Difference between revisions of "Cardinality"

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(Created page with "In mathematics, the '''cardinality''' of a set is a measure of the "number of elements of the set". For example, the set A = {2, 4, 6} contains 3 el...")
 
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== Description ==
 
== Description ==
  
There are two approaches to cardinality one which compares sets directly using bijections and injections, and another which uses cardinal numbers.
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There are two approaches to cardinality: one which compares sets directly using [[Bijection|bijections]] and [[Injective function|injections]], and another which uses [[Cardinal number|cardinal numbers]].
  
The cardinality of a set is also called its size, when no confusion with other notions of size[2] is possible.
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The cardinality of a set is also called its size, when no confusion with other notions of size is possible.
  
The cardinality of a set A is usually denoted | A |, with a vertical bar on each side; this is the same notation as absolute value and the meaning depends on context. Alternatively, the cardinality of a set A may be denoted by n(A), A, card(A), or # A.
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The cardinality of a set A is usually denoted | A |, with a vertical bar on each side; this is the same notation as [[absolute value]] and the meaning depends on context. Alternatively, the cardinality of a set A may be denoted by n(A), A, card(A), or # A.
  
 
== See also ==
 
== See also ==
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* [[Aleph number]]
 
* [[Aleph number]]
 
* [[Beth number]]
 
* [[Beth number]]
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* [[Bijection]]
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* [[Cardinal number]]
 
* [[Countable set]]
 
* [[Countable set]]
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* [[Injective function]]
 
* [[Ordinality]]
 
* [[Ordinality]]
 
* [[Set (mathematics)]]
 
* [[Set (mathematics)]]

Revision as of 09:25, 22 September 2016

In mathematics, the cardinality of a set is a measure of the "number of elements of the set".

For example, the set A = {2, 4, 6} contains 3 elements, and therefore A has a cardinality of 3.

Description

There are two approaches to cardinality: one which compares sets directly using bijections and injections, and another which uses cardinal numbers.

The cardinality of a set is also called its size, when no confusion with other notions of size is possible.

The cardinality of a set A is usually denoted | A |, with a vertical bar on each side; this is the same notation as absolute value and the meaning depends on context. Alternatively, the cardinality of a set A may be denoted by n(A), A, card(A), or # A.

See also

External links