[數撚圍爐區] What is Mathematics? (4)
吾不會數學
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the language of science
係咪得我一個覺得several variables 呢本書難
queen呀
咩書?
maths都唔係science
腐皮甜甜地幾好食
留名
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
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proveA <-> 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
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
Prove that if the cardinalities of A and B are the same, then their power sets have the same cardinality.A <-> B 有bijection f:A -> B咪consider F: P(A) -> P(B) defined by
Google完都唔係好睇得明人哋D solution
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
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
所以B的subset的elements都可以用A的elements黎label, which corresponds to a subset of A
math as a tool 同 doing math itself 係兩樣野黎
咁樣prove 係咪包含咗 A,B 係countable or uncountable 兩個case
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
你只需要establish一個bijection (or 兩邊injection or 兩邊surjection) 就可以
消化下先 thanks
好似課課都見到compact set咁
無論analysis, geometry, 甚至algebra, applied math都會見到 
Prof.話對exam好重要 唔知佢會用嚟問啲咩
黎黎去去一係construct一個open cover再提煉一個 finite subcover
Topo呢課冇聽書 睇下YouTube 先
睇下YouTube 先1+1≠2
例如：
1個宇宙＋1個宇宙=另1個宇宙
例如：
1個宇宙＋1個宇宙=另1個宇宙