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Difference between revisions of "Intersection of sets"

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One of the basic operations on sets. Suppose one has a finite or infinite collection of sets <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052030/i0520301.png" /> (the subscript <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052030/i0520302.png" /> serves to distinguish the elements of the given collection). Then the set of those elements that are contained in all these sets (the set of elements common to all <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052030/i0520303.png" />) is called the intersection of these sets.
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One of the basic operations on sets. Suppose one has a finite or infinite collection of sets $\{A_\alpha\}$ (the subscript $\alpha$ serves to distinguish the elements of the given collection). Then the set of those elements that are contained in all these sets (the set of elements common to all $A_\alpha$) is called the intersection of these sets.
  
The intersection of these sets is denoted by <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/i/i052/i052030/i0520304.png" />.
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The intersection of these sets is denoted by $\bigcap A_\alpha$.
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[[Category:Set theory]]

Latest revision as of 19:46, 8 November 2014

One of the basic operations on sets. Suppose one has a finite or infinite collection of sets $\{A_\alpha\}$ (the subscript $\alpha$ serves to distinguish the elements of the given collection). Then the set of those elements that are contained in all these sets (the set of elements common to all $A_\alpha$) is called the intersection of these sets.

The intersection of these sets is denoted by $\bigcap A_\alpha$.

How to Cite This Entry:
Intersection of sets. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Intersection_of_sets&oldid=16440
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article