# Aleph Product is Aleph

## Theorem

Let $x$ be an ordinal.

Then:

$\left|{\aleph_x \times \aleph_x}\right| = \aleph_x$

where $\aleph$ denotes the aleph mapping.

## Proof

 $\displaystyle \left\vert{\aleph_x \times \aleph_x }\right\vert$ $=$ $\displaystyle \left\vert{\aleph_x}\right\vert$ Non-Finite Cardinal is equal to Cardinal Product $\displaystyle$ $=$ $\displaystyle \aleph_x$ Aleph is Infinite Cardinal

$\blacksquare$