Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof of Bolzano-Weierstrass theorem using Axiom of Completeness.

  1. Sep 26, 2010 #1
    This is an analysis exercise, I don't get the definition of S. Could anyone explain, please?
    See the attached pic.
     

    Attached Files:

  2. jcsd
  3. Sep 26, 2010 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It might help you to look at an example. Let an = (-1)n/n. Plot a few of these: -1, 1/2, -1/3, 1/4, ...

    Now what x would be in your set S? Can you see any x ≤ 0 is in S but any x > 0 isn't?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook