INFINITE SET


Meaning of INFINITE SET in English

< mathematics > A set with an infinite number of elements. There are several possible definitions, e.g.

(i) ("Dedekind infinite") A set X is infinite if there exists a bijection (one-to-one mapping) between X and some proper subset of X.

(ii) A set X is infinite if there exists an injection from N (the set of natural number s) to X.

In the presence of the Axiom of Choice all such definitions are equivalent.

(1995-03-27)

FOLDOC computer English dictionary.      Английский словарь по компьютерам FOLDOC.