cardinal number, or cardinal for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal number,...

into Cardinal and Ordinal Numbers (1958, 2nd ed. 1965). Any finite natural number can be used in at least two ways: as an ordinal and as a cardinal. Cardinal...

In mathematics, the cardinality of a set is a measure of the number of elements of the set. For example, the set A = { 2 , 4 , 6 } {\displaystyle A=\{2...

linguistics, and more precisely in traditional grammar, a cardinal numeral (or cardinal number word) is a part of speech used to count. Examples in English...

Look up Cardinal or cardinal in Wiktionary, the free dictionary. Cardinal or The Cardinal may refer to: Cardinalidae, a family of North and South American...

Continuing in this manner, it is possible to define a cardinal number ℵα for every ordinal number α, as described below. The concept and notation are due...

field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers. Cardinals with such properties are, as the...

(five) is a number, numeral and digit. It is the natural number, and cardinal number, following 4 and preceding 6, and is a prime number. It has garnered...

(cardinality of the empty set, i.e. 0 elements, where 0 is thus the smallest cardinal number) in the set of natural numbers. Today, different mathematicians use...

In mathematics, a Mahlo cardinal is a certain kind of large cardinal number. Mahlo cardinals were first described by Paul Mahlo (1911, 1912, 1913). As...

size (its cardinality), there are many nonisomorphic well-orderings of any infinite set, as explained below. Whereas the notion of cardinal number is associated...

cardinal is inaccessible if it cannot be obtained from smaller cardinals by the usual operations of cardinal arithmetic. More precisely, a cardinal κ...

ordering: cardinal numbers and ordinal numbers. A natural number can be used to express the size of a finite set; more precisely, a cardinal number is a measure...

weakly compact cardinal is a certain kind of cardinal number introduced by Erdős & Tarski (1961); weakly compact cardinals are large cardinals, meaning that...

(often used in combination with a cardinal number, e.g. fourscore to mean 80), but also often used as an indefinite number (e.g. the newspaper headline "Scores...

\mathbb {R} } , sometimes called the continuum. It is an infinite cardinal number and is denoted by c {\displaystyle {\mathfrak {c}}} (lowercase Fraktur...

The College of Cardinals, more formally called the Sacred College of Cardinals, is the body of all cardinals of the Catholic Church. As of 19 April 2024...

place of a given work within a music catalogue, the opus number is paired with a cardinal number; for example, Beethoven's Piano Sonata No. 14 in C-sharp...

A cardinal (Latin: Sanctae Romanae Ecclesiae cardinalis; lit. 'cardinal of the Holy Roman Church') is a senior member of the clergy of the Catholic Church...

particularly in set theory, the beth numbers are a certain sequence of infinite cardinal numbers (also known as transfinite numbers), conventionally written ℶ 0...

measurable cardinal is a certain kind of large cardinal number. In order to define the concept, one introduces a two-valued measure on a cardinal κ, or more...

The four cardinal directions, or cardinal points, are the four main compass directions: north, south, east, and west, commonly denoted by their initials...

cardinal is a cardinal number that is equal to its own cofinality. More explicitly, this means that κ {\displaystyle \kappa } is a regular cardinal if...

(meaning "one, unique"). Linguistically, one is a cardinal number used for counting and expressing the number of items in a collection of things. One is commonly...

However, the cardinal number of α is still a minimal cardinal not less than or equal to the cardinality of X. (If we restrict to cardinal numbers of well-orderable...

mathematics, limit cardinals are certain cardinal numbers. A cardinal number λ is a weak limit cardinal if λ is neither a successor cardinal nor zero. This...

posits that the cardinality of the set of the real numbers is ℵ 1 {\displaystyle \aleph _{1}} ; i.e. the smallest infinite cardinal number after ℵ 0 {\displaystyle...

feminine given name, which means "second cardinal number" and "splendid". It comes from the Arabic cardinal number for second in feminine form ثانية and...

the existence of cardinals with the given property. Existence of a cardinal number κ of a given type implies the existence of cardinals of most of the types...

bijection between them. More generally, two sets are said to have the same cardinal number if there exists a bijection between them. A bijective function from...