Definition:Extended Absolute Value

Definition
Let $\overline{\R}$ denote the extended real numbers.

Extend the absolute value $\left\vert{\cdot}\right\vert$ on $\R$ to $\overline{\R} = \R \cup \left\{{+\infty, -\infty}\right\}$ by defining:


 * $\left\vert{-\infty}\right\vert = \left\vert{+\infty}\right\vert = +\infty$

Thus, the extended absolute value is a mapping $\left\vert{\cdot}\right\vert: \overline{\R} \to \overline{\R}$.

Also see

 * Absolute Value
 * Extended Absolute Value is Multiplicative
 * Triangle Inequality for Extended Absolute Value