Definition:Extended Real Number Line/Definition 1

Definition
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:
 * $\forall x \in \R: x < +\infty$
 * $\forall x \in \R: -\infty < x$

Also see

 * Equivalence of Definitions of Extended Real Number Line