[數撚圍爐區] abc conjecture is still a conjecture (3)

夢追人 2018-10-19 18:32:35

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高山一実 2018-10-19 18:46:38

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夢追人 2018-10-19 18:50:17

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RicKula 2018-10-19 19:37:41

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RicKula 2018-10-19 19:49:33

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吾不會數學 2018-10-20 01:17:05

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吾不會數學 2018-10-20 04:15:18

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夢追人 2018-10-20 12:43:21

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吾不會數學 2018-10-20 12:46:53

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五河琴里 2018-10-20 12:47:33 其實一直都唔太明Cantor set點解要咁寫

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同咁

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有咩分別? 為咗show Cantor set is closed?

同埋有條問題唔明
Show that it is impossible to write

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where for each n ∈ N, F_n is a closed set containing no nonempty open intervals.

寫做咁

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點解又唔得?

吾不會數學 2018-10-20 12:51:09 1. set 無 "limit"
2. F_n 同 [-n, n] 唔同架喎, 除非你證到果兩個union係一樣

五河琴里 2018-10-20 12:54:02 F_n 同 [-n, n] 點唔同? [-n,n]都係closed唔係咩?

高山一実 2018-10-20 13:00:12 closed set同closed set containing no nonempty open intervals嘅分別

RicKula 2018-10-20 13:02:23

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五河琴里 2018-10-20 13:05:14 即係single point set?

吾不會數學 2018-10-20 13:06:43 no
cantor set係例子

高山一実 2018-10-20 13:09:00

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吾不會數學 2018-10-20 13:12:24

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吾不會數學 2018-10-20 13:18:38

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吾不會數學 2018-10-20 13:23:56 between give you a hint: show that the lebesgue measure of F_n is zero for all n.

五河琴里 2018-10-20 13:26:56 Abbott本嘢冇教Lebesgue measure

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吾不會數學 2018-10-20 13:31:27 er...咁諗下 R\F_n 可以係D乜...然後數下有幾多點

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咦原來用lebesgue measure好似用左牛刀

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中途都會證到我第一行ge野

吾不會數學 2018-10-20 13:32:05

no
cantor set係例子
between give you a hint: show that the lebesgue measure of F_n is zero for all n.
Abbott本嘢冇教Lebesgue measure
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er...咁諗下 R\F_n 可以係D乜...然後數下F_n可以有幾多點
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咦原來用lebesgue measure好似用左牛刀
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中途都會證到我第一行ge野

五河琴里 2018-10-20 13:32:33 即係要搵到佢uncountable方法？

吾不會數學 2018-10-20 13:34:07 即係你要證 F_n 係countable, 但\mathbb{R} is uncountable

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