# 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.
In fact, if the total positive value is of the same infinite cardinality as the total of the negative value, the net value of the world is undefined.
This could be done by adding stages to the decision procedure such that values of greater infinite cardinality are always given lexical priority over lower-level values, the latter serving as tiebreakers (37)

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