infinite set
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)