Definition:Extended Natural Numbers/Definition 1

Definition
Let $\N$ be the set of natural numbers.

The extended natural numbers are the elements of the ordered set $\struct {\N \cup \set \infty, \le}$, where
 * $\infty$ is a new element, called infinity
 * $\le$ is the ordering on the extended natural numbers.

Also see

 * Equivalence of Definitions of Extended Natural Numbers