Definition:Cardinality

Definition
Two sets (either finite or infinite) which are equivalent are said to have the same cardinality.

The cardinality of a set $S$ is written $\card S$.

Cardinality of Natural Numbers
When the natural numbers are defined as von Neumann construction of natural numbers, the cardinality function can be viewed as the identity mapping on $\N$.

That is:
 * $\forall n \in N: \card n := n$

Also see

 * Definition:Cardinal
 * Definition:Set Equivalence


 * Cardinality of Finite Set is Well-Defined