Proof of Bolzano-Weierstrass theorem using Axiom of Completeness.

kindlychung

I don';t get the definition of S.

elimqiu

Since {a(n)} is bounded, there are real numbers L, M such that L < a(n) n(k) such that s - 1/(k+1) < b(k+1) = a(n(k+1)) < s + 1/(k+1) By induction, we get a subsequence {b(n)} of {a(n)} such that s - 1/n < b(n) < s + 1/n and the expected conclusion follows.

kindlychung

I see, thank you.

wangyangkee

为老外顶帖，，，赚积分，，，