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Intersection

Intersection

Intersection[list₁,list₂,…]

gives a sorted list of the elements common to all the list_i.

Details and Options

If the list_i 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 list_i must have the same head, but it need not be List.
Intersection[list₁,…,SameTest->test] applies test to each pair of elements in the list_i 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

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Basic 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)

SameTest (3)

Use equivalence classes based on absolute value:

Use equivalence classes based on Floor:

Use Total of list elements:

Applications (1)

Find divisors common to 45 and 78:

Properties & Relations (1)

If there is no intersection, the result is {}:

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