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咦我state錯左最尾條theorem
應該係 there exists x such that x_n -> x, where x_0 = x, x_{n + 1} = f(x_n)
:^(
唔怪得望落句野怪怪地咁
對於任何一個collection of non-empty sets, 我地都可以每一個set揀個member代表個set.
(Banach-Tarski Paradox) 可以將一個實心波切開5份, 之後可以砌返兩個同原本一模一樣的實心波
設 X 有一個partial ordering, 對於任何一個可以用呢個partial ordering完全排好次序的subset都有一個upper bound, 咁 X 就會有一個maximal element.
1. 對於任何 a, a ≤ a
2. 如果 a ≤ b, b ≤ a的話, 則b = a
3. 如果 a ≤ b, b ≤ c的話, 則a ≤ c
房A ≤ 房B 當且僅當:
1. B所在的樓層不低於A
2. A 有一條唔會落樓的路行到去 B.
[limegreen] Let X be a compact metric space and f: X -> X be a continuous function, then there exists x in X such that x is in the closure of the sequence {x_n}, where x_0 = x, x_{n + 1} = f(x_n)
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