In mathematics, the cardinality of a set is the number of its elements. The cardinality of a set may also be called its size, when no confusion with other...

rank among the infinite cardinals. Cardinality is defined in terms of bijective functions. Two sets have the same cardinality if, and only if, there is...

In set theory, the cardinality of the continuum is the cardinality or "size" of the set of real numbers R {\displaystyle \mathbb {R} } , sometimes called...

Within data modelling, cardinality is the numerical relationship between rows of one table and rows in another. Common cardinalities include one-to-one,...

term cardinality refers to the uniqueness of data values contained in a particular column (attribute) of a database table. The lower the cardinality, the...

Look up Cardinal or cardinal in Wiktionary, the free dictionary. Cardinal or The Cardinal most commonly refers to Cardinalidae, a family of North and...

lowercase Greek letter omega), also has cardinality ℵ 0 {\displaystyle \aleph _{0}} . A set has cardinality ℵ 0 {\displaystyle \aleph _{0}} if and only...

Calculating the exact cardinality of the distinct elements of a multiset requires an amount of memory proportional to the cardinality, which is impractical...

particular maximum-cardinality matching in which prioritized vertices are matched first. The problem of finding a maximum-cardinality matching in hypergraphs...

computation or estimation of the cardinality of finite sets. The cardinality of an infinite set is commonly represented by a cardinal number, exactly as the number...

Look up cardinality in Wiktionary, the free dictionary. Cardinality may refer to: Cardinality of a set, a measure of the "number of elements" of a set...

A cardinal is a senior member of the clergy of the Catholic Church. As titular members of the clergy of the Diocese of Rome, they serve as advisors to...

numbers to X. The cardinality of X is neither finite nor equal to ℵ 0 {\displaystyle \aleph _{0}} (aleph-null). The set X has cardinality strictly greater...

) Perhaps the simplest cardinal invariants of a topological space X {\displaystyle X} are its cardinality and the cardinality of its topology, denoted...

of cardinality κ {\displaystyle \kappa } . Then X {\displaystyle X} has cardinality at most 2 2 κ {\displaystyle 2^{2^{\kappa }}} and cardinality at most...

example, the cardinality of ω 0 = ω {\displaystyle \omega _{0}=\omega } is ℵ 0 {\displaystyle \aleph _{0}} , which is also the cardinality of ω 2 {\displaystyle...

{\displaystyle 2^{\aleph _{0}}\!} , the cardinality of the power set of the natural numbers. The cardinality of the continuum is the size of the set of...

numbers is the same size (cardinality) as the set of integers: they are both countable sets. Cantor gave two proofs that the cardinality of the set of integers...

ordinals. That is, the successor cardinal is the cardinality of the least ordinal into which a set of the given cardinality can be mapped one-to-one, but...

are no intermediate cardinal numbers between ℵ 0 {\displaystyle \aleph _{0}} and the cardinality of the continuum (the cardinality of the set of real numbers):...

Equinumerous sets are said to have the same cardinality (number of elements). The study of cardinality is often called equinumerosity (equalness-of-number)...

[citation needed] The number of multisets of cardinality k, with elements taken from a finite set of cardinality n, is sometimes called the multiset coefficient...

known as cardinality; informally, this is the size of a set. In the above examples, the cardinality of the set A is 4, while the cardinality of set B...

set, and I is a linearly independent set, then the cardinality of I is not larger than the cardinality of G. In particular if V is finitely generated, then...

The Cardinal is a 1963 American drama film produced independently, directed by Otto Preminger and distributed by Columbia Pictures. The screenplay was...

form a set of the same cardinality as the α-th number class. The cardinality of the (α + 1)-th number class is the cardinality immediately following that...

refined with respect to cardinality. A theory is κ-categorical (or categorical in κ) if it has exactly one model of cardinality κ up to isomorphism. Morley's...

_{<\kappa }} of sets of cardinality less than κ {\displaystyle \kappa } and all functions between them is closed under colimits of cardinality less than κ {\displaystyle...

uncountable cardinal κ: κ is weakly compact. for every λ<κ, natural number n ≥ 2, and function f: [κ]n → λ, there is a set of cardinality κ that is homogeneous...

of subsets of S of cardinality less than or equal to κ is sometimes denoted by Pκ(S) or [S]κ, and the set of subsets with cardinality strictly less than...