Definition:Pointwise Addition of Integer-Valued Functions

Definition

Let $S$ be a non-empty set.

Let $f, g: S \to \Z$ be integer-valued functions.

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

$f + g: S \to \Z:$

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

where the $+$ on the right hand side is integer addition.

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

Also see

• Pointwise Addition on Integer-Valued Functions is Associative
• Pointwise Addition on Integer-Valued Functions is Commutative

• Definition:Pointwise Operation on Integer-Valued Functions