Definition:Absolute Value of Mapping

Definition

Let $D$ be an ordered integral domain, and let $\left\vert{\, \cdot \,}\right\vert_D$ be its absolute value.

Let $S$ be a set, and let $f: S \to D$ be a mapping.

Then the absolute value of $f$, denoted $\left\vert{f}\right\vert_D: S \to D$, is defined as:

$\forall s \in S: \left\vert{f}\right\vert_D \left({s}\right) := \left\vert{f \left({s}\right)}\right\vert_D$

where $\left\vert{f \left({s}\right)}\right\vert_D$ denotes the absolute value function on $D$.

Absolute value thence is an instance of a pointwise operation on a mapping.