# Cardinality of a Set

## Cardinality of a Set

in mathematics, a generalization of the concept of number of elements of a set. The cardinality of a set is the property that the set shares with all sets (quantitatively) equivalent to the set (two sets are said to be equivalent if there is a one-to-one correspondence between them). Instead of “cardinality” we often use the term “cardinal number.” The smallest infinite cardinal number is x_{0}, (Aleph-null), which is the cardinal number of the natural numbers. The concept of the cardinal number of a set was introduced by G. Cantor (1878), the founder of set theory, who proved that the cardinal number *c* of the real numbers is greater than X o, thereby showing that infinite sets can be classified in terms of their cardinal numbers. (*See*SET THEORY.)