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| − | {{stub}}
| + | *[[Intersection (set theory)]] |
| − | | + | *[[Intersection (geometry)]] |
| − | The '''intersection''' of two or more [[set]]s is the set of [[element]]s which 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>. The intersection of two or more sets 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>.
| + | *[[Intersection theory]] |
| − | | + | {{disambig}} |
| − | For any sets <math>A, B</math>, <math>A \cap B \subset A</math> and <math>A \cap B \subset B</math>. Thus <math>A \cap B = A</math> if and only if <math>A \subset B</math>.
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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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Latest revision as of 17:58, 28 December 2024
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