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Cardinality is the number of elements in a set. The cardinality of any finite set is a natural number. Cardinalities of certain sets manifest the cardinals, a type of generalization of the natural numbers. Given a set A, the cardinality of the set A is denoted as \left| A\right|.

Comparing Sets[edit]

Generalizations of "counting" sets are useful in the context of infinite sets: sets with an infinite "number" of elements. Some cardinalities of some infinite sets are bigger than cardinalities of other infinite sets.

Sets of equal size[edit]

Given two sets, A and B, if there exists a bijection f:A\to B or f:B\to A, then \left| A\right|=\left| B\right|.