Proposition: Closed Formula for the Maximum and Minimum of Two Numbers

For any two real numbers $x,y\in\mathbb R$ the maximum and minimum can be calculated using the following formulae:

$$\begin{array}{rcl}\max(x,y)&=&\frac 12(x+y+|x-y|),\\ \min(x,y)&=&\frac 12(x+y-|x-y|),\end{array}$$

where $|x-y|$ denotes the distance between $x$ and $y$.