Definition:Pointwise Addition of Real-Valued Functions

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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:

$f + g: S \to \R:$
$\forall s \in S: \left({f + g}\right) \left({s}\right) := f \left({s}\right) + g \left({s}\right)$

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