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.

单词	infinite set
释义	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.
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