An ordinal $\alpha$ is a cardinal number or cardinal if
\[\forall \beta < \alpha : \beta \lnequ \alpha.\]The class of all cardinals is denoted by $\Card$.
Every natural number is a cardinal, called a finite cardinal. A cardinal is infinite if it is not finite.
$\Card$ is a proper class.
Proof. Show that
\[\Ord \subseteq \bigcup \Card.\]
Every infinite cardinal is a limit ordinal.
Proof. By SUC > Proposition 2.
For every ordinal $\alpha$ there is a cardinal greater than $\alpha$.