User:Kiwi Unicycle

In mathematics, the intersection A &cap; B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.

For explanation of the symbols used in this article, refer to the table of mathematical symbols.

Basic definition
, English and Russian alphabet, considering only the shapes of the letters and ignoring their pronunciation]] The intersection of two sets A and B, denoted by $A &cap; B$, is the set of all objects that are members of both the sets $A$ and $B$. In symbols,


 * A \cap B = \{ x: x \in A \text{ and } x \in B\}.

That is, x is an element of the intersection A &cap; B if and only if x is both an element of A and an element of B.

For example:
 * The intersection of the sets {1, 2, 3} and {2, 3, 4} is {2, 3}.
 * The number 9 is in the intersection of the set of prime numbers {2, 3, 5, 7, 11, ...} and the set of odd numbers {1, 3, 5, 7, 9, 11, ...}, because 9 is not prime.

Intersection is an associative operation; that is, for any sets A, B, and C, one has A &cap; (B &cap; C) = (A &cap; B) &cap; C. Intersection is also commutative; for any A and B, one has A &cap; B = B &cap; A. It thus makes sense to talk about in