Definition:Extended Natural Numbers

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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