What is cardinality?

  • (noun): (mathematics) the number of elements in a set or group (considered as a property of that grouping).


In mathematics, the cardinality of a set is a measure of the "number of elements of the set". For example, the set A = {2, 4, 6} contains 3 elements, and therefore A has a cardinality of 3. There are two approaches to cardinality – one which compares sets directly using bijections and injections, and another which uses cardinal numbers.

Read more about Cardinality.

Some articles on cardinality:

Paradoxes Of Set Theory - Paradoxes of The Infinite Set - Je Le Vois, Mais Je Ne Crois Pas
... proving that the set of points of a square has the same cardinality as that of the points on just an edge of the square the cardinality of the continuum ... This demonstrates that the "size" of sets as defined by cardinality alone is not the only useful way of comparing sets ...
Cardinality Of The Continuum
... In set theory, the cardinality of the continuum is the cardinality or “size” of the set of real numbers, sometimes called the continuum ... Symbolically, if the cardinality of is denoted as, the cardinality of the continuum is This was proven by Georg Cantor in his 1874 uncountability proof, part of his ... Cantor defined cardinality in terms of bijective functions two sets have the same cardinality if and only if there exists a bijective function between them ...
Cantor's Paradox - Statements and Proofs
... This fact is a direct consequence of Cantor's theorem on the cardinality of the power set of a set ... Then (in the von Neumann formulation of cardinality) C is a set and therefore has a power set 2C which, by Cantor's theorem, has cardinality strictly larger than ... Demonstrating a cardinality (namely that of 2C) larger than C, which was assumed to be the greatest cardinal number, falsifies the definition of C ...
Cardinality (SQL Statements)
... In SQL (Structured Query Language), the term cardinality refers to the uniqueness of data values contained in a particular column (attribute) of a database table ... The lower the cardinality, the more duplicated elements in a column ... Thus, a column with the lowest possible cardinality would have the same value for every row ...