# 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

• Results about the extended natural numbers can be found here.