Definition:Pointwise Addition of Rational-Valued Functions

Definition
Let $S$ be a non-empty set. Let $f, g: S \to \Q$ be rational-valued functions.

Then the pointwise sum of $f$ and $g$ is defined as:
 * $f + g: S \to \Q:$
 * $\forall s \in S: \map {\paren {f + g} } s := \map f s + \map g s$

where the $+$ on the is integer addition.

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

Also see

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


 * Definition:Pointwise Operation on Rational-Valued Functions