Difference between revisions of "Difference of two sets"
From Encyclopedia of Mathematics
(TeX) |
(mention Relative complement, cite Halmos) |
||
| Line 1: | Line 1: | ||
{{TEX|done}} | {{TEX|done}} | ||
| + | |||
An operation on sets. Let $A$ and $B$ be two sets (where the second need not be contained in the first). Then the set of those elements of $A$ that are not elements of $B$ is called the difference of these sets. | An operation on sets. Let $A$ and $B$ be two sets (where the second need not be contained in the first). Then the set of those elements of $A$ that are not elements of $B$ is called the difference of these sets. | ||
| Line 7: | Line 8: | ||
====Comments==== | ====Comments==== | ||
| − | See also [[Symmetric difference of sets | + | When $B$ is a subset of $A$, the difference is often termed the ''complement'' or ''[[relative complement]]'' of $B$ in $A$. |
| + | |||
| + | See also [[Symmetric difference of sets]]. | ||
| + | |||
| + | ====References==== | ||
| + | <table> | ||
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> P. R. Halmos, ''Naive Set Theory'', Springer (1960) ISBN 0-387-90092-6</TD></TR> | ||
| + | </table> | ||
Revision as of 08:21, 29 December 2015
An operation on sets. Let $A$ and $B$ be two sets (where the second need not be contained in the first). Then the set of those elements of $A$ that are not elements of $B$ is called the difference of these sets.
The difference between two sets $A$ and $B$ is denoted by $A\setminus B$.
Comments
When $B$ is a subset of $A$, the difference is often termed the complement or relative complement of $B$ in $A$.
See also Symmetric difference of sets.
References
| [a1] | P. R. Halmos, Naive Set Theory, Springer (1960) ISBN 0-387-90092-6 |
How to Cite This Entry:
Difference of two sets. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Difference_of_two_sets&oldid=31399
Difference of two sets. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Difference_of_two_sets&oldid=31399
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article