Computing Dictionary
infinite set definition
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 numbers) to X.
In the presence of the
Axiom of Choice all such definitions are equivalent.
(1995-03-27)
