[數撚圍爐區] What is Mathematics? (4)

1001 回覆
26 Like 4 Dislike
2018-12-04 11:31:04
the language of science
2018-12-04 11:50:44
係咪得我一個覺得several variables 呢本書難
2018-12-04 12:12:00
queen呀
2018-12-04 12:12:15
咩書?
2018-12-04 12:14:04
maths都唔係science
2018-12-04 12:16:15
腐皮甜甜地幾好食
2018-12-04 12:24:07
2018-12-04 12:24:46
留名
2018-12-04 12:31:31
2018-12-04 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 有冇巴打可以淺白D講解下應該要點prove
2018-12-04 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
2018-12-04 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 有冇巴打可以淺白D講解下應該要點prove
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

頭先上面寫到1999 sor
2018-12-04 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
2018-12-04 14:26:08
math as a tool 同 doing math itself 係兩樣野黎
2018-12-04 14:28:53
咁樣prove 係咪包含咗 A,B 係countable or uncountable 兩個case
2018-12-04 14:31:15
prove cardinality equals 唔關係咪countable事
你只需要establish一個bijection (or 兩邊injection or 兩邊surjection) 就可以
2018-12-04 14:32:21
消化下先 thanks
2018-12-04 16:25:04
好似課課都見到compact set咁
2018-12-04 16:29:20
無論analysis, geometry, 甚至algebra, applied math都會見到
2018-12-04 16:30:25
Prof.話對exam好重要 唔知佢會用嚟問啲咩
2018-12-04 16:35:11
黎黎去去一係construct一個open cover再提煉一個 finite subcover
2018-12-04 16:41:13
Topo呢課冇聽書 睇下YouTube 先
2018-12-04 16:47:08
1+1≠2
例如:
1個宇宙+1個宇宙=另1個宇宙
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