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## Negative part of a function

### Definition

 $f:X\to Y$ $(Y\subseteq \overline{\mathbb R})\land (0\in Y)$
 $f^-$
 $f^-:X\to Y$
 $f^-(x) := \mathrm{max}(-f(x),0)$

### Ramifications

#### Discussion

Notice that $f^-(x)\ge 0$.