Difference between revisions of "Element"

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=== Elements Within Elements ===
 
=== Elements Within Elements ===
  
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>.
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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 the set <math>\{3,\,4\}</math>.
  
 
== See Also ==
 
== See Also ==
 
*[[Cardinality]]
 
*[[Cardinality]]
 
*[[Set theory]]
 
*[[Set theory]]

Revision as of 19:18, 6 March 2008

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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 $1$, $2$, and the set $\{3,\,4\}$.

See Also