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There can be more than one primitive object, such as points (pictured above), that form an intersection. The intersection can be viewed collectively as all of the shared objects (i.e., the intersection
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Considering a road to correspond to the set of all its locations, a road intersection (cyan) of two roads (green, blue) corresponds to the intersection of their sets.
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of two or more objects is another object consisting of everything that is contained in all of the objects simultaneously. For example, in
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which belong to all of them. Unlike the
Euclidean definition, this does not presume that the objects under consideration lie in a common
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is the only number in the intersection of these two sets. In this case, the intersection has mathematical meaning: the number
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is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in
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Calcolo geometrico secondo l'Ausdehnungslehre di H. Grassmann: preceduto dalle operazioni della logica deduttiva
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The intersection of D and E is shown in grayish purple. The intersection of A with any of B, C, D, or E is the
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to each of original objects. In this approach an intersection can be sometimes undefined, such as for
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as general operation symbol, not specialized for intersection. From there, it was used by
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1179:(in Italian). Torino: Edizione cremonese (Facsimile-Reprint at Rome, 1960). p. 82.
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This article is about a broad mathematical concept. For the point where roads meet, see
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152:(purple) in two points (red). The disk (yellow) intersects the line in the
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The intersection (red) of two disks (white and red with black boundaries).
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Peano also created the large symbols for general intersection and
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that can be easily solved. Intersections between quadrics lead to
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The red dot represents the point at which the two lines intersect.
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682:{\displaystyle B=\{x:{\text{ x is an integer divisible by 3}}\}}
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Calcolo geometrico secondo l'Ausdehnungslehre di H. Grassmann
915:. In general the determination of an intersection leads to
132:
605:. A more elaborate example (involving infinite sets) is:
456:{\displaystyle A\cap B=\{x:x\in A{\text{ and }}x\in B\}}
200:, the intersection of sets is defined to be the set of
641:{\displaystyle A=\{x:{\text{ x is an even integer}}\}}
247:. In both cases the concept of intersection relies on
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60:. Unsourced material may be challenged and removed.
991: with: history of the symbol. You can help by
870:). Other types of geometric intersection include:
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1199:Earliest Uses of Symbols of Set Theory and Logic
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903:– linear geometric objects embedded in a higher-
935:(sphere, cylinder, hyperboloid, etc.) lead to
927:. Intersection problems between a line and a
211:Intersection is one of the basic concepts of
778:contained in the intersection of the set of
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192:are not parallel, their intersection is the
1067:Dimensionally Extended 9-Intersection Model
301:. Unsourced material may be challenged and
1047:of more than two classes in his 1908 book
760:{\displaystyle A\cap B=\{6,12,18,\dots \}}
255:defines intersections in its own way with
1036:(1858–1932) for intersection, in 1888 in
384:is the set of elements which are in both
321:Learn how and when to remove this message
120:Learn how and when to remove this message
885:Intersection of a polyhedron with a line
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931:(circle, ellipse, parabola, etc.) or a
196:at which they meet. More generally, in
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866:) or does not exist (if the lines are
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899:Determination of the intersection of
231:defines an intersection (usually, of
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673: x is an integer divisible by 3
299:adding citations to reliable sources
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58:adding citations to reliable sources
29:
1151:A History of Mathematical Notations
215:. An intersection can have various
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820:This section is an excerpt from
703:{\displaystyle {\text{ , then}}}
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956:Intersection is denoted by the
811:is the only even prime number.
770:As another example, the number
45:needs additional citations for
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1177:Formulario mathematico, tomo V
1175:Peano, Giuseppe (1908-01-01).
1148:Cajori, Florian (2007-01-01).
1127:Peano, Giuseppe (1888-01-01).
971:Unicode Mathematical Operators
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1:
1106:. American Mathematical Soc.
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1030:Die Ausdehnungslehre von 1844
598:{\displaystyle A\cap B=\{1\}}
560:{\displaystyle B=\{1,2,4,6\}}
510:{\displaystyle A=\{1,3,5,7\}}
372:The intersection of two sets
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25:Intersection (disambiguation)
907:space – is a simple task of
344:several intersection objects
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1061:Constructive solid geometry
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911:, namely the solution of a
156:between the two red points.
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913:system of linear equations
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803:even. In fact, the number
632: x is an even integer
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1077:Intersection (set theory)
890:Line segment intersection
790:{2, 4, 6, 8, 10, …}
783:{2, 3, 5, 7, 11, …}
368:Intersection (set theory)
342:, possibly empty), or as
880:Line–sphere intersection
235:) as an object of lower
223:is the most common in a
1154:. Torino: Cosimo, Inc.
875:Line–plane intersection
822:Intersection (geometry)
148:(black) intersects the
1133:(in Italian). Torino:
1049:Formulario mathematico
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295:improve this section
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943:that can be solved
937:quadratic equations
792:, because although
257:intersection theory
249:logical conjunction
21:Intersection (road)
1216:Weisstein, Eric W.
1082:Union (set theory)
1024:was first used by
921:solved numerically
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396:. Formally,
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354:In set theory
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348:possibly zero
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338:results in a
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280:This section
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43:This article
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1243:Intersection
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1022:INTERSECTION
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1000:January 2014
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993:adding to it
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967:INTERSECTION
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787:even numbers
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293:Please help
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178:intersection
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154:line segment
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110:January 2014
107:
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52:Please help
47:verification
44:
1011:The symbol
905:dimensional
815:In geometry
184:, when two
174:mathematics
1088:References
263:Uniqueness
198:set theory
80:newspapers
1224:MathWorld
752:…
722:∩
578:∩
445:∈
431:∈
410:∩
336:operation
311:June 2023
282:does not
237:dimension
166:empty set
1237:Category
1185:23485397
1055:See also
1019:∩
964:∩
952:Notation
868:parallel
838:geometry
241:incident
239:that is
219:, but a
213:geometry
202:elements
933:quadric
848:is the
567:, then
303:removed
288:sources
94:scholar
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1014:U+2229
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959:U+2229
863:vertex
176:, the
146:circle
96:
89:
82:
75:
67:
1045:union
969:from
901:flats
858:point
854:lines
840:, an
233:flats
221:point
206:space
194:point
190:plane
188:in a
186:lines
101:JSTOR
87:books
1181:OCLC
1156:ISBN
1108:ISBN
517:and
390:and
378:and
286:any
284:cite
150:line
144:The
73:news
1028:in
995:.
836:In
801:not
776:not
774:is
350:).
340:set
297:by
172:In
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1051:.
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973:.
797:is
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740:12
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251:.
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743:,
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719:A
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636:}
628::
625:x
622:{
619:=
616:A
593:}
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546:4
543:,
540:2
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490:3
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309:(
305:.
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117:(
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108:(
98:·
91:·
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27:.
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