Difference between revisions of "Element"

Revision as of 18:18, 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 can also be sets. For example, $B = \{1,\,2,\,\{3,\,4\}\}$ . The elements of $B$ are $1$ , $2$ , and the set $\{3,\,4\}$ .

@@ Line 11: / Line 11: @@
 === 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>.
+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 ==
 *[[Cardinality]]
 *[[Set theory]]