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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 , the cardinality of the set is denoted as .
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
Given two sets, and , if there exists a bijection or , then .