cardinality

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Noun

cardinality (plural cardinalities)

1. (set theory, of a set) The number of elements a given set contains.

   The empty set has a cardinality of zero.

   • 2006, Michael Smithson, Jay Verkuilen, Fuzzy Set Theory: Applications in the Social Sciences, SAGE Publications, page 37 ↗,

     For fuzzy sets, the concept of set size or cardinality is both richer and more problematic than it is for crisp sets. It is richer because, as we shall see, we may use more than one kind of cardinality.

   • 2012, Adolf Grünbaum, Robert S. Cohen, Marx W. Wartofsky, Philosophical Problems of Space and Time, 2nd Edition, Springer, page 487 ↗,

     Clearly, in this example, the sensitivity to the cardinalities takes the weaker form F[M(A)] = \overset{=}{A} of a single-valued function from the measure to the cardinality rather than the stronger form M(A) = f(\overset{=}{A}) of a function from the cardinality to the measure.

2. (data modeling, databases) The property of a relationship between a database table and another one, specifying whether it is one-to-one, one-to-many, many-to-one, or many-to-many.
3. (religion) The status of a cardinal.

Synonyms

• (in set theory) power

Related terms

• cardinal

Translations

• French: cardinalité
• German: Mächtigkeit, Kardinalität
• Italian: cardinalità, numerosità, potenza
• Portuguese: cardinalidade
• Russian: мо́щность (мно́жества)
• Spanish: cardinalidad

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