Proving Bolzano-Weierstrass Theorem: A Short Guide

[glebovg]

Does anyone know the shortest way to prove Bolzano-Weierstrass theorem?

 

[kru_]

The length of your proof will depend on what theorems you're allowing yourself to call upon. I recall having to show first that all sequences have monotonic subsequences, and that any bounded monotonic subsequence must converge. Bolzano-Weierstrass is a consequence of that.

 

[Deveno]

it also depends on which version of the theorem you're proving.

i always liked the: "the lion lives somewhere in the jungle" proof.

 

[kru_]

I always thought lions lived on the savannah...

 

[Deveno]

this is true, but it doesn't affect the proof :)