1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Application of Bolanzo-Weierstrauss

  1. Aug 31, 2011 #1
    Let {xn}n = 1[itex]\infty[/itex] be a bounded sequence

    and

    {xnj} be a convergent subsequence, each one converging to L.

    Want to show that {xn[}[/itex]n = 1[itex]\infty[/itex] converges to L.

    My proof is as follows.

    Suppose that {xn}n = 1[itex]\infty[/itex] does not converge to L; this implies that there is a subsequence |{xnj}-L|[itex]\geq[/itex][itex]\epsilon[/itex]. However by B-W there exists a subsequence of that subsequence that converges, and it must converge to L. However this is a contradiction.

    Is this sufficient?
     
  2. jcsd
  3. Sep 1, 2011 #2
    What exactly is it that you need to prove??
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook