Set of Natural Numbers is Ordinal

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The set of natural numbers $\N$ is an ordinal.


From Natural Number is Ordinal, every element of $\N$ is an ordinal.

From Union of Set of Ordinals is Ordinal, $\bigcup \N$ is therefore itself an ordinal.

From Set of Natural Numbers Equals its Union:

$\bigcup \N = \N$

Hence the result.