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)