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