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About: Intersection

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In mathematics, the intersection of two or more objects is another object consisting of everything that is contained in all of the objects simultaneously. For example, in Euclidean geometry, when two lines in a plane are not parallel, their intersection is the point at which they meet. More generally, in set theory, the intersection of sets is defined to be the set of elements which belong to all of them. Unlike the Euclidean definition, this does not presume that the objects under consideration lie in a common space.

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  • In mathematics, the intersection of two or more objects is another object consisting of everything that is contained in all of the objects simultaneously. For example, in Euclidean geometry, when two lines in a plane are not parallel, their intersection is the point at which they meet. More generally, in set theory, the intersection of sets is defined to be the set of elements which belong to all of them. Unlike the Euclidean definition, this does not presume that the objects under consideration lie in a common space. Intersection is one of the basic concepts of geometry. An intersection can have various geometric shapes, but a point is the most common in a plane geometry. Incidence geometry defines an intersection (usually, of flats) as an object of lower dimension that is incident to each of original objects. In this approach an intersection can be sometimes undefined, such as for parallel lines. In both cases the concept of intersection relies on logical conjunction. Algebraic geometry defines intersections in its own way with intersection theory. (en)
  • 교점(交點)은 수학에서 둘 이상의 물체가 동시에 포함되는 점이다. 유클리드 기하학에서는 평면 내 두 직선이 평행하지 않을 때 이들이 만나는 점을 교점으로 부른다. 집합론에서는 이 둘 모두에 속하는 원소 집합으로 정의된다. (ko)
  • 交点是指线与线、线与面相交的点。在幾何學上（准确地说在欧几里德空间中），兩條直線如非平行，必存在交點。引申下去，一切事物相交接的時間或空間乃至對應的集合交集之元素，都可被稱為交點。 (zh)
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  • 교점(交點)은 수학에서 둘 이상의 물체가 동시에 포함되는 점이다. 유클리드 기하학에서는 평면 내 두 직선이 평행하지 않을 때 이들이 만나는 점을 교점으로 부른다. 집합론에서는 이 둘 모두에 속하는 원소 집합으로 정의된다. (ko)
  • 交点是指线与线、线与面相交的点。在幾何學上（准确地说在欧几里德空间中），兩條直線如非平行，必存在交點。引申下去，一切事物相交接的時間或空間乃至對應的集合交集之元素，都可被稱為交點。 (zh)
  • In mathematics, the intersection of two or more objects is another object consisting of everything that is contained in all of the objects simultaneously. For example, in Euclidean geometry, when two lines in a plane are not parallel, their intersection is the point at which they meet. More generally, in set theory, the intersection of sets is defined to be the set of elements which belong to all of them. Unlike the Euclidean definition, this does not presume that the objects under consideration lie in a common space. (en)
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  • Intersection (en)
  • 교점 (ko)
  • 交點 (zh)
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