Definition:Pointwise Negation of Real-Valued Function

Definition

Let $S$ be a non-empty set.

Let $f: S \to \R$ be real-valued function.

Then the pointwise negation of $f$ is defined as:

$-f: S \to \R:$

$\forall s \in S: \map {\paren {-f} } s := - \map f s$

where the $-$ on the right hand side is real-number negation.

Thus pointwise negation is seen to be an instance of a pointwise operation on real-valued functions.

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