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Let $k\in \mathbb Z$; is there a name for the function $f(k)$ below? $$ f(k) = \text{max}(k, 0) $$

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In optimization, the generalized form of your function $f(x,c) = \max(x-c,0)$ is often referred to as a hinge function. –  cardinal Mar 6 '11 at 19:44
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up vote 9 down vote accepted

This could be called the "positive part" of $k$ and denoted $f(k)=k^+$.

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Write $|x| = |x|_{+} + |x|_{-}$, where $|x|_{\pm} = \pm x \theta(\pm x)$, where $\theta$ is the Heaviside step function. Then your function is the restriction of the function $|x|_{+}$, the positive part of the absolute value function, that is, on $\mathbb{Z}$.

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