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: Real analysis

  1. Feb 16, 2006 #1
    I'm trying to show that this set is compact {0} union {2^-m + 2^-n} where n,m are integers and m is less than n

    I'm thinking that since it's bounded below by 0 and the set contains it's bound that if I can show that it's closed and bounded above that will be a proof but i'm not really sure how i would do that
    Say there's an collection of open sets who's union is (-2, 2^-m + 2^-n + 2) that since that's an open cover then and you can have a finite subcover of something like (-1, 2^-m + 2^-n +1) that'll still contain the set therefore the set is compact.

    I don't know if either of those are correct or if i'm heading in the right direction. Can anyone help?
  2. jcsd
  3. Feb 17, 2006 #2
    Zero is in the set, so any cover of the set must cover zero. Can you show that all but a finite number of points in the set are covered by this cover on {0}?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook