Positive part function

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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 \ge 0 \\ 0, & x < 0 \\\end{array}\right.