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