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:

$x^{+}:=\{\begin{array}{cc}x,& x\ge 0\\ 0,x<0\\ \end{array}$

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