\begin{definition}[Definition:Extended Absolute Value]
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 $\size{\, \cdot \,}: \overline \R \to \overline \R$.
\end{definition}