Definition:Order Type of Natural Numbers

Definition
Consider the set of natural numbers $$\left({\N, \le}\right)$$ where $$\le$$ is interpreted in its conventional meaning.

That is, $$\N$$ arranged in increasing order $$0, 1, 2, \ldots$$

The order type of $$\left({\N, \le}\right)$$ is denoted $$\omega$$ (omega).