infinite set


infinite set

[′in·fə·nət ′set] (mathematics) A set with more elements than any fixed integer; such a set can be put into a one to one correspondence with a proper subset of itself.

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 existsa bijection (one-to-one mapping) between X and some propersubset 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 definitionsare equivalent.