# Category:Definitions/Extended Natural Numbers

This category contains definitions related to Extended Natural Numbers.
Related results can be found in Category:Extended Natural Numbers.

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.

## Pages in category "Definitions/Extended Natural Numbers"

The following 3 pages are in this category, out of 3 total.