# Draft:Cardinality

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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

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