Cardinality

Definitions

1. The number of elements a given set contains.
   countable, uncountable
2. The number of terms that can inhabit a type; the possible values of a type.
   countable, uncountable
3. 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.
   countable, uncountable
4. The status of being cardinalitial
   countable, uncountable

Equivalents

Examples

“The empty set⟳ has a cardinality of zero.”

“The cardinality of a set⟳ A is the least ordinal α such that there exists a bijection between A and α. We sometimes use⟳ the notation #92;alpha#61;#124;A#124; to indicate⟳ this.”

“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.”

“Clearly, in this example, the sensitivity to the cardinalities takes the weaker form⟳ F#91;M(A)#93;#61;#92;overset#123;#61;#125;#123;A#125; of a single-valued function from the measure⟳ to the cardinality rather than the stronger form⟳ M(A)#61;f(#92;overset#123;#61;#125;#123;A#125;) of a function from the cardinality to the measure⟳.”

“For many types, such as String, the set⟳ of possible values is unlimited. Such types have⟳ an infinite cardinality.”

CEFR level