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| − | The '''intersection''' of two or more [[set]]s is the set of [[element]]s that are common to all of them. Thus, the intersection of the sets <math>\{1, 2, 3\}</math> and <math>\{1, 3, 5\}</math> is the set <math>\{1, 3\}</math>.
| + | *[[Intersection (set theory)]] |
| − | | + | *[[Intersection (geometry)]] |
| − | Intersection is denoted by the symbol <math>\cap</math>, so the preceding example could be written <math>\{1, 2, 3\} \cap \{1, 3, 5\} = \{1, 3\}</math>. One can also use the symbol for intersection in the way one uses a capital sigma (<math>\Sigma</math>) for sums, i.e. <math>\bigcap_{i = 1}^n A_i = A_1 \cap A_2 \cap \ldots \cap A_n</math> is the intersection of the <math>n</math> sets <math>A_1, A_2, \ldots, A_n</math>. | + | {{disambig}} |
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| − | ==Properties==
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| − | *For any sets <math>A, B</math>, <math>A \cap B \subseteq A</math> and <math>A \cap B \subseteq B</math>. Thus <math>A \cap B = A</math> if and only if <math>A \subseteq B</math>.
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| − | ==Geometric Definition==
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| − | In [[geometry]], a [[line]] may be considered to be a set of [[point]]s with a particular property (the property of being on that line). Then the intersection of two lines reduces to the set definition of intersection. This also extends to other curves and surfaces.
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| − | Especially in the geometric context, two objects are said to ''intersect'' if their intersection is non-[[empty set | empty]].
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| − | == See also ==
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| − | * [[Subset]] | |
| − | * [[Union]]
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| − | {{stub}} | |
Revision as of 17:55, 28 December 2024
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