Does any one know the shortest way to prove Bolzano-Weierstrass theorem?
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.
it also depends on which version of the theorem you're proving.
i always liked the: "the lion lives somewhere in the jungle" proof.
I always thought lions lived on the savannah...
this is true, but it doesn't affect the proof :)
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