Cardinal Number Less than Ordinal/Corollary

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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

By Set Equivalence is Equivalence Relation:

$x \sim x$

By Cardinal Number Less than Ordinal:

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

$\blacksquare$


Sources