cardinality

Noun

Meaning

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

Synonyms

Hypernyms

Related terms

Examples

A generalized form of the diagonal argument was used by Cantor to prove Cantor's theorem : for every set S the power set of S; that is, the set of all subsets of S (here written as P(S)), has a larger cardinality than S itself. Source: Internet

All bases of a vector space have the same cardinality (number of elements), called the dimension of the vector space. Source: Internet

All transcendence bases have the same cardinality, equal to the transcendence degree of the extension. Source: Internet

And yet Cantor's diagonal argument shows that real numbers have higher cardinality. Source: Internet

A simple example of a space which is not separable is a discrete space of uncountable cardinality. Source: Internet

A subset S of L is called algebraically independent over K if no non-trivial polynomial relation with coefficients in K exists among the elements of S. The largest cardinality of an algebraically independent set is called the transcendence degree of L/K. Source: Internet

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