Definition:Cardinal Number

Definition
Let $S$ be a set.

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


 * $\ds \card S = \bigcap \set {x \in \On : x \sim S}$

where $\On$ is the class of all ordinals.

Compare cardinality.

Also see

 * Definition:Cardinal, where cardinal numbers are defined as equivalence classes of sets rather than as ordinal numbers.