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 Supremum of a Set Proof

  1. Feb 12, 2012 #1
    1. The problem statement, all variables and given/known data
    Let S be a non empty set that is bounded about and β = sup S. Prove that for each ε > 0 there exists a point x in S such that x > β - ε.

    2. Relevant equations

    3. The attempt at a solution

    I don't really know how to begin this. I know it's true; I'm looking at the problem and I'm like, "Well, duh," but I can't prove it. I know that x ≤ β, and that β - ε ≤ x. Is there more that I have to do?

    edit: never mind. I'm an idiot. Proof by contradiction makes this really easy.
    Last edited: Feb 12, 2012
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted