Definition:Pointwise Addition of Real-Valued Functions

From ProofWiki
Jump to: navigation, search

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 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


Sources