term cardinality was coined for generalizing to infinite sets the concept of the number of elements. More precisely, two sets have the same cardinality if...

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

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

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

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...

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

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

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...

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

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...

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

In set theory, the concept of cardinality is significantly developable without recourse to actually defining cardinal numbers as objects in the theory...

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...

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...

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...

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...

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...

members are related by chromatic transposition. In diatonic set theory cardinality equals variety when, for any melodic line L in a particular scale S,...

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...

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...

set A is a subset of B, if and only if the cardinality of their intersection is equal to the cardinality of A. Formally: A ⊆ B  if and only if  | A ∩...

if and only if for every natural number, the set has a subset whose cardinality is that natural number. If the axiom of choice holds, then a set is infinite...

A of cardinality κ that is homogeneous for f. That is, for every n, the function f is constant on the subsets of cardinality n from A. A cardinal κ is...

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...

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

is equal to c {\displaystyle {\mathfrak {c}}} , the cardinality of the continuum (the cardinality of the set of the real numbers), and the third beth...