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Bolzano-Weierstrass theorem

  1. Oct 31, 2011 #1
    Does any one know the shortest way to prove Bolzano-Weierstrass theorem?
     
  2. jcsd
  3. Oct 31, 2011 #2
    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.
     
  4. Oct 31, 2011 #3

    Deveno

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

    i always liked the: "the lion lives somewhere in the jungle" proof.
     
  5. Oct 31, 2011 #4
    I always thought lions lived on the savannah...
     
  6. Oct 31, 2011 #5

    Deveno

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