Definition:Cardinal Number

Definition
Let $S$ be a set.

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


 * $\vert S \vert = \displaystyle \bigcap \left\{ x \in \operatorname{On} : x \sim S \right\}$

where $\operatorname{On}$ is the class of all ordinals.

Compare cardinality.

Also see

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