Ordinal Number Equivalent to Cardinal Number

Theorem
Let $x$ be an ordinal.

Let $\vert x \vert$ denote the cardinal number of $x$.

Then:


 * $x \sim \vert x \vert$

Proof
By the fact that Set Equivalence an Equivalence Relation, $x \sim x$.

Therefore, $x$ is equivalent to some ordinal.

By Condition for Set Equivalent to Cardinal Number, $x \sim \vert x \vert$.