infinite set

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)