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)
