Supremums and infimums

  • Thread starter kmeado07
  • Start date
  • #1
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Homework Statement



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|)


Homework Equations





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.
 

Answers and Replies

  • #2
statdad
Homework Helper
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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?
 

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