Definition:Pointwise Addition of Integer-Valued Functions

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Let $S$ be a non-empty set.

Let $f, g: S \to \Z$ be integer-valued functions.

Then the pointwise sum of $f$ and $g$ is defined as:

$f + g: S \to \Z:$
$\forall s \in S: \map {\paren {f + g} } s := \map f s + \map g s$

where the $+$ on the right hand side is integer addition.

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

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