infinite set

(redirected from Infinite cardinality)

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 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.
References in periodicals archive ?
undefined time value); we define such concept to have an infinite cardinality.
Let the concept C contain at least one sub-concept with non-zero or infinite cardinality.
This way, the Time concept gets infinite cardinality.