\begin{definition}[Definition:Extended Real Number Line/Definition 1]
The '''extended real number line''' $\overline \R$ is defined as:
:$\overline \R := \R \cup \set {+\infty, -\infty}$
that is, the set of real numbers together with two auxiliary symbols:
:$+\infty$, '''positive infinity'''
:$-\infty$, '''negative infinity'''
such that:
:$\forall x \in \R: x < +\infty$
:$\forall x \in \R: -\infty < x$
\end{definition}