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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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1190:(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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163:(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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693:{\displaystyle B=\{x:{\text{ x is an integer divisible by 3}}\}}
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Calcolo geometrico secondo l'Ausdehnungslehre di H. Grassmann
926:. In general the determination of an intersection leads to
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616:. A more elaborate example (involving infinite sets) is:
467:{\displaystyle A\cap B=\{x:x\in A{\text{ and }}x\in B\}}
211:, the intersection of sets is defined to be the set of
652:{\displaystyle A=\{x:{\text{ x is an even integer}}\}}
258:. In both cases the concept of intersection relies on
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71:. Unsourced material may be challenged and removed.
1002: with: history of the symbol. You can help by
881:). Other types of geometric intersection include:
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1210:Earliest Uses of Symbols of Set Theory and Logic
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914:– linear geometric objects embedded in a higher-
946:(sphere, cylinder, hyperboloid, etc.) lead to
938:. Intersection problems between a line and a
222:Intersection is one of the basic concepts of
789:contained in the intersection of the set of
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203:are not parallel, their intersection is the
1078:Dimensionally Extended 9-Intersection Model
312:. Unsourced material may be challenged and
1058:of more than two classes in his 1908 book
771:{\displaystyle A\cap B=\{6,12,18,\dots \}}
266:defines intersections in its own way with
1047:(1858–1932) for intersection, in 1888 in
395:is the set of elements which are in both
332:Learn how and when to remove this message
131:Learn how and when to remove this message
896:Intersection of a polyhedron with a line
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942:(circle, ellipse, parabola, etc.) or a
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910:Determination of the intersection of
242:defines an intersection (usually, of
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684: x is an integer divisible by 3
310:adding citations to reliable sources
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69:adding citations to reliable sources
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1162:A History of Mathematical Notations
226:. An intersection can have various
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831:This section is an excerpt from
714:{\displaystyle {\text{ , then}}}
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967:Intersection is denoted by the
822:is the only even prime number.
781:As another example, the number
56:needs additional citations for
1202:
1188:Formulario mathematico, tomo V
1186:Peano, Giuseppe (1908-01-01).
1159:Cajori, Florian (2007-01-01).
1138:Peano, Giuseppe (1888-01-01).
982:Unicode Mathematical Operators
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1:
1117:. American Mathematical Soc.
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1041:Die Ausdehnungslehre von 1844
609:{\displaystyle A\cap B=\{1\}}
571:{\displaystyle B=\{1,2,4,6\}}
521:{\displaystyle A=\{1,3,5,7\}}
383:The intersection of two sets
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36:Intersection (disambiguation)
918:space – is a simple task of
355:several intersection objects
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1072:Constructive solid geometry
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1088:Intersection (set theory)
901:Line segment intersection
801:{2, 4, 6, 8, 10, …}
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379:Intersection (set theory)
353:, possibly empty), or as
891:Line–sphere intersection
246:) as an object of lower
234:is the most common in a
1165:. Torino: Cosimo, Inc.
886:Line–plane intersection
833:Intersection (geometry)
159:(black) intersects the
1144:(in Italian). Torino:
1060:Formulario mathematico
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861:line–line intersection
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810:a prime number, it is
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948:quadratic equations
803:, because although
268:intersection theory
260:logical conjunction
32:Intersection (road)
1227:Weisstein, Eric W.
1093:Union (set theory)
1035:was first used by
932:solved numerically
906:Intersection curve
857:Euclidean geometry
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407:. Formally,
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365:In set theory
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359:possibly zero
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349:results in a
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291:This section
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54:This article
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1254:Intersection
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1033:INTERSECTION
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798:even numbers
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304:Please help
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189:intersection
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165:line segment
127:
121:January 2014
118:
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63:Please help
58:verification
55:
18:Intersecting
1022:The symbol
916:dimensional
826:In geometry
195:, when two
185:mathematics
1099:References
274:Uniqueness
209:set theory
91:newspapers
1235:MathWorld
763:…
733:∩
589:∩
456:∈
442:∈
421:∩
347:operation
322:June 2023
293:does not
248:dimension
177:empty set
1248:Category
1196:23485397
1066:See also
1030:∩
975:∩
963:Notation
879:parallel
849:geometry
252:incident
250:that is
230:, but a
224:geometry
213:elements
944:quadric
859:is the
578:, then
314:removed
299:sources
105:scholar
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1025:U+2229
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970:U+2229
874:vertex
187:, the
157:circle
107:
100:
93:
86:
78:
1056:union
980:from
912:flats
869:point
865:lines
851:, an
244:flats
232:point
217:space
205:point
201:plane
199:in a
197:lines
112:JSTOR
98:books
1192:OCLC
1167:ISBN
1119:ISBN
528:and
401:and
389:and
297:any
295:cite
161:line
155:The
84:news
1039:in
1006:.
847:In
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787:not
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351:set
308:by
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730:A
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329:(
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320:(
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119:(
109:·
102:·
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38:.
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