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: 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

    statdad

    User Avatar
    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]

    and

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


    What do the two right-hand-sides simplify to?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook