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Homework Help: Bounded sequence implies convergent subsequence

  1. Sep 19, 2007 #1
    How can you deduce that nad bounded sequence in R has a convergent subsequence?
  2. jcsd
  3. Sep 19, 2007 #2


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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.
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