Definition:Pointwise Multiplication of Integer-Valued Functions

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Let $S$ be a non-empty set.

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

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

$f \times g: S \to \Z:$
$\forall s \in S: \map {\paren {f \times g} } s := \map f s \times \map g s$

where the $\times$ on the right hand side is integer multiplication.

Also denoted as

Using the other common notational forms for multiplication, this definition can also be written:

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


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

Also see