Bolzano-Weierstrass theorem

  • Thread starter glebovg
  • Start date
  • #1
164
1
Does any one know the shortest way to prove Bolzano-Weierstrass theorem?
 

Answers and Replies

  • #2
85
0
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.
 
  • #3
Deveno
Science Advisor
906
6
it also depends on which version of the theorem you're proving.

i always liked the: "the lion lives somewhere in the jungle" proof.
 
  • #4
85
0
I always thought lions lived on the savannah...
 
  • #5
Deveno
Science Advisor
906
6
this is true, but it doesn't affect the proof :)
 

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