Definition:Pointwise Addition of Integer-Valued Functions
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Definition
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.