Positive part function

Definition

The positive part function is a function that takes as input any real number and outputs the same number if it is nonnegative, and 0 if it is negative. The positive part of $x$ is denoted $x^{+}$. It can also be defined as $\max\{x,0\}$.

It can also be described using a piecewise definition:

$x^{+}:=\left\lbrace {\begin{array}{rl}x,&x\geq 0\\0,&x<0\\\end{array}}\right.$

Graph