Extended Natural Numbers

Last updated Nov 1, 2022

The Extended Natural Numbers is the set $\bar{\mathbb{N}} := \mathbb{N} \cup {\infty}$ where $\infty$ has the following properties

1. $\forall n \in \bar{\mathbb{N}}$, $\infty \geq n$
2. $\forall n \in \bar{\mathbb{N}}$, $\infty + n = \infty$
3. $\forall n \in \bar{\mathbb{N}}$, $\infty * n = \infty$

That is, the Extended Natural Numbers is a Compactification of $\mathbb{N}$.

• Natural Numbers