Definition:Pointwise Addition of Real-Valued Functions

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Definition

Let $S$ be a non-empty set.

Let $f, g: S \to \R$ be real-valued functions.


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

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

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


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


Also see


Sources

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