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!

Explanation of the Bolzano-Weierstrass theorem proof

  1. Oct 7, 2012 #1
    1. The problem statement, all variables and given/known data

    Every bounded sequence has a convergent subsequence.

    2. Relevant equations

    Suppose that closed intervals I_0 [itex]\supset[/itex] I_1[itex]\supset[/itex] ... [itex]\supset[/itex] I_m and natural numbers n[itex]_{1}[/itex] < n[itex]_{2}[/itex] <
    ... < n[itex]_{m}[/itex] have been chosen such that for each 0 [itex]\leq[/itex] k [itex]\leq[/itex] m,
    (2)
    |I[itex]_{k}[/itex]| = [itex]b-a/2^{k}[/itex], x[itex]_{n}_{k}[/itex][itex]\in[/itex]I[itex]_{k}[/itex]n and x[itex]_{n}[/itex] [itex]\in[/itex] I[itex]_{k}[/itex] for infinitely many n.

    3. The attempt at a solution
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Explanation of the Bolzano-Weierstrass theorem proof
Loading...