cardinality

Etymology

cardinal + -ity.

noun

1. (set theory, of a set) The number of elements a given set contains.
   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 α=|A| to indicate this. 2005, Johan de Jong, “Set Theory”, in The Stacks Project, retrieved 2018-02-26
   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. 2006, Michael Smithson, Jay Verkuilen, Fuzzy Set Theory: Applications in the Social Sciences, SAGE Publications, page 37
   {{quote-book|en|year=2012|author=Adolf Grünbaum; Robert S. Cohen; Marx W. Wartofsky|title=Philosophical Problems of Space and Time|edition=2nd|pageurl=https://books.google.com.au/books?id=m3ugBwAAQBAJ&pg=PA487&dq=%22cardinality%22%7C%22cardinalities%22&hl=en&sa=X&ved=0ahUKEwjcj5ywv_DaAhWCg5AKHcJHCdYQ6AEIjQEwEw#v=onepage&q=%22cardinality%22%7C%22cardinalities%22&f=false|page=487|publisher=Springer
2. (type theory) The number of terms that can inhabit a type; the possible values of a type.
   For many types, such as String, the set of possible values is unlimited. Such types have an infinite cardinality. 2021, Martin Odersky et al., chapter 19, in Programming in Scala, 5th edition, Artima
3. (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.
4. (religion) The status of being cardinalitial