Information icon.svg The 2019 RMF board election has started!
We are electing 3 board members for the 2019-2021 term.
Vote here and read their campaign slogans here!

Draft:Cardinality

From RationalWiki
Jump to: navigation, search
Mathematics Articles on RationalWiki

mathematics

Conservapedian mathematics  -  Fermat's last theorem  -  Fibonacci sequence  -  Golden Ratio  -  Gödel's incompleteness theorems  -  Hypatia of Alexandria  -  Information  -  Mathematics  -  Metric system  -  Metric system  -  Phli (fun)  -  Pyramid  -  Rene Descartes  -  Sophie Germain  -  Statistics  -  wikiFactor  -  Zero  -


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|.