Definition:Extended Absolute Value

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

Extend the absolute value $\size {\, \cdot \,}$ on $\R$ to $\overline \R$ by defining:


 * $\size {-\infty} = \size {+\infty} = +\infty$

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

Also see

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