Non-Finite Cardinal is equal to Cardinal Product/Corollary

Corollary to Non-Finite Cardinal is equal to Cardinal Product
Let $S$ be a set that is equinumerous to its cardinal number.

Let $\left|{ S }\right|$ denote the cardinal number of $S$.

Let:
 * $\left|{S}\right| \ge \omega$

where $\omega$ denotes the minimal infinite successor set.

Then:
 * $\left|{S \times S}\right| = \left|{S}\right|$

Proof
By the hypothesis:
 * $S \sim \left|{S}\right|$

By Cartesian Product Preserves Cardinality:
 * $S \times S \sim \left|{S}\right| \times \left|{S}\right|$

Therefore: