1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?