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Bounded sequence implies convergent subsequence

  1. Sep 19, 2007 #1

    Scousergirl

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    How can you deduce that nad bounded sequence in R has a convergent subsequence?
     
    Scousergirl, Sep 19, 2007
  2. jcsd
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  3. Sep 19, 2007 #2

    morphism

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    This is the Bolzano–Weierstrass theorem. Any decent calculus or analysis textbook should have a proof of it. Or search online. Or use this hint: Prove that a bounded sequence of real numbers has a monotone subsequence.
     
    morphism, Sep 19, 2007
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