Cardinality - Revision history

Karl Jones at 15:36, 22 September 2016

2016-09-22T15:36:33Z

Karl Jones at 15:25, 22 September 2016

2016-09-22T15:25:24Z

Karl Jones: 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..."

2016-09-22T15:22:34Z

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..."

New page

In [[mathematics]], the '''cardinality''' of a [[Set (mathematics)|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[2] 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]]
* [[Countable set]]
* [[Ordinality]]
* [[Set (mathematics)]]

== External links ==

* [https://en.wikipedia.org/wiki/Cardinality Cardinality] @ Wikipedia

[[Category:Mathematics]]
[[Category:Set theory]]

@@ Line 17: / Line 17: @@
 * [[Bijection]]
 * [[Cardinal number]]
 * [[Countable set]]
 * [[Injective function]]

@@ Line 5: / Line 5: @@
 == Description ==
-There are two approaches to cardinality – one which compares sets directly using bijections and injections, and another which uses cardinal numbers.
+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.
+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 ==
@@ Line 15: / Line 15: @@
 * [[Aleph number]]
 * [[Beth number]]
 * [[Countable set]]
 * [[Ordinality]]
 * [[Set (mathematics)]]