# Cardinality of a Set

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## 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 x0, (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. (SeeSET THEORY.)

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
(1).The minimum cardinality of a set in the class of optimal and near optimal sets [L.sub.85,7] is m = 3.
The cardinality of a set X is denoted by the symbol [absolute value of X].
The determining number of a graph G = (V(G), E(G)) is the minimum cardinality of a set S [subset or equal to] V(G) such that the automorphism group of the graph obtained from G by fixing every vertex in S is trivial.
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