[數撚圍爐區] What is Mathematics? (4)

今朝冇酒 2018-12-4 11:29:01 此回覆已被刪除

FactsLikeJade 2018-12-4 11:31:04 the language of science

幸福安泰吻 2018-12-4 11:50:44 係咪得我一個覺得several variables 呢本書難

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吾不會數學 2018-12-4 12:12:00 queen呀

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吾不會數學 2018-12-4 12:12:15 咩書?

FactsLikeJade 2018-12-4 12:14:04 maths都唔係science

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吾不會數學 2018-12-4 12:16:15 腐皮甜甜地幾好食

夢追人 2018-12-4 12:24:07

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打人打飛機添呀 2018-12-4 12:24:46 留名

吾不會數學 2018-12-4 12:31:31

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幸福安泰吻 2018-12-4 14:16:31 Prove that if the cardinalities of A and B are the same, then their power sets have the same cardinality.

Google完都唔係好睇得明人哋D solution

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有冇巴打可以淺白D講解下應該要點prove

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吾不會數學 2018-12-4 14:21:46 A <-> B 有bijection f:A -> B咪
a <-> f(a) = b for every a in A, b in B
而家咪consider F: P(A) -> P(B) defined by
F(S) = {f(a) | a in S} for S in P(A)
咁你咪證F係一個bijection

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吾不會數學 2018-12-4 14:22:56

Prove that if the cardinalities of A and B are the same, then their power sets have the same cardinality.

Google完都唔係好睇得明人哋D solution
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有冇巴打可以淺白D講解下應該要點prove
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A <-> B 有bijection f:A -> B咪consider F: P(A) -> P(B) defined by
F(S) = {f(a) | a in S} for S in P(A)
咁你咪證F係一個bijection
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頭先上面寫到1999 sor

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美利堅帝國 2018-12-4 14:24:38 此回覆已被刪除

吾不會數學 2018-12-4 14:25:31 個key idea係你發現 B 入面的elements都可以用 A入面的elements黎label
所以B的subset的elements都可以用A的elements黎label, which corresponds to a subset of A

吾不會數學 2018-12-4 14:26:08 math as a tool 同 doing math itself 係兩樣野黎

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幸福安泰吻 2018-12-4 14:28:53 咁樣prove 係咪包含咗 A,B 係countable or uncountable 兩個case

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吾不會數學 2018-12-4 14:31:15 prove cardinality equals 唔關係咪countable事

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你只需要establish一個bijection (or 兩邊injection or 兩邊surjection) 就可以

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幸福安泰吻 2018-12-4 14:32:21 消化下先 thanks

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幸福安泰吻 2018-12-4 16:25:04 好似課課都見到compact set咁

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吾不會數學 2018-12-4 16:29:20 無論analysis, geometry, 甚至algebra, applied math都會見到

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幸福安泰吻 2018-12-4 16:30:25 Prof.話對exam好重要唔知佢會用嚟問啲咩

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吾不會數學 2018-12-4 16:35:11 黎黎去去一係construct一個open cover再提煉一個 finite subcover

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幸福安泰吻 2018-12-4 16:41:13 Topo呢課冇聽書

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睇下YouTube 先

結束一黨專政 2018-12-4 16:47:08 1+1≠2
例如：
1個宇宙＋1個宇宙=另1個宇宙