1. Limited time only! Sign up for a free 30min personal 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!

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