Definition:Extended Natural Numbers

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

Definition 1
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

Definition 2
The extended natural numbers are the order completion of the ordered set of natural numbers.

Also see

 * Definition:Extended Real Number Line
 * Definition:Infinity