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Difference between revisions of "Element"
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An '''element''', also called a '''member''', is an object contained within a [[set]] or [[class]].
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An '''element''', also called a '''member''', is an object contained within a [[set]] or class.
  
 
<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.
  
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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>.
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To show that an element is contained within a set, the <math>\in</math> symbol is used. The opposite of <math>\in</math> is <math>\notin</math>, which means the element is not contained within the set.
  
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The opposite of this would be <math>\notin</math>, which means the element is not contained within the [[set]].
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=== Sets as Elements ===
  
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=== Elements Within Elements ===
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Elements can also be sets. For example, <math>B = \{1,\,2,\,\{3,\,4\}\}</math>. The elements of <math>B</math> are <math>1</math>, <math>2</math>, and <math>\{3,\,4\}</math>.
  
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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>.
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== See Also ==
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*[[Cardinality]]
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*[[Set theory]]
  
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=== Cardinality ===
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[[Category:Set theory]]
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[[Category:Definition]]
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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]].
 
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==See Also==
 
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* [[Set]]
 

Latest revision as of 14:59, 3 April 2012

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

Sets as Elements

Elements can also be sets. For example, $B = \{1,\,2,\,\{3,\,4\}\}$. The elements of $B$ are $1$, $2$, and $\{3,\,4\}$.

See Also

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