# Supremums and infimums

## 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|)

## 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

Homework Helper
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

$$\sup\{x,y\} = y$$

and

$$\inf\{x,y\} = x$$

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