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Prove that inf S = - sup {-s: s in S}

  1. Jul 25, 2011 #1
    1. The problem statement, all variables and given/known data

    Let S be a nonempty subset of R that is bounded below. Prove that inf S = - sup {-s: s in S}

    3. The attempt at a solution

    Let a0 = inf S. Thus, for all s in S, a0 is less or equal to s; or -a0 greater or equal to -s.
    If u is any upper bound for -S, u is greater or equal to -a0; or -u less or equal to a0.

    and here I have difficulty proceeding further. I don't quite see the logic anymore :-(

    Any help is greatly appreciated.


    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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