catflap.org Online Dictionary Query |
From The Free On-line Dictionary of Computing (27 SEP 03) : [ foldoc ]
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 numbers) to X.
In the presence of the Axiom of Choice all such definitions
are equivalent.
(1995-03-27)