# Cardinal Number Less than Ordinal/Corollary

## Corollary to Cardinal Number Less than Ordinal

Let $x$ be an ordinal.

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

Then:

$\left|{x}\right| \le x$

## Proof

$x \sim x$
$\left|{x}\right| \le x$

$\blacksquare$