Finding Supremums and Infimums for Real Numbers | Homework

[kmeado07]

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.

 

[statdad]

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

\sup\{x,y\} = y <br />

and

\inf\{x,y\} = <br /> x


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