Definition of "cardinality"

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 | {\displaystyle \alpha =|A|} to indicate this.

2005, Johan de Jong, “Set Theory”, in The Stacks Project‎, retrieved 2018-2-26

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

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

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

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