Definition:Order Type of Natural Numbers
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Definition
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).
Sources
- 1968: A.N. Kolmogorov and S.V. Fomin‎: Introductory Real Analysis: $\S 3.3$
- 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $2$: Partial Order Relations