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==Origin==
==Origin==
[[Latin]] ''intersectiōn-em'' ([http://en.wikipedia.org/wiki/Vitruvius Vitruvius]), n. of [[action]] from ''intersecāre''
[[Latin]] ''intersectiōn-em'' ([https://en.wikipedia.org/wiki/Vitruvius Vitruvius]), n. of [[action]] from ''intersecāre''
*[http://en.wikipedia.org/wiki/16th_century 1559]
*[https://en.wikipedia.org/wiki/16th_century 1559]
==Definitions==
==Definitions==
*1: The [[action]] or [[fact]] of intersecting or crossing
*1: The [[action]] or [[fact]] of intersecting or crossing
:b. [[Geometry]], the [[point]] (or [[line]]) of intersection; the point common to two lines or a line and a [[surface]] (or the line common to two surfaces) which intersect.
:b. [[Geometry]], the [[point]] (or [[line]]) of intersection; the point common to two lines or a line and a [[surface]] (or the line common to two surfaces) which intersect.
*3:a. [[Logic]]. The [[relation]] of two classes that intersect, i.e. each of which partly includes and partly excludes the other.
*3:a. [[Logic]]. The [[relation]] of two classes that intersect, i.e. each of which partly includes and partly excludes the other.
:b. Logic and [[Mathematics]]. The [http://en.wikipedia.org/wiki/Set set] which comprises all the elements common to [[two]] or more given sets, and no others; also, the operation of forming such a set.
:b. Logic and [[Mathematics]]. The [https://en.wikipedia.org/wiki/Set set] which comprises all the elements common to [[two]] or more given sets, and no others; also, the operation of forming such a set.
==Description==
==Description==
In [[mathematics]], the intersection (denoted as ∩) of two sets A and B is the set that contains all [[elements]] of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.
In [[mathematics]], the intersection (denoted as ∩) of two sets A and B is the set that contains all [[elements]] of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.
The intersection of the sets {1, 2, 3} and {2, 3, 4} is {2, 3}.
The intersection of the sets {1, 2, 3} and {2, 3, 4} is {2, 3}.
The [[number]] [[9]] is not in the intersection of the set of [http://en.wikipedia.org/wiki/Prime_number prime numbers] {2, 3, 5, 7, 11, …} and the set of [http://en.wikipedia.org/wiki/Odd_numbers odd numbers] {1, 3, 5, 7, 9, 11, …}.
The [[number]] [[9]] is not in the intersection of the set of [https://en.wikipedia.org/wiki/Prime_number prime numbers] {2, 3, 5, 7, 11, …} and the set of [https://en.wikipedia.org/wiki/Odd_numbers odd numbers] {1, 3, 5, 7, 9, 11, …}.
If the intersection of two sets A and B is empty, that is they have no elements in common, then they are said to be disjoint, denoted: A ∩ B = ∅. For example the sets {1, 2} and {3, 4} are disjoint, written {1, 2} ∩ {3, 4} = ∅.
If the intersection of two sets A and B is empty, that is they have no elements in common, then they are said to be disjoint, denoted: A ∩ B = ∅. For example the sets {1, 2} and {3, 4} are disjoint, written {1, 2} ∩ {3, 4} = ∅.
More generally, one can take the intersection of several sets at once. The intersection of A, B, C, and D, for example, is A ∩ B ∩ C ∩ D = A ∩ (B ∩ (C ∩ D)). Intersection is an associative operation; thus, A ∩ (B ∩ C) = (A ∩ B) ∩ C.
More generally, one can take the intersection of several sets at once. The intersection of A, B, C, and D, for example, is A ∩ B ∩ C ∩ D = A ∩ (B ∩ (C ∩ D)). Intersection is an associative operation; thus, A ∩ (B ∩ C) = (A ∩ B) ∩ C.
If the sets A and B are closed under complement then the intersection of A and B may be written as the complement of the union of their complements, derived easily from [http://en.wikipedia.org/wiki/De_Morgan%27s_laws De Morgan's laws]: A ∩ B = (Ac ∪ Bc)c[http://en.wikipedia.org/wiki/Intersection_%28set_theory%29]
If the sets A and B are closed under complement then the intersection of A and B may be written as the complement of the union of their complements, derived easily from [https://en.wikipedia.org/wiki/De_Morgan%27s_laws De Morgan's laws]: A ∩ B = (Ac ∪ Bc)c[https://en.wikipedia.org/wiki/Intersection_%28set_theory%29]
[[Category: Mathematics]]
[[Category: Mathematics]]
