# Definition of cardinality in US English:

## cardinality

### nounPlural cardinalities

Mathematics
• The number of elements in a set or other grouping, as a property of that grouping.

• ‘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.’
• ‘The Skolem-Lowenheim theorem asserts that any first-order theory having an infinite model has other models of all smaller infinite cardinalities.’
• ‘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).’
• ‘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.’

## cardinality

/ˌkärdəˈnalədē//ˌkɑrdəˈnælədi/