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Let A be a nonempty set of real numbers which

  1. Oct 3, 2011 #1
    1. The problem statement, all variables and given/known data

    Let A be a nonempty set of real numbers which is bounded below. Let -A be the set of all real numbers -x, where x is in A. Prove that inf A = -sup(-A).

    2. Relevant equations

    Definitions of upper bound, lower bound, least upper bound, and least lower bound.

    3. The attempt at a solution

    Here's what I have so far:


    Almost there! I just need to derive a contradiction on my assumption that gamma is an upper bound for -A.
  2. jcsd
  3. Oct 4, 2011 #2

    By the way, if you help me with this problem I'll give you another one.
    Last edited by a moderator: Apr 26, 2017
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