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!

Give a counter-example that shows Bolzano-Weirstrass is unvalid in IR2

  1. Feb 16, 2013 #1
    1. The problem statement, all variables and given/known data
    Give a counter-example that shows Bolzano-Weirstrass is unvalid in IR2.

    Intro:
    Bolzano-Weirtrass theorem says that if a sequence (IN->IR) is bounded then there exists a convergent sub-sequence. (this is shown using the Cauchy sequence concept, showing that a Cauchy sequence is bounded and using the lemma of monotonic sub-sequences)

    However, this is not valid valid in IR2, if a sequence (IN->IR2) is bounded then we can't assure that the exists a convergent sub-sequence.

    2. Relevant equations



    3. The attempt at a solution
    It's not easy since you have the tendency of using a pattern. But I guess
    Xn=(Cos(n),Sin(n)) might work...
     
  2. jcsd
  3. Feb 16, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Re: Give a counter-example that shows Bolzano-Weirstrass is unvalid in

    Can you explain your notation? What are IN, IR and IR2? Bolzano Weierstrass is valid for sequences in ##R^2##.
     
  4. Feb 16, 2013 #3
    Re: Give a counter-example that shows Bolzano-Weirstrass is unvalid in

    IR=real number set
    IN=natural number set

    I'm sorry, I thought Bolzano-Weirtrass was not valid im IR^2, my book was not clear in that part. I've consulted Wikipedia and confirmed that it is valid in IR^2. Sorry for the mistake.

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




Similar Discussions: Give a counter-example that shows Bolzano-Weirstrass is unvalid in IR2
Loading...