Category:Definitions/Negative Parts

This category contains definitions related to Negative Parts.
Related results can be found in Category:Negative Parts.

Let $X$ be a set, and let $f: X \to \overline \R$ be an extended real-valued function.

Then the negative part of $f$, $f^-: X \to \overline \R$, is the extended real-valued function defined by:

$\forall x \in X: \map {f^-} x := -\min \set {0, \map f x}$

where the minimum is taken with respect to the extended real ordering.