Definition:Absolute Value of Mapping/Real-Valued Function

Definition
Let $S$ be a set, and let $f: S \to \R$ be a real-valued function.

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


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

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

Absolute value thence is an instance of a pointwise operation on real-valued functions.

Also see

 * Definition:Absolute Value of Mapping for the absolute value of more general mappings
 * Definition:Pointwise Operation on Real-Valued Functions for other operations on real-valued functions