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MathematicsThe number of elements in a set or other grouping, as a property of that grouping.

*‘Cantor conjectured that there are no infinite cardinalities between the size of the natural numbers and the size of the real numbers (and so there are no sets S as described above).’**‘The Skolem-Lowenheim theorem asserts that any first-order theory having an infinite model has other models of all smaller infinite cardinalities.’**‘We understand that sets have a cardinality, that is, that collections have a number associated with them and it doesn't really matter what the members of that set are.’**‘Hausdorff proved further results on the cardinality of Borel sets in 1916.’**‘Frege's approach to providing a logical analysis of cardinality, the natural numbers, infinity and mathematical induction were groundbreaking, and have had a lasting importance within mathematical logic.’*

**Pronunciation**

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