\begin{definition}[Definition:Order Type of Natural Numbers]
Consider the ordered set $\struct {\N, \le}$ consisting of the set of natural numbers $\N$ under the usual ordering $\le$.
That is, $\N$ arranged in increasing order $0, 1, 2, \ldots$
The order type of $\struct {\N, \le}$ is denoted $\omega$ ('''omega''').
\end{definition}