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Inequality proof involving Infs and Sups

  1. Sep 25, 2011 #1
    1. The problem statement, all variables and given/known data
    Let F and G be bounded functions on S. If f(x) <= g(x) for all x in S prove that inf{f(x):x belongs to S} <= inf{g(x):x belongs to S}

    2. Relevant equations

    3. The attempt at a solution
    Basically the idea is to let L0 = inf{f(x):x belongs to S} and L1 = inf{g(x):x belongs to S} and show that L0 <=L1
  2. jcsd
  3. Sep 25, 2011 #2
    I suggest contradiction. Assume there is some value of x where g(x) is less than the inf of all possible f(x)'s, then see if you can show why that just don't make no sense.
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