# What is the name of the function $f(k) = \text{max}(k,0)$ on $\mathbb Z$? [duplicate]

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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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## marked as duplicate by Jonas Meyer, Davide Giraudo, Conifold, Brian Fitzpatrick, amWhyAug 15 '14 at 19:49

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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

## 2 Answers

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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