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Supremums and infimums

  1. Jan 6, 2009 #1
    1. The problem statement, all variables and given/known data

    Show that for all x,y in R (real numbers), sup{x,y}=1/2(x+Y+|X-Y|), and inf{x,y}=1/2(X+Y-|x-y|)

    2. Relevant equations

    3. The attempt at a solution

    i know that the supremum is the lowest upper bound and that the infimum is the largest lower bound. However i really don't know how to apply that to solving this question.
  2. jcsd
  3. Jan 6, 2009 #2


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    Homework Helper

    If you have two numbers, one has to be at least as big (greater-than-or-equal-to) the other. Assume that [tex] x \le y [/tex]. Then

    [tex] \sup\{x,y\} = y


    [tex] \inf\{x,y\} =

    What do the two right-hand-sides simplify to?
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