Ordinal is Finite iff Natural Number
This article is not under active maintenance.
While the contents of this page could be useful, they are currently not being maintained.
The correctness, lay-out and usefulness of the article may be compromised, so use whatever you get from here with caution.
Let $x$ be an ordinal.
By definition of the natural numbers, it follows that $x \sim n$ for some $n$.
By Finite Ordinal is equal to Natural Number, it follows that $x$ is equal to $n$.