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Element: Difference between revisions

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<math>A=\{1,\,2,\,3,\,4\}</math> means set <math>A</math> contains the elements 1, 2, 3 and 4.
<math>A=\{1,\,2,\,3,\,4\}</math> means set <math>A</math> contains the elements 1, 2, 3 and 4.


To show that an element is contained within a [[set]], the <math>\in</math> symbol is used. If <math>A=\{2,\,3\}</math>, then <math>2\in A</math>.
To show that an element is contained within a set, the <math>\in</math> symbol is used. If <math>A=\{2,\,3\}</math>, then <math>2\in A</math>.


The opposite of this would be <math>\notin</math>, which means the element is not contained within the [[set]].
The opposite of this would be <math>\notin</math>, which means the element is not contained within the set.


=== Elements Within Elements ===
=== Elements Within Elements ===


Elements can also be [[set]]s. For example, <math>B = \{1,\,2,\,\{3,\,4\}\}</math>. The elements of <math>B</math> are not 1, 2, 3, and 4. Actually, there are only three elements of <math>B</math>: <math>1</math>, <math>2</math>, and the [[set]] <math>\{3,\,4\}</math>.
Elements can also be sets. For example, <math>B = \{1,\,2,\,\{3,\,4\}\}</math>. The elements of <math>B</math> are not 1, 2, 3, and 4. Actually, there are only three elements of <math>B</math>: <math>1</math>, <math>2</math>, and the set <math>\{3,\,4\}</math>.


=== Cardinality ===
=== Cardinality ===


The amount of elements in a [[set]] is known as [[cardinality]]. If <math>C=\{1,\,2,\,3\}</math>, then the cardinality of <math>C</math> is <math>3</math>. Informally, cardinality is the size of a [[set]].
The amount of elements in a set is known as [[cardinality]]. If <math>C=\{1,\,2,\,3\}</math>, then the cardinality of <math>C</math> is <math>3</math>. Informally, cardinality is the size of a set.
 
 
==See Also==
* [[Set]]

Revision as of 11:48, 1 November 2006

This article is a stub. Help us out by expanding it.

An element, also called a member, is an object contained within a set or class.

$A=\{1,\,2,\,3,\,4\}$ means set $A$ contains the elements 1, 2, 3 and 4.

To show that an element is contained within a set, the $\in$ symbol is used. If $A=\{2,\,3\}$, then $2\in A$.

The opposite of this would be $\notin$, which means the element is not contained within the set.

Elements Within Elements

Elements can also be sets. For example, $B = \{1,\,2,\,\{3,\,4\}\}$. The elements of $B$ are not 1, 2, 3, and 4. Actually, there are only three elements of $B$: $1$, $2$, and the set $\{3,\,4\}$.

Cardinality

The amount of elements in a set is known as cardinality. If $C=\{1,\,2,\,3\}$, then the cardinality of $C$ is $3$. Informally, cardinality is the size of a set.

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