Is there a name for the function $\max(x, 0)$? Is there a name for the function $ \max(x, 0) $?
For comparison, the function $ \max(x, -x) $ is known as the absolute value or modulus of x, and has its own notation $ |x| $.

This is called the positive part of the real number $x$, and often denoted by $x^+$.
Likewise, the negative part of $x$ is $x^-=\max\{-x,0\}$ and the pair of nonnegative real numbers $(x^+,x^-)$ is fully characterized by the pair of identities $$x=x^+-x^-,\qquad\lvert x\rvert=x^++x^-.$$
