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Difference between revisions of "Difference of two sets"

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An operation on sets. Let <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031700/d0317001.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031700/d0317002.png" /> be two sets (where the second need not be contained in the first). Then the set of those elements of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031700/d0317003.png" /> that are not elements of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031700/d0317004.png" /> is called the difference of these sets.
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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.
  
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The difference between two sets <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031700/d0317005.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031700/d0317006.png" /> is denoted by <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031700/d0317007.png" />.
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The difference between two sets $A$ and $B$ is denoted by $A\setminus B$.
  
  
  
 
====Comments====
 
====Comments====
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See also [[Symmetric difference of sets|Symmetric difference of sets]].
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When $B$ is a subset of $A$, the difference is often termed the ''complement'' or ''[[relative complement]]'' of $B$ in $A$.
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See also [[Symmetric difference of sets]].
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====References====
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<table>
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<TR><TD valign="top">[a1]</TD> <TD valign="top">  P. R. Halmos, ''Naive Set Theory'', Springer (1960) {{ISBN|0-387-90092-6}}</TD></TR>
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</table>

Latest revision as of 05:43, 22 April 2023

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=13938
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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