# Set of Natural Numbers is Smallest Ordinal Greater than All Natural Numbers

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## Theorem

The set of natural numbers $\N$ is the smallest ordinal which is greater than all natural numbers.

## Proof

From Set of Natural Numbers is Ordinal, $\N$ is an ordinal.

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## Sources

- 2010: Raymond M. Smullyan and Melvin Fitting:
*Set Theory and the Continuum Problem*(revised ed.) ... (previous) ... (next): Chapter $5$: Ordinal Numbers: $\S 3$ Some ordinals