": " numbers", "probability": 0.84619140625}], "temperature": 1.0}, {"id": 40, "seek": 111157, "start": 1102.85, "end": 1111.57, "text": "الأن في الحالة هذه I in one to one correspondence within actual numbers أو بنسميها innumerable صح؟", "tokens": [6027, 33456, 8978, 21542, 6027, 3660, 29538, 286, 294, 472, 281, 472, 38135, 1951, 3539, 3547, 34051, 44945, 38251, 1829, 11296, 7714, 15583, 712, 20328, 5016, 22807], "avg_logprob": -0.3024553528853825, "compression_ratio": 1.050420168067227, "no_speech_prob": 0.0, "words": [{"start": 1102.85, "end": 1103.21, "word": "الأن", "probability": 0.4774169921875}, {"start": 1103.21, "end": 1103.33, "word": " في", "probability": 0.84423828125}, {"start": 1103.33, "end": 1103.73, "word": " الحالة", "probability": 0.98681640625}, {"start": 1103.73, "end": 1104.03, "word": " هذه", "probability": 0.8701171875}, {"start": 1104.03, "end": 1104.49, "word": " I", "probability": 0.666015625}, {"start": 1104.49, "end": 1105.31, "word": " in", "probability": 0.77392578125}, {"start": 1105.31, "end": 1105.59, "word": " one", "probability": 0.95263671875}, {"start": 1105.59, "end": 1105.71, "word": " to", "probability": 0.833984375}, {"start": 1105.71, "end": 1105.89, "word": " one", "probability": 0.94873046875}, {"start": 1105.89, "end": 1106.55, "word": " correspondence", "probability": 0.93701171875}, {"start": 1106.55, "end": 1107.11, "word": " within", "probability": 0.34326171875}, {"start": 1107.11, "end": 1107.55, "word": " actual", "probability": 0.76318359375}, {"start": 1107.55, "end": 1108.17, "word": " numbers", "probability": 0.85205078125}, {"start": 1108.17, "end": 1109.03, "word": " أو", "probability": 0.59130859375}, {"start": 1109.03, "end": 1109.77, "word": " بنسميها", "probability": 0.8753662109375}, {"start": 1109.77, "end": 1110.43, "word": " innumerable", "probability": 0.5974934895833334}, {"start": 1110.43, "end": 1111.57, "word": " صح؟", "probability": 0.9039713541666666}], "temperature": 1.0}, {"id": 41, "seek": 113980, "start": 1113.28, "end": 1139.8, "text": "الان ال set I denominable يعني ممكن ترقيمها بالأعداد الطبيعية إذا ممكن نسمي عناصرها xn-n عدد طبيعي اللي هي x1, x2, x3 الاخرى أي set denominable أو in one to one correspondence with natural numbers ممكن ترقيم عناصرها ك list by the natural numbers إذا I هي كل عناصرها رقمناهم بالأعداد الطبيعية", "tokens": [6027, 7649, 2423, 992, 286, 16244, 712, 37495, 22653, 3714, 43020, 6055, 2288, 4587, 32640, 11296, 20666, 10721, 22488, 18513, 41950, 21292, 3615, 10632, 11933, 15730, 3714, 43020, 8717, 38251, 1829, 18871, 33546, 2288, 11296, 2031, 77, 12, 77, 6225, 3215, 3215, 23032, 21292, 3615, 1829, 13672, 1829, 39896, 2031, 16, 11, 2031, 17, 11, 2031, 18, 2423, 47283, 2288, 7578, 36632, 992, 16244, 712, 34051, 294, 472, 281, 472, 38135, 365, 3303, 3547, 3714, 43020, 6055, 2288, 4587, 32640, 18871, 33546, 2288, 11296, 9122, 1329, 538, 264, 3303, 3547, 11933, 15730, 286, 39896, 28242, 18871, 33546, 2288, 11296, 12602, 4587, 2304, 8315, 16095, 20666, 10721, 22488, 18513, 41950, 21292, 3615, 10632], "avg_logprob": -0.22856747365630833, "compression_ratio": 1.7890295358649788, "no_speech_prob": 0.0, "words": [{"start": 1113.28, "end": 1113.74, "word": "الان", "probability": 0.8251953125}, {"start": 1113.74, "end": 1113.94, "word": " ال", "probability": 0.69482421875}, {"start": 1113.94, "end": 1114.18, "word": " set", "probability": 0.720703125}, {"start": 1114.18, "end": 1114.42, "word": " I", "probability": 0.4423828125}, {"start": 1114.42, "end": 1115.06, "word": " denominable", "probability": 0.66552734375}, {"start": 1115.06, "end": 1115.38, "word": " يعني", "probability": 0.845458984375}, {"start": 1115.38, "end": 1115.7, "word": " ممكن", "probability": 0.982177734375}, {"start": 1115.7, "end": 1116.56, "word": " ترقيمها", "probability": 0.96064453125}, {"start": 1116.56, "end": 1117.32, "word": " بالأعداد", "probability": 0.80841064453125}, {"start": 1117.32, "end": 1118.0, "word": " الطبيعية", "probability": 0.955078125}, {"start": 1118.0, "end": 1118.34, "word": " إذا", "probability": 0.50225830078125}, {"start": 1118.34, "end": 1118.76, "word": " ممكن", "probability": 0.913818359375}, {"start": 1118.76, "end": 1119.34, "word": " نسمي", "probability": 0.87109375}, {"start": 1119.34, "end": 1119.98, "word": " عناصرها", "probability": 0.8487548828125}, {"start": 1119.98, "end": 1120.9, "word": " xn", "probability": 0.4947509765625}, {"start": 1120.9, "end": 1121.58, "word": "-n", "probability": 0.4942626953125}, {"start": 1121.58, "end": 1121.84, "word": " عدد", "probability": 0.7550455729166666}, {"start": 1121.84, "end": 1122.22, "word": " طبيعي", "probability": 0.9515380859375}, {"start": 1122.22, "end": 1122.38, "word": " اللي", "probability": 0.60467529296875}, {"start": 1122.38, "end": 1122.5, "word": " هي", "probability": 0.7880859375}, {"start": 1122.5, "end": 1122.94, "word": " x1,", "probability": 0.805908203125}, {"start": 1123.1, "end": 1123.52, "word": " x2,", "probability": 0.888916015625}, {"start": 1123.64, "end": 1124.08, "word": " x3", "probability": 0.9501953125}, {"start": 1124.08, "end": 1125.12, "word": " الاخرى", "probability": 0.596466064453125}, {"start": 1125.12, "end": 1125.3, "word": " أي", "probability": 0.4072265625}, {"start": 1125.3, "end": 1125.64, "word": " set", "probability": 0.97119140625}, {"start": 1125.64, "end": 1126.34, "word": " denominable", "probability": 0.821044921875}, {"start": 1126.34, "end": 1127.1, "word": " أو", "probability": 0.740234375}, {"start": 1127.1, "end": 1127.8, "word": " in", "probability": 0.66552734375}, {"start": 1127.8, "end": 1128.04, "word": " one", "probability": 0.9091796875}, {"start": 1128.04, "end": 1128.2, "word": " to", "probability": 0.7451171875}, {"start": 1128.2, "end": 1128.4, "word": " one", "probability": 0.9501953125}, {"start": 1128.4, "end": 1129.14, "word": " correspondence", "probability": 0.95458984375}, {"start": 1129.14, "end": 1129.5, "word": " with", "probability": 0.919921875}, {"start": 1129.5, "end": 1129.9, "word": " natural", "probability": 0.425537109375}, {"start": 1129.9, "end": 1130.54, "word": " numbers", "probability": 0.8564453125}, {"start": 1130.54, "end": 1131.32, "word": " ممكن", "probability": 0.981689453125}, {"start": 1131.32, "end": 1131.92, "word": " ترقيم", "probability": 0.97216796875}, {"start": 1131.92, "end": 1132.5, "word": " عناصرها", "probability": 0.9798583984375}, {"start": 1132.5, "end": 1132.76, "word": " ك", "probability": 0.97900390625}, {"start": 1132.76, "end": 1133.16, "word": " list", "probability": 0.88330078125}, {"start": 1133.16, "end": 1134.54, "word": " by", "probability": 0.9072265625}, {"start": 1134.54, "end": 1134.76, "word": " the", "probability": 0.85595703125}, {"start": 1134.76, "end": 1135.14, "word": " natural", "probability": 0.841796875}, {"start": 1135.14, "end": 1135.68, "word": " numbers", "probability": 0.79443359375}, {"start": 1135.68, "end": 1136.0, "word": " إذا", "probability": 0.5262451171875}, {"start": 1136.0, "end": 1136.72, "word": " I", "probability": 0.8681640625}, {"start": 1136.72, "end": 1137.1, "word": " هي", "probability": 0.408203125}, {"start": 1137.1, "end": 1137.38, "word": " كل", "probability": 0.89453125}, {"start": 1137.38, "end": 1137.96, "word": " عناصرها", "probability": 0.9888916015625}, {"start": 1137.96, "end": 1138.66, "word": " رقمناهم", "probability": 0.901953125}, {"start": 1138.66, "end": 1139.2, "word": " بالأعداد", "probability": 0.941650390625}, {"start": 1139.2, "end": 1139.8, "word": " الطبيعية", "probability": 0.9822998046875}], "temperature": 1.0}, {"id": 42, "seek": 116721, "start": 1145.09, "end": 1167.21, "text": "لحظة احنا بدنا نصل الى تناقض احنا بدنا القرآن وفرضنا ال contrary هيو Assume ال contrary ان I is countable بدنا نصل الى تناقض طيب هي الفترة I هي الفترة I هي الفترة I هذه I", "tokens": [1211, 5016, 19913, 3660, 1975, 5016, 8315, 47525, 8315, 8717, 36520, 2423, 7578, 6055, 8315, 4587, 11242, 1975, 5016, 8315, 47525, 8315, 25062, 2288, 148, 48506, 4032, 5172, 43042, 8315, 2423, 19506, 39896, 2407, 6281, 2540, 2423, 19506, 16472, 286, 307, 1207, 712, 47525, 8315, 8717, 36520, 2423, 7578, 6055, 8315, 4587, 11242, 23032, 1829, 3555, 39896, 27188, 2655, 25720, 286, 39896, 27188, 2655, 25720, 286, 39896, 27188, 2655, 25720, 286, 29538, 286], "avg_logprob": -0.26478039493431915, "compression_ratio": 1.8541666666666667, "no_speech_prob": 0.0, "words": [{"start": 1145.09, "end": 1145.61, "word": "لحظة", "probability": 0.80047607421875}, {"start": 1145.61, "end": 1145.85, "word": " احنا", "probability": 0.6822509765625}, {"start": 1145.85, "end": 1146.09, "word": " بدنا", "probability": 0.8466796875}, {"start": 1146.09, "end": 1146.41, "word": " نصل", "probability": 0.95458984375}, {"start": 1146.41, "end": 1146.65, "word": " الى", "probability": 0.77734375}, {"start": 1146.65, "end": 1147.21, "word": " تناقض", "probability": 0.958984375}, {"start": 1147.21, "end": 1147.47, "word": " احنا", "probability": 0.8396809895833334}, {"start": 1147.47, "end": 1147.77, "word": " بدنا", "probability": 0.87109375}, {"start": 1147.77, "end": 1148.35, "word": " القرآن", "probability": 0.6682586669921875}, {"start": 1148.35, "end": 1149.97, "word": " وفرضنا", "probability": 0.8033447265625}, {"start": 1149.97, "end": 1150.11, "word": " ال", "probability": 0.91552734375}, {"start": 1150.11, "end": 1150.65, "word": " contrary", "probability": 0.5712890625}, {"start": 1150.65, "end": 1151.23, "word": " هيو", "probability": 0.4146728515625}, {"start": 1151.23, "end": 1152.91, "word": " Assume", "probability": 0.60528564453125}, {"start": 1152.91, "end": 1153.31, "word": " ال", "probability": 0.90625}, {"start": 1153.31, "end": 1154.01, "word": " contrary", "probability": 0.8408203125}, {"start": 1154.01, "end": 1154.97, "word": " ان", "probability": 0.75244140625}, {"start": 1154.97, "end": 1155.35, "word": " I", "probability": 0.424560546875}, {"start": 1155.35, "end": 1155.65, "word": " is", "probability": 0.923828125}, {"start": 1155.65, "end": 1156.25, "word": " countable", "probability": 0.95751953125}, {"start": 1156.25, "end": 1156.55, "word": " بدنا", "probability": 0.849365234375}, {"start": 1156.55, "end": 1156.83, "word": " نصل", "probability": 0.985595703125}, {"start": 1156.83, "end": 1157.07, "word": " الى", "probability": 0.96630859375}, {"start": 1157.07, "end": 1157.69, "word": " تناقض", "probability": 0.991455078125}, {"start": 1157.69, "end": 1158.61, "word": " طيب", "probability": 0.7513020833333334}, {"start": 1158.61, "end": 1158.75, "word": " هي", "probability": 0.402099609375}, {"start": 1158.75, "end": 1159.27, "word": " الفترة", "probability": 0.9811197916666666}, {"start": 1159.27, "end": 1159.57, "word": " I", "probability": 0.99072265625}, {"start": 1159.57, "end": 1159.87, "word": " هي", "probability": 0.381103515625}, {"start": 1159.87, "end": 1160.41, "word": " الفترة", "probability": 0.98095703125}, {"start": 1160.41, "end": 1160.77, "word": " I", "probability": 0.986328125}, {"start": 1160.77, "end": 1162.41, "word": " هي", "probability": 0.55078125}, {"start": 1162.41, "end": 1162.93, "word": " الفترة", "probability": 0.9900716145833334}, {"start": 1162.93, "end": 1163.85, "word": " I", "probability": 0.9970703125}, {"start": 1163.85, "end": 1166.89, "word": " هذه", "probability": 0.371337890625}, {"start": 1166.89, "end": 1167.21, "word": " I", "probability": 0.99072265625}], "temperature": 1.0}, {"id": 43, "seek": 119510, "start": 1168.25, "end": 1195.11, "text": "و في اندس اي هاد الفترة اي هاد يعني عناصرها هي مرقمة اكس واحد اكس اتنين الى ملا نهاية افرض ان اكس واحد موجود هان اول عنصر في الفترة موجود هان فممكن اختار فترة مغلقة اسميها اي واحد ممكن اختار فترة مغلقة", "tokens": [2407, 8978, 16472, 3215, 3794, 1975, 1829, 8032, 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{"start": 1168.99, "end": 1169.53, "word": " اي", "probability": 0.513427734375}, {"start": 1169.53, "end": 1169.83, "word": " هاد", "probability": 0.2454833984375}, {"start": 1169.83, "end": 1170.25, "word": " الفترة", "probability": 0.9573567708333334}, {"start": 1170.25, "end": 1170.51, "word": " اي", "probability": 0.761962890625}, {"start": 1170.51, "end": 1170.79, "word": " هاد", "probability": 0.9365234375}, {"start": 1170.79, "end": 1170.87, "word": " يعني", "probability": 0.781494140625}, {"start": 1170.87, "end": 1171.39, "word": " عناصرها", "probability": 0.78863525390625}, {"start": 1171.39, "end": 1171.55, "word": " هي", "probability": 0.47021484375}, {"start": 1171.55, "end": 1172.25, "word": " مرقمة", "probability": 0.779296875}, {"start": 1172.25, "end": 1173.75, "word": " اكس", "probability": 0.7052408854166666}, {"start": 1173.75, "end": 1174.13, "word": " واحد", "probability": 0.98388671875}, {"start": 1174.13, "end": 1174.43, "word": " اكس", "probability": 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"probability": 0.97607421875}, {"start": 1180.89, "end": 1181.03, "word": " في", "probability": 0.60888671875}, {"start": 1181.03, "end": 1181.55, "word": " الفترة", "probability": 0.99072265625}, {"start": 1181.55, "end": 1182.59, "word": " موجود", "probability": 0.9825846354166666}, {"start": 1182.59, "end": 1182.89, "word": " هان", "probability": 0.907958984375}, {"start": 1182.89, "end": 1186.51, "word": " فممكن", "probability": 0.9181315104166666}, {"start": 1186.51, "end": 1187.11, "word": " اختار", "probability": 0.9791666666666666}, {"start": 1187.11, "end": 1187.55, "word": " فترة", "probability": 0.9915364583333334}, {"start": 1187.55, "end": 1188.15, "word": " مغلقة", "probability": 0.9659423828125}, {"start": 1188.15, "end": 1190.35, "word": " اسميها", "probability": 0.9002685546875}, {"start": 1190.35, "end": 1190.69, "word": " اي", "probability": 0.761474609375}, {"start": 1190.69, "end": 1191.19, "word": " واحد", "probability": 0.990478515625}, {"start": 1191.19, "end": 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نهاية و كل الفترات هذول محتوى .. كل واحدة منهم محتوى داخل الـ I و كل واحدة من الفترات هذه صممناها بحيث ان XN لا ينتمي إلى IN لكل N بساوي واحد اتنين إلى ملا نهاية صح؟ إذا لو استمرنا في العملية هذه", "tokens": [2407, 8032, 4117, 15730, 3714, 43020, 8717, 14851, 29973, 30731, 3714, 15040, 8717, 11296, 10632, 4032, 28242, 27188, 2655, 2288, 9307, 8032, 8848, 12610, 3714, 33753, 2407, 7578, 4386, 28242, 36764, 24401, 3660, 9154, 16095, 3714, 33753, 2407, 7578, 11778, 47283, 1211, 2423, 39184, 286, 4032, 28242, 36764, 24401, 3660, 9154, 27188, 2655, 2288, 9307, 29538, 20328, 2304, 2304, 8315, 11296, 4724, 5016, 1829, 12984, 16472, 1783, 45, 20193, 7251, 29399, 2304, 1829, 30731, 6892, 5296, 28820, 426, 4724, 3794, 995, 45865, 36764, 24401, 1975, 2655, 1863, 9957, 30731, 3714, 15040, 8717, 11296, 10632, 20328, 5016, 22807, 11933, 15730, 45164, 44713, 29973, 8315, 8978, 18863, 42213, 10632, 29538], "avg_logprob": -0.182196099823768, "compression_ratio": 1.9494949494949494, "no_speech_prob": 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{"start": 1531.51, "end": 1531.77, "word": " X", "probability": 0.634765625}], "temperature": 1.0}, {"id": 56, "seek": 155525, "start": 1533.73, "end": 1555.25, "text": "تمام؟ الآن في البرهان هذا وجدنا ان في صي أنصر جديد في I مختلف عن كل عناصرها معناته هذه ال list ليست ترقيم كامل ل I في عناصر أخرى زي صي مش مرقمة و هذا تناقض", "tokens": [2655, 15042, 2304, 22807, 6024, 48506, 8978, 2423, 26890, 3224, 7649, 23758, 49610, 3215, 8315, 16472, 8978, 20328, 1829, 14739, 9381, 2288, 10874, 16254, 3215, 8978, 286, 3714, 46456, 46538, 18871, 28242, 18871, 33546, 2288, 11296, 20449, 8315, 47395, 29538, 2423, 1329, 32239, 14851, 6055, 2288, 4587, 32640, 9122, 10943, 1211, 5296, 286, 8978, 18871, 33546, 2288, 5551, 34740, 7578, 30767, 1829, 20328, 1829, 37893, 3714, 2288, 4587, 46007, 4032, 23758, 6055, 8315, 4587, 11242], "avg_logprob": -0.19274259868421054, "compression_ratio": 1.6204819277108433, "no_speech_prob": 0.0, "words": [{"start": 1533.73, "end": 1534.69, "word": "تمام؟", "probability": 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1575.25, "text": "لأن إحنا عندنا ال set I هذي countable و infinite و denomable إذن هي list تبع كل عناصرها فكيف طلع فيه أنصر جديد مختلف عن عناصرها فهذا تناقض إذن هذا التناقض بثبت أن فرضنا أن الفترة I", "tokens": [1211, 33456, 11933, 5016, 8315, 43242, 8315, 2423, 992, 286, 8032, 8848, 1829, 1207, 712, 4032, 13785, 4032, 1441, 298, 712, 11933, 8848, 1863, 39896, 1329, 6055, 3555, 3615, 28242, 18871, 33546, 2288, 11296, 6156, 4117, 33911, 23032, 1211, 3615, 8978, 3224, 14739, 9381, 2288, 10874, 16254, 3215, 3714, 46456, 46538, 18871, 18871, 33546, 2288, 11296, 6156, 3224, 15730, 6055, 8315, 4587, 11242, 11933, 8848, 1863, 23758, 16712, 8315, 4587, 11242, 4724, 12984, 3555, 2655, 14739, 6156, 43042, 8315, 14739, 27188, 2655, 25720, 286], "avg_logprob": -0.2531249915852266, "compression_ratio": 1.5210526315789474, "no_speech_prob": 0.0, "words": [{"start": 1556.63, "end": 1557.03, "word": "لأن", "probability": 0.573974609375}, {"start": 1557.03, "end": 1557.33, "word": " إحنا", 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"word": " هي", "probability": 0.52392578125}, {"start": 1562.29, "end": 1562.77, "word": " list", "probability": 0.7666015625}, {"start": 1562.77, "end": 1563.23, "word": " تبع", "probability": 0.9225260416666666}, {"start": 1563.23, "end": 1563.55, "word": " كل", "probability": 0.9521484375}, {"start": 1563.55, "end": 1564.21, "word": " عناصرها", "probability": 0.923095703125}, {"start": 1564.21, "end": 1565.35, "word": " فكيف", "probability": 0.9215494791666666}, {"start": 1565.35, "end": 1565.65, "word": " طلع", "probability": 0.9607747395833334}, {"start": 1565.65, "end": 1565.83, "word": " فيه", "probability": 0.776123046875}, {"start": 1565.83, "end": 1566.19, "word": " أنصر", "probability": 0.9339192708333334}, {"start": 1566.19, "end": 1566.53, "word": " جديد", "probability": 0.9703776041666666}, {"start": 1566.53, "end": 1567.03, "word": " مختلف", "probability": 0.9801432291666666}, {"start": 1567.03, "end": 1567.39, "word": " عن", "probability": 0.9970703125}, {"start": 1567.39, "end": 1568.81, "word": " عناصرها", "probability": 0.9249267578125}, {"start": 1568.81, "end": 1570.65, "word": " فهذا", "probability": 0.8391927083333334}, {"start": 1570.65, "end": 1571.23, "word": " تناقض", "probability": 0.86279296875}, {"start": 1571.23, "end": 1571.93, "word": " إذن", "probability": 0.7724609375}, {"start": 1571.93, "end": 1572.09, "word": " هذا", "probability": 0.904296875}, {"start": 1572.09, "end": 1572.59, "word": " التناقض", "probability": 0.987548828125}, {"start": 1572.59, "end": 1573.11, "word": " بثبت", "probability": 0.94921875}, {"start": 1573.11, "end": 1573.31, "word": " أن", "probability": 0.56201171875}, {"start": 1573.31, "end": 1573.83, "word": " فرضنا", "probability": 0.96533203125}, {"start": 1573.83, "end": 1574.07, "word": " أن", "probability": 0.6337890625}, {"start": 1574.07, "end": 1574.95, "word": " الفترة", "probability": 0.96484375}, {"start": 1574.95, "end": 1575.25, "word": " I", "probability": 0.95947265625}], "temperature": 1.0}, {"id": 58, "seek": 160622, "start": 1577.54, "end": 1606.22, "text": "كانت countable كان فرض خاطر وبالتالي الفترة I تطلع uncountable اذا الان الفترة I uncountable وانا عندي R equivalent لفترة مغلقة 01 ممكن نوجد bijection بينهم اذا ال R تطلع uncountable كما هو مطلوب اذا هذا هو برهان", "tokens": [41361, 2655, 1207, 712, 25961, 6156, 43042, 16490, 41193, 2288, 46599, 6027, 2655, 6027, 1829, 27188, 2655, 25720, 286, 6055, 9566, 1211, 3615, 6219, 792, 712, 1975, 15730, 2423, 7649, 27188, 2655, 25720, 286, 6219, 792, 712, 4032, 7649, 995, 18871, 16254, 497, 10344, 5296, 5172, 2655, 25720, 3714, 17082, 1211, 28671, 23185, 3714, 43020, 8717, 29245, 3215, 3228, 1020, 313, 49374, 16095, 1975, 15730, 2423, 497, 6055, 9566, 1211, 3615, 6219, 792, 712, 9122, 15042, 31439, 3714, 9566, 1211, 37746, 1975, 15730, 23758, 31439, 4724, 2288, 3224, 7649], "avg_logprob": -0.23854166136847602, "compression_ratio": 1.702127659574468, "no_speech_prob": 0.0, "words": [{"start": 1577.54, "end": 1578.14, 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1584.8, "end": 1585.34, "word": " الفترة", "probability": 0.9697265625}, {"start": 1585.34, "end": 1585.6, "word": " I", "probability": 0.9814453125}, {"start": 1585.6, "end": 1586.6, "word": " uncountable", "probability": 0.8341471354166666}, {"start": 1586.6, "end": 1587.52, "word": " وانا", "probability": 0.8914388020833334}, {"start": 1587.52, "end": 1587.84, "word": " عندي", "probability": 0.888671875}, {"start": 1587.84, "end": 1588.46, "word": " R", "probability": 0.07928466796875}, {"start": 1588.46, "end": 1591.4, "word": " equivalent", "probability": 0.5126953125}, {"start": 1591.4, "end": 1592.56, "word": " لفترة", "probability": 0.8701171875}, {"start": 1592.56, "end": 1593.08, "word": " مغلقة", "probability": 0.8338623046875}, {"start": 1593.08, "end": 1593.66, "word": " 01", "probability": 0.50341796875}, {"start": 1593.66, "end": 1595.22, "word": " ممكن", "probability": 0.920166015625}, {"start": 1595.22, "end": 1596.14, "word": " نوجد", "probability": 0.85693359375}, {"start": 1596.14, "end": 1596.8, "word": " bijection", "probability": 0.7216389973958334}, {"start": 1596.8, "end": 1597.34, "word": " بينهم", "probability": 0.960693359375}, {"start": 1597.34, "end": 1598.48, "word": " اذا", "probability": 0.833984375}, {"start": 1598.48, "end": 1598.76, "word": " ال", "probability": 0.83740234375}, {"start": 1598.76, "end": 1599.0, "word": " R", "probability": 0.6494140625}, {"start": 1599.0, "end": 1599.46, "word": " تطلع", "probability": 0.9796142578125}, {"start": 1599.46, "end": 1600.3, "word": " uncountable", "probability": 0.9695638020833334}, {"start": 1600.3, "end": 1600.64, "word": " كما", "probability": 0.964599609375}, {"start": 1600.64, "end": 1600.86, "word": " هو", "probability": 0.98486328125}, {"start": 1600.86, "end": 1601.32, "word": " مطلوب", "probability": 0.8538818359375}, {"start": 1601.32, "end": 1605.08, "word": " اذا", "probability": 0.453125}, {"start": 1605.08, "end": 1605.38, "word": " هذا", "probability": 0.8330078125}, {"start": 1605.38, "end": 1605.64, "word": " هو", "probability": 0.97705078125}, {"start": 1605.64, "end": 1606.22, "word": " برهان", "probability": 0.891845703125}], "temperature": 1.0}, {"id": 59, "seek": 163535, "start": 1608.05, "end": 1635.35, "text": "النظرية اللي فادت هي طبعا برهان بيعتمد على شوفنا ال nested interval theorem وبالتالي هذا برهان مختلف عن البرهان اللي بنعطيه في مبادئ الرياضيات في برهان تاني برضه لنظرية هذه يعطى في مبادئ الرياضيات اللي هو باستخدام counter diagonal argument مشهور يعني البرهان", "tokens": [6027, 1863, 19913, 2288, 10632, 13672, 1829, 6156, 18513, 2655, 39896, 23032, 3555, 3615, 995, 4724, 2288, 3224, 7649, 4724, 1829, 34268, 2304, 3215, 15844, 13412, 38688, 8315, 2423, 15646, 292, 15035, 20904, 46599, 6027, 2655, 6027, 1829, 23758, 4724, 2288, 3224, 7649, 3714, 46456, 46538, 18871, 2423, 26890, 3224, 7649, 13672, 1829, 44945, 3615, 9566, 1829, 3224, 8978, 3714, 3555, 18513, 19986, 2423, 16572, 46958, 1829, 9307, 8978, 4724, 2288, 3224, 7649, 6055, 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1610.75, "end": 1610.99, "word": " على", "probability": 0.8408203125}, {"start": 1610.99, "end": 1611.61, "word": " شوفنا", "probability": 0.7111002604166666}, {"start": 1611.61, "end": 1612.25, "word": " ال", "probability": 0.57421875}, {"start": 1612.25, "end": 1612.71, "word": " nested", "probability": 0.621826171875}, {"start": 1612.71, "end": 1613.35, "word": " interval", "probability": 0.951171875}, {"start": 1613.35, "end": 1613.93, "word": " theorem", "probability": 0.80029296875}, {"start": 1613.93, "end": 1615.23, "word": " وبالتالي", "probability": 0.92783203125}, {"start": 1615.23, "end": 1615.43, "word": " هذا", "probability": 0.8564453125}, {"start": 1615.43, "end": 1615.89, "word": " برهان", "probability": 0.984375}, {"start": 1615.89, "end": 1616.45, "word": " مختلف", "probability": 0.994140625}, {"start": 1616.45, "end": 1616.71, "word": " عن", "probability": 0.97509765625}, {"start": 1616.71, "end": 1617.21, "word": " البرهان", "probability": 0.911865234375}, {"start": 1617.21, "end": 1617.37, "word": " اللي", "probability": 0.95703125}, {"start": 1617.37, "end": 1617.95, "word": " بنعطيه", "probability": 0.9080078125}, {"start": 1617.95, "end": 1618.11, "word": " في", "probability": 0.9404296875}, {"start": 1618.11, "end": 1618.51, "word": " مبادئ", "probability": 0.9285888671875}, {"start": 1618.51, "end": 1619.23, "word": " الرياضيات", "probability": 0.90078125}, {"start": 1619.23, "end": 1621.73, "word": " في", "probability": 0.6611328125}, {"start": 1621.73, "end": 1622.11, "word": " برهان", "probability": 0.9884033203125}, {"start": 1622.11, "end": 1622.45, "word": " تاني", "probability": 0.9908854166666666}, {"start": 1622.45, "end": 1622.69, "word": " برضه", "probability": 0.9573567708333334}, {"start": 1622.69, "end": 1623.27, "word": " لنظرية", "probability": 0.9033203125}, {"start": 1623.27, "end": 1623.67, "word": " هذه", "probability": 0.77392578125}, {"start": 1623.67, "end": 1625.11, "word": " يعطى", "probability": 0.70654296875}, {"start": 1625.11, "end": 1625.27, "word": " في", "probability": 0.92041015625}, {"start": 1625.27, "end": 1625.69, "word": " مبادئ", "probability": 0.99365234375}, {"start": 1625.69, "end": 1626.85, "word": " الرياضيات", "probability": 0.97734375}, {"start": 1626.85, "end": 1628.59, "word": " اللي", "probability": 0.946533203125}, {"start": 1628.59, "end": 1628.71, "word": " هو", "probability": 0.95947265625}, {"start": 1628.71, "end": 1629.53, "word": " باستخدام", "probability": 0.9842122395833334}, {"start": 1629.53, "end": 1630.13, "word": " counter", "probability": 0.86328125}, {"start": 1630.13, "end": 1630.71, "word": " diagonal", "probability": 0.84130859375}, {"start": 1630.71, "end": 1631.49, "word": " argument", "probability": 0.85693359375}, {"start": 1631.49, "end": 1634.69, "word": " مشهور", "probability": 0.9871419270833334}, {"start": 1634.69, "end": 1634.85, "word": " يعني", "probability": 0.779052734375}, {"start": 1634.85, "end": 1635.35, "word": " البرهان", "probability": 0.9036865234375}], "temperature": 1.0}, {"id": 60, "seek": 165857, "start": 1636.77, "end": 1658.57, "text": "يرجع إلى العالم الرياضي Cantor يسمى Cantor دي اقنع ال argument بثبت ان الفترة المفتوحة من سفر لواحد is uncountable وبالتالي R is uncountable لأن R في byjection بينها وبين ال open interval من سفر لواحد الآن في نتيجة على نظرية الأخيرة هذه", "tokens": [13546, 7435, 3615, 30731, 18863, 45340, 2423, 16572, 46958, 1829, 26697, 284, 7251, 38251, 7578, 26697, 284, 11778, 1829, 1975, 4587, 1863, 3615, 2423, 6770, 4724, 12984, 3555, 2655, 16472, 27188, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 9154, 8608, 5172, 2288, 5296, 14407, 24401, 307, 6219, 792, 712, 46599, 6027, 2655, 6027, 1829, 497, 307, 6219, 792, 712, 5296, 33456, 497, 8978, 538, 1020, 313, 49374, 11296, 46599, 9957, 2423, 1269, 15035, 9154, 8608, 5172, 2288, 5296, 14407, 24401, 6024, 48506, 8978, 8717, 31371, 7435, 3660, 15844, 8717, 19913, 2288, 10632, 16247, 9778, 48923, 29538], "avg_logprob": -0.2892219357344569, "compression_ratio": 1.5833333333333333, "no_speech_prob": 0.0, "words": [{"start": 1636.77, "end": 1637.47, "word": "يرجع", "probability": 0.77490234375}, {"start": 1637.47, "end": 1637.61, "word": " إلى", "probability": 0.65234375}, {"start": 1637.61, "end": 1637.97, "word": " العالم", "probability": 0.9794921875}, {"start": 1637.97, "end": 1638.53, "word": " الرياضي", "probability": 0.943115234375}, {"start": 1638.53, "end": 1639.11, "word": " Cantor", "probability": 0.5838623046875}, {"start": 1639.11, "end": 1640.99, "word": " يسمى", "probability": 0.545166015625}, {"start": 1640.99, "end": 1641.61, "word": " Cantor", "probability": 0.85595703125}, {"start": 1641.61, "end": 1641.81, "word": " دي", "probability": 0.49072265625}, {"start": 1641.81, "end": 1642.15, "word": " اقنع", "probability": 0.50860595703125}, {"start": 1642.15, "end": 1642.23, "word": " ال", "probability": 0.79443359375}, {"start": 1642.23, "end": 1642.97, "word": " argument", "probability": 0.65869140625}, {"start": 1642.97, "end": 1643.75, "word": " بثبت", "probability": 0.814697265625}, {"start": 1643.75, "end": 1643.87, "word": " ان", "probability": 0.6708984375}, {"start": 1643.87, "end": 1644.27, "word": " الفترة", "probability": 0.9886067708333334}, {"start": 1644.27, "end": 1644.75, "word": " المفتوحة", "probability": 0.970703125}, {"start": 1644.75, "end": 1644.91, "word": " من", "probability": 0.97412109375}, {"start": 1644.91, "end": 1645.21, "word": " سفر", "probability": 0.7003173828125}, {"start": 1645.21, "end": 1645.79, "word": " لواحد", "probability": 0.734375}, {"start": 1645.79, "end": 1646.85, "word": " is", "probability": 0.732421875}, {"start": 1646.85, "end": 1647.79, "word": " uncountable", "probability": 0.9099934895833334}, {"start": 1647.79, "end": 1648.43, "word": " وبالتالي", "probability": 0.90712890625}, {"start": 1648.43, "end": 1648.83, "word": " R", "probability": 0.78271484375}, {"start": 1648.83, "end": 1649.33, "word": " is", "probability": 0.88671875}, {"start": 1649.33, "end": 1650.07, "word": " uncountable", "probability": 0.9361979166666666}, {"start": 1650.07, "end": 1650.35, "word": " لأن", "probability": 0.6873779296875}, {"start": 1650.35, "end": 1650.67, "word": " R", "probability": 0.359130859375}, {"start": 1650.67, "end": 1650.85, "word": " في", "probability": 0.70068359375}, {"start": 1650.85, "end": 1651.45, "word": " byjection", "probability": 0.455322265625}, {"start": 1651.45, "end": 1651.99, "word": " بينها", "probability": 0.77001953125}, {"start": 1651.99, "end": 1652.87, "word": " وبين", "probability": 0.7320556640625}, {"start": 1652.87, "end": 1652.99, "word": " ال", "probability": 0.9521484375}, {"start": 1652.99, "end": 1653.31, "word": " open", "probability": 0.8662109375}, {"start": 1653.31, "end": 1653.87, "word": " interval", "probability": 0.9814453125}, {"start": 1653.87, "end": 1654.13, "word": " من", "probability": 0.982421875}, {"start": 1654.13, "end": 1654.47, "word": " سفر", "probability": 0.9480794270833334}, {"start": 1654.47, "end": 1655.15, "word": " لواحد", "probability": 0.9020182291666666}, {"start": 1655.15, "end": 1656.37, "word": " الآن", "probability": 0.56903076171875}, {"start": 1656.37, "end": 1656.55, "word": " في", "probability": 0.71142578125}, {"start": 1656.55, "end": 1657.07, "word": " نتيجة", "probability": 0.9923095703125}, {"start": 1657.07, "end": 1657.23, "word": " على", "probability": 0.78125}, {"start": 1657.23, "end": 1657.67, "word": " نظرية", "probability": 0.872802734375}, {"start": 1657.67, "end": 1658.19, "word": " الأخيرة", "probability": 0.91748046875}, {"start": 1658.19, "end": 1658.57, "word": " هذه", "probability": 0.7216796875}], "temperature": 1.0}, {"id": 61, "seek": 168599, "start": 1659.35, "end": 1685.99, "text": "الـ set هذه الـ R minus Q اللي هي الـ set of all irrationals أيضًا is uncountable والبرهان هنا نفس البرهان اللي بنعطيه في المبادئ برهان by contradiction assume and contrary إن ال set R minus Q is countable وإحنا عندنا نظرية في المبادئ أخدنا بتقول إن لو في عندي مجموعتين A وB", "tokens": [6027, 39184, 992, 29538, 2423, 39184, 497, 3175, 1249, 13672, 1829, 39896, 2423, 39184, 992, 295, 439, 3418, 2405, 1124, 36632, 11242, 14111, 995, 307, 6219, 792, 712, 16070, 26890, 3224, 7649, 34105, 8717, 36178, 2423, 26890, 3224, 7649, 13672, 1829, 44945, 3615, 9566, 1829, 3224, 8978, 9673, 3555, 18513, 19986, 4724, 2288, 3224, 7649, 538, 34937, 6552, 293, 19506, 36145, 2423, 992, 497, 3175, 1249, 307, 1207, 712, 4032, 28814, 5016, 8315, 43242, 8315, 8717, 19913, 2288, 10632, 8978, 9673, 3555, 18513, 19986, 5551, 9778, 3215, 8315, 39894, 39648, 36145, 45164, 8978, 18871, 16254, 3714, 7435, 2304, 45367, 2655, 9957, 316, 4032, 33], "avg_logprob": -0.23586310205005465, "compression_ratio": 1.6835443037974684, "no_speech_prob": 0.0, "words": [{"start": 1659.35, "end": 1659.89, "word": "الـ", "probability": 0.5858154296875}, {"start": 1659.89, "end": 1660.11, "word": " set", 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"probability": 0.7892252604166666}, {"start": 1664.31, "end": 1665.43, "word": " أيضًا", "probability": 0.808837890625}, {"start": 1665.43, "end": 1665.71, "word": " is", "probability": 0.5498046875}, {"start": 1665.71, "end": 1666.59, "word": " uncountable", "probability": 0.9542643229166666}, {"start": 1666.59, "end": 1668.31, "word": " والبرهان", "probability": 0.788818359375}, {"start": 1668.31, "end": 1668.59, "word": " هنا", "probability": 0.9443359375}, {"start": 1668.59, "end": 1668.99, "word": " نفس", "probability": 0.95166015625}, {"start": 1668.99, "end": 1669.45, "word": " البرهان", "probability": 0.9747314453125}, {"start": 1669.45, "end": 1669.55, "word": " اللي", "probability": 0.94775390625}, {"start": 1669.55, "end": 1669.93, "word": " بنعطيه", "probability": 0.95078125}, {"start": 1669.93, "end": 1670.05, "word": " في", "probability": 0.9208984375}, {"start": 1670.05, "end": 1670.69, "word": " المبادئ", "probability": 0.9754638671875}, {"start": 1670.69, "end": 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2231.02, "word": " هذه", "probability": 0.64404296875}, {"start": 2231.02, "end": 2231.22, "word": " هدا", "probability": 0.35906982421875}, {"start": 2231.22, "end": 2231.4, "word": " هي", "probability": 0.80126953125}, {"start": 2231.4, "end": 2232.48, "word": " أنصرها", "probability": 0.604949951171875}, {"start": 2232.48, "end": 2235.76, "word": " فما", "probability": 0.794189453125}, {"start": 2235.76, "end": 2236.14, "word": " هو", "probability": 0.99072265625}, {"start": 2236.14, "end": 2238.6, "word": " بيناجيب", "probability": 0.666015625}, {"start": 2238.6, "end": 2238.9, "word": " lower", "probability": 0.8623046875}, {"start": 2238.9, "end": 2239.38, "word": " bound", "probability": 0.8994140625}, {"start": 2239.38, "end": 2239.92, "word": " او", "probability": 0.755126953125}, {"start": 2239.92, "end": 2240.34, "word": " اكبر", "probability": 0.90234375}, {"start": 2240.34, "end": 2240.66, "word": " lower", "probability": 0.8994140625}, {"start": 2240.66, "end": 2241.2, "word": " bound", "probability": 0.90673828125}, {"start": 2241.2, "end": 2241.7, "word": " اكبر", "probability": 0.8839518229166666}, {"start": 2241.7, "end": 2241.98, "word": " lower", "probability": 0.88134765625}, {"start": 2241.98, "end": 2242.4, "word": " bound", "probability": 0.892578125}, {"start": 2242.4, "end": 2245.02, "word": " طب", "probability": 0.71923828125}, {"start": 2245.02, "end": 2245.46, "word": " نلاحظ", "probability": 0.83367919921875}, {"start": 2245.46, "end": 2245.92, "word": " سالب", "probability": 0.7376302083333334}, {"start": 2245.92, "end": 2246.36, "word": " نص", "probability": 0.986328125}, {"start": 2246.36, "end": 2248.46, "word": " اصغر", "probability": 0.8887939453125}, {"start": 2248.46, "end": 2248.64, "word": " من", "probability": 0.99755859375}, {"start": 2248.64, "end": 2249.16, "word": " سالب", "probability": 0.96923828125}, {"start": 2249.16, "end": 2249.52, "word": " ربع", "probability": 0.9052734375}, {"start": 2249.52, "end": 2250.12, "word": " اصغر", "probability": 0.9757080078125}, {"start": 2250.12, "end": 2250.36, "word": " من", "probability": 0.9970703125}], "temperature": 1.0}, {"id": 82, "seek": 227201, "start": 2251.63, "end": 2272.01, "text": "بعد هيك سالب سادس اه فاعتقد ان هذا هيطلع سالب نص هذا اكبر lower bound", "tokens": [3555, 22488, 39896, 4117, 8608, 6027, 3555, 8608, 18513, 3794, 1975, 3224, 6156, 995, 34268, 28543, 16472, 23758, 39896, 9566, 1211, 3615, 8608, 6027, 3555, 8717, 9381, 23758, 1975, 4117, 26890, 3126, 5472], "avg_logprob": -0.20875460260054646, "compression_ratio": 1.2127659574468086, "no_speech_prob": 0.0, "words": [{"start": 2251.63, "end": 2252.17, "word": "بعد", "probability": 0.6588134765625}, {"start": 2252.17, "end": 2252.53, "word": " هيك", "probability": 0.84033203125}, {"start": 2252.53, "end": 2253.07, "word": " سالب", "probability": 0.7666829427083334}, {"start": 2253.07, "end": 2254.69, "word": " سادس", "probability": 0.7607421875}, {"start": 2254.69, "end": 2257.65, "word": " اه", "probability": 0.744384765625}, {"start": 2257.65, "end": 2267.71, "word": " فاعتقد", "probability": 0.8067626953125}, {"start": 2267.71, "end": 2267.87, "word": " ان", "probability": 0.818359375}, {"start": 2267.87, "end": 2268.03, "word": " هذا", "probability": 0.73583984375}, {"start": 2268.03, "end": 2268.47, "word": " هيطلع", "probability": 0.9384765625}, {"start": 2268.47, "end": 2268.97, "word": " سالب", "probability": 0.9557291666666666}, {"start": 2268.97, "end": 2269.37, "word": " نص", "probability": 0.981689453125}, {"start": 2269.37, "end": 2270.85, "word": " هذا", "probability": 0.68505859375}, {"start": 2270.85, "end": 2271.31, "word": " اكبر", "probability": 0.8497721354166666}, {"start": 2271.31, "end": 2271.59, "word": " lower", "probability": 0.8623046875}, {"start": 2271.59, "end": 2272.01, "word": " bound", "probability": 0.84521484375}], "temperature": 1.0}, {"id": 83, "seek": 230544, "start": 2278.87, "end": 2305.45, "text": "طيب لو طبقنا المضارية هذه أنا أخدت S بساوي الكلام هذا و A بساوي واحد اذا ال supremum ل S أربعة بساوي A زائد ال supremum ل S صح؟", "tokens": [9566, 1829, 3555, 45164, 23032, 3555, 4587, 8315, 9673, 11242, 9640, 10632, 29538, 41850, 5551, 9778, 3215, 2655, 318, 4724, 3794, 995, 45865, 2423, 28820, 10943, 23758, 4032, 316, 4724, 3794, 995, 45865, 36764, 24401, 1975, 15730, 2423, 23710, 449, 5296, 318, 5551, 25513, 27884, 4724, 3794, 995, 45865, 316, 30767, 16373, 3215, 2423, 23710, 449, 5296, 318, 20328, 5016, 22807], "avg_logprob": -0.21055947220133198, "compression_ratio": 1.474820143884892, "no_speech_prob": 0.0, "words": [{"start": 2278.87, "end": 2279.27, "word": "طيب", "probability": 0.9557291666666666}, {"start": 2279.27, "end": 2279.47, "word": " لو", "probability": 0.97998046875}, {"start": 2279.47, "end": 2280.13, "word": " طبقنا", "probability": 0.97998046875}, {"start": 2280.13, "end": 2281.29, "word": " المضارية", "probability": 0.684295654296875}, {"start": 2281.29, "end": 2281.73, "word": " 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"probability": 0.8907877604166666}], "temperature": 1.0}, {"id": 84, "seek": 233434, "start": 2307.32, "end": 2334.34, "text": "و ال a بساوي واحد و ال suprem ل s بساوي واحد فبطلع ال suprem ل s أربعة بساوي اتنين تمام؟ الان بنجيب ال infimum ل s أربعة بنفس الطريقة ممكن اثبات", "tokens": [2407, 2423, 257, 4724, 3794, 995, 45865, 36764, 24401, 4032, 2423, 23710, 5296, 262, 4724, 3794, 995, 45865, 36764, 24401, 6156, 3555, 9566, 1211, 3615, 2423, 23710, 5296, 262, 5551, 25513, 27884, 4724, 3794, 995, 45865, 1975, 2655, 1863, 9957, 46811, 10943, 22807, 2423, 7649, 4724, 1863, 7435, 1829, 3555, 2423, 1536, 332, 449, 5296, 262, 5551, 25513, 27884, 44945, 36178, 41950, 16572, 28671, 3714, 43020, 1975, 12984, 3555, 9307], "avg_logprob": -0.19289171821634535, "compression_ratio": 1.683453237410072, "no_speech_prob": 0.0, "words": [{"start": 2307.32, "end": 2307.6, "word": "و", "probability": 0.85595703125}, {"start": 2307.6, "end": 2307.76, "word": " ال", "probability": 0.61328125}, {"start": 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"word": " suprem", "probability": 0.822265625}, {"start": 2316.54, "end": 2316.8, "word": " ل", "probability": 0.97119140625}, {"start": 2316.8, "end": 2317.08, "word": " s", "probability": 0.66015625}, {"start": 2317.08, "end": 2317.6, "word": " أربعة", "probability": 0.71923828125}, {"start": 2317.6, "end": 2318.46, "word": " بساوي", "probability": 0.9736328125}, {"start": 2318.46, "end": 2319.18, "word": " اتنين", "probability": 0.9688720703125}, {"start": 2319.18, "end": 2320.5, "word": " تمام؟", "probability": 0.715087890625}, {"start": 2320.5, "end": 2323.46, "word": " الان", "probability": 0.619873046875}, {"start": 2323.46, "end": 2325.9, "word": " بنجيب", "probability": 0.7617431640625}, {"start": 2325.9, "end": 2326.06, "word": " ال", "probability": 0.98876953125}, {"start": 2326.06, "end": 2326.7, "word": " infimum", "probability": 0.9041341145833334}, {"start": 2326.7, "end": 2326.88, "word": " ل", "probability": 0.9755859375}, {"start": 2326.88, "end": 2327.2, "word": " s", "probability": 0.7763671875}, {"start": 2327.2, "end": 2327.88, "word": " أربعة", "probability": 0.904296875}, {"start": 2327.88, "end": 2329.04, "word": " بنفس", "probability": 0.909423828125}, {"start": 2329.04, "end": 2330.48, "word": " الطريقة", "probability": 0.962890625}, {"start": 2330.48, "end": 2333.66, "word": " ممكن", "probability": 0.985595703125}, {"start": 2333.66, "end": 2334.34, "word": " اثبات", "probability": 0.8258056640625}], "temperature": 1.0}, {"id": 85, "seek": 236759, "start": 2340.49, "end": 2367.59, "text": "إذا هنا similar example similar example اتنين اربعة واحد ايه", "tokens": [28814, 15730, 34105, 2531, 1365, 2531, 1365, 1975, 2655, 1863, 9957, 1975, 25513, 27884, 36764, 24401, 1975, 1829, 3224], "avg_logprob": -0.3683593854308128, "compression_ratio": 1.1527777777777777, "no_speech_prob": 0.0, "words": [{"start": 2340.49, "end": 2340.83, "word": "إذا", "probability": 0.4613037109375}, {"start": 2340.83, "end": 2341.19, "word": " هنا", "probability": 0.92919921875}, {"start": 2341.19, "end": 2350.07, "word": " similar", "probability": 0.490966796875}, {"start": 2350.07, "end": 2357.59, "word": " example", "probability": 0.6142578125}, {"start": 2357.59, "end": 2364.09, "word": " similar", "probability": 0.229736328125}, {"start": 2364.09, "end": 2364.89, "word": " example", "probability": 0.9794921875}, {"start": 2364.89, "end": 2366.45, "word": " اتنين", "probability": 0.78271484375}, {"start": 2366.45, "end": 2366.79, "word": " اربعة", "probability": 0.8328450520833334}, {"start": 2366.79, "end": 2367.21, "word": " واحد", "probability": 0.980224609375}, {"start": 2367.21, "end": 2367.59, "word": " ايه", "probability": 0.89697265625}], "temperature": 1.0}, {"id": 86, "seek": 239592, "start": 2368.49, "end": 2395.93, "text": "ممكن من خلاله نثبت ان الانفمام ان الانفمام لست a زياد s بيساوي a زياد الانفمام ل s وبالتالي ان انا لو بدي اجرب على جزء a", "tokens": [2304, 43020, 9154, 16490, 1211, 6027, 3224, 8717, 12984, 3555, 2655, 16472, 2423, 7649, 5172, 2304, 10943, 16472, 2423, 7649, 5172, 2304, 10943, 5296, 14851, 257, 30767, 1829, 18513, 262, 4724, 1829, 3794, 995, 45865, 257, 30767, 1829, 18513, 2423, 7649, 5172, 2304, 10943, 5296, 262, 46599, 6027, 2655, 6027, 1829, 16472, 1975, 8315, 45164, 4724, 16254, 1975, 7435, 25513, 15844, 10874, 11622, 38207, 257], "avg_logprob": -0.2663352159839688, "compression_ratio": 1.7131147540983607, "no_speech_prob": 0.0, "words": [{"start": 2368.49, "end": 2369.13, "word": "ممكن", "probability": 0.6844482421875}, {"start": 2369.13, "end": 2369.67, "word": " من", "probability": 0.974609375}, {"start": 2369.67, "end": 2370.31, "word": " خلاله", "probability": 0.9873046875}, {"start": 2370.31, "end": 2371.85, "word": " نثبت", "probability": 0.9393310546875}, {"start": 2371.85, "end": 2372.03, "word": " ان", "probability": 0.6552734375}, {"start": 2372.03, "end": 2372.85, "word": " الانفمام", "probability": 0.7110107421875}, {"start": 2372.85, "end": 2378.33, "word": " ان", "probability": 0.73876953125}, {"start": 2378.33, "end": 2379.21, "word": " الانفمام", "probability": 0.92294921875}, {"start": 2379.21, "end": 2380.17, "word": " لست", "probability": 0.6162109375}, {"start": 2380.17, "end": 2380.49, "word": " a", "probability": 0.5263671875}, {"start": 2380.49, "end": 2381.01, "word": " زياد", "probability": 0.5230305989583334}, {"start": 2381.01, "end": 2381.37, "word": " s", "probability": 0.5283203125}, {"start": 2381.37, "end": 2382.57, "word": " بيساوي", "probability": 0.713232421875}, {"start": 2382.57, "end": 2382.87, "word": " a", "probability": 0.8076171875}, {"start": 2382.87, "end": 2383.37, "word": " زياد", "probability": 0.88720703125}, {"start": 2383.37, "end": 2383.99, "word": " الانفمام", "probability": 0.8880859375}, {"start": 2383.99, "end": 2384.13, "word": " ل", "probability": 0.9326171875}, {"start": 2384.13, "end": 2384.49, "word": " s", "probability": 0.327880859375}, {"start": 2384.49, "end": 2389.31, "word": " وبالتالي", 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"seek": 255332, "start": 2529.7, "end": 2553.32, "text": "خمس اربع و هكذا فهنلاحظ ان الاتنين اتنين upper bound لان هو هيكون اكبر عنصر و ينتبه للست لو في اي upper bound تاني لو في any upper bound", "tokens": [9778, 2304, 3794, 1975, 25513, 3615, 4032, 8032, 4117, 15730, 6156, 3224, 1863, 15040, 5016, 19913, 16472, 2423, 9307, 1863, 9957, 1975, 2655, 1863, 9957, 6597, 5472, 5296, 7649, 31439, 39896, 30544, 1975, 4117, 26890, 18871, 9381, 2288, 4032, 7251, 29399, 3555, 3224, 24976, 14851, 45164, 8978, 1975, 1829, 6597, 5472, 6055, 7649, 1829, 45164, 8978, 604, 6597, 5472], "avg_logprob": -0.17213542113701502, "compression_ratio": 1.5629629629629629, "no_speech_prob": 0.0, "words": [{"start": 2529.7, "end": 2530.2, "word": "خمس", "probability": 0.9405924479166666}, {"start": 2530.2, "end": 2530.74, "word": " اربع", "probability": 0.6211751302083334}, {"start": 2530.74, "end": 2532.32, "word": " و", "probability": 0.7744140625}, {"start": 2532.32, "end": 2532.94, "word": " هكذا", 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0.91455078125}, {"start": 2552.86, "end": 2553.32, "word": " bound", "probability": 0.923828125}], "temperature": 1.0}, {"id": 93, "seek": 257637, "start": 2557.83, "end": 2576.37, "text": "of S4 فهذا بيقدي انه اتنين اصغر من او ساوي ال V لانه اتنين عنصر في الست S4 صح؟ اذا اتنين upper bound واضح انه اتنين اكبر من او ساوي كل عناصر S4 صح؟", "tokens": [2670, 318, 19, 6156, 3224, 15730, 4724, 1829, 4587, 16254, 16472, 3224, 1975, 2655, 1863, 9957, 1975, 9381, 17082, 2288, 9154, 1975, 2407, 8608, 995, 45865, 2423, 691, 5296, 7649, 3224, 1975, 2655, 1863, 9957, 18871, 9381, 2288, 8978, 2423, 14851, 318, 19, 20328, 5016, 22807, 1975, 15730, 1975, 2655, 1863, 9957, 6597, 5472, 4032, 46958, 5016, 16472, 3224, 1975, 2655, 1863, 9957, 1975, 4117, 26890, 9154, 1975, 2407, 8608, 995, 45865, 28242, 18871, 33546, 2288, 318, 19, 20328, 5016, 22807], "avg_logprob": -0.18826219330473645, "compression_ratio": 1.704225352112676, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 2557.83, "end": 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