Intersection [list1,list2,…]
gives a sorted list of the elements common to all the listi.
Intersection
Intersection [list1,list2,…]
gives a sorted list of the elements common to all the listi.
Details and Options
- If the listi are considered as sets, Intersection gives their intersection.
- Intersection [list1,list2,…] can be input in StandardForm and InputForm as list1⋂list2⋂…. The character ⋂ can be entered as inter or \[Intersection] .
- The listi must have the same head, but it need not be List .
- Intersection [list1,…,SameTest->test] applies test to each pair of elements in the listi to determine whether they should be considered the same.
- Intersection [a,b] can be entered in StandardForm and InputForm as a⋂b or a \[Intersection] b .
Examples
open all close allBasic Examples (2)
Find elements common to all the lists given:
Enter using inter:
Generalizations & Extensions (1)
Intersection works with any head, not just List :
Options (3)
Applications (1)
Find divisors common to 45 and 78:
Properties & Relations (1)
If there is no intersection, the result is {}:
See Also
Union Complement SymmetricDifference UniqueElements And BitAnd SequenceAlignment IntersectingQ DisjointQ ContainsAny ContainsNone
Characters: \[Intersection]
Function Repository: StringIntersection VennGraphPlot
Tech Notes
History
Introduced in 1988 (1.0) | Updated in 1996 (3.0)
Text
Wolfram Research (1988), Intersection, Wolfram Language function, https://reference.wolfram.com/language/ref/Intersection.html (updated 1996).
CMS
Wolfram Language. 1988. "Intersection." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/Intersection.html.
APA
Wolfram Language. (1988). Intersection. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Intersection.html
BibTeX
@misc{reference.wolfram_2025_intersection, author="Wolfram Research", title="{Intersection}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/Intersection.html}", note=[Accessed: 16-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_intersection, organization={Wolfram Research}, title={Intersection}, year={1996}, url={https://reference.wolfram.com/language/ref/Intersection.html}, note=[Accessed: 16-November-2025]}