Max is Half of Sum Plus Absolute Difference

Theorem
For all numbers $a, b$ where $a, b$ in $\N, \Z, \Q$ or $\R$:
 * $\max \set {a, b} = \frac 1 2 \paren {a + b + \size {a - b} }$

Also see

 * Min is Half of Sum Less Absolute Difference