Описание тега cartesian-product

The Cartesian product, named after René Descartes, of two sets A and B is the set of all ordered pairs ab, where a is element of A and b is element of B.

The Cartesian product of two or more sets is the Cartesian product of the Cartesian product of n-1 sets with the nth set.

Example:

3 sets: {a,b,c}, {1,2}, {S,T}
Cartesian product: a1S a1T a2S a2T b1S b1T b2S b2T c1S c1T c2S c2T

The Cartesian product of a set and the empty set is the empty set.

The size of the Cartesian product of two sets of size A and B is A*B.

Notation:

 A X B := {(a, b) | a ∈ A, b ∈ B}