Definition:Pointwise Addition of Real-Valued Functions

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

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

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

Also see

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


 * Pointwise Operation on Real-Valued Functions