An ordinal $\alpha$ is a cardinal number / 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#PROP-CARD.
For every ordinal $\alpha$ there is a cardinal greater than $\alpha$.