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

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