# cardinality

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Related to cardinality: Cardinality of a Set

## cardinality

(mathematics)
The number of elements in a set. If two sets have the same number of elements (i.e. there is a bijection between them) then they have the same cardinality. A cardinality is thus an isomorphism class in the category of sets.

aleph 0 is defined as the cardinality of the first infinite ordinal, omega (the number of natural numbers).

## cardinality

A quantity relationship between elements. For example, one-to-one, one-to-many and many-to-one express cardinality. See cardinal number.
References in periodicals archive ?
Here [[??].bar] (c'), [[??].bar](c") denotes minimum and maximum cardinality of a single valued neutrosophic rough set with respect to lower approximation and is defined as,
the set of features is F = [U.sub.a] with cardinality N = [M.sub.a].
Cardinality violation: Li [12] gave a novel linear program called rectangle LP and presented an improved approximation algorithm (exp(0(1/[[epsilon].sup.2]))) using at most (1 + [epsilon])k facilities for hard uniform CkM problem.
A multiresolving set of a minimum cardinality is called a minimum multiresolving set or a multibasis of G and this cardinality is the multidimension [dim.sub.M](G) of G.
The code length L, code weight w, code cardinality [absolute value of (C)], autocorrelation [[lambda].sub.xyz], and cross-correlation [mathematical expression not reproducible] of EG-nMPC are given by
SQL Server would make assumptions about the cardinality estimate of a TVF, frequently assuming incorrectly.
The set [mathematical expression not reproducible] has multiple roots in [bar.F.sub.q]} has low cardinality, and one has a nice description of the multiplicities of the roots.
(ii) Transform (16) and (17) into two objectives [f.sub.1] and [f.sub.2] which must be optimized under a fixed cardinality of features (as MOACO must determine the number of selected features firstly).
It is a little surprising that here a number of results can be obtained immediately by means of a cardinality argument (Propositions A and B below), yet there are cases requiring more advanced knowledge.
While transforming relationship sets cardinality of <<one-to-many>>, in addition for object properties would be created and tagged as inverse object properties.
Criterion 1: We include in H only those partitions in which all equivalence classes have the same cardinality. This cardinality we shall call n.
The NP-hardness of finding the minimum cardinality of a closed monopoly in a graph is easy to observe as stated by Linial et al.

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