Difference between revisions of "Cardinality"
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Karl Jones (Talk | contribs) (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 | + | 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 | + | 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. | + | 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]] | ||
| + | * [[Bijection]] | ||
| + | * [[Cardinal number]] | ||
* [[Countable set]] | * [[Countable set]] | ||
| + | * [[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
- Aleph number
- Beth number
- Bijection
- Cardinal number
- Countable set
- Injective function
- Ordinality
- Set (mathematics)
External links
- Cardinality @ Wikipedia
