Definition:Cardinal Number

Definition
Let $S$ be a set.

The cardinal number of $S$ is defined as follows:


 * $\operatorname{Card} \left({S}\right) = \bigcap \left\{ x \in \operatorname{On} : x \sim S \right\}$

Also see

 * The definition of cardinal, where cardinals are defined as equivalence classes of sets rather than as ordinal numbers.