How to represent $\max(x, y)$ in terms of absolute?

Question

We can represent Absolute in terms of Max:

$|x| = \max(x, -x)$

but how to represent $\max(x, y)$ in terms of Absolute

Answer 1

Here's one way to do it: $$ \max(x,y) = \frac{x+y}{2} + \frac{|x-y|}{2} . $$