Definition:Pointwise Addition of Real-Valued Functions

Definition
Let $S$ be a set, and let $f,g : S \to \R$ be real-valued functions.

Then the pointwise sum of $f$ and $g$, $f + g: S \to \R$, is defined by (for all $s \in S$):


 * $\left({f + g}\right) \left({s}\right) := f \left({s}\right) + g \left({s}\right)$

where the $+$ on the right is real addition.

Pointwise addition thence is an instance of a pointwise operation on real-valued functions.

Also see

 * Pointwise Addition is Associative
 * Pointwise Addition is Commutative
 * Pointwise Operation on Real-Valued Functions