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

We can represent Absolute in terms of Max:

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

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

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