The Cartesian product of set A by set B is the set of all ordered pairs for which the origin is an element of set A and the endpoint is an element in set B.
Symbol
The symbolism “A ☓ B” is read as: “A Cartesian product B”.
- The Cartesian product is not commutative.
- The Cartesian product is also defined by: A ☓ B = {(x, y) | x ∈ A ∧ y ∈ B}.
- The Cartesian product A ☓ A is generally noted as A\(^{2}\) and is called the Cartesian square of A.
Example
Consider the sets A = {a, b, c} and B = {0, 1, 2}.
Therefore: A ☓ B = {(a, 0), (a, 1), (a, 2), (b, 0), (b, 1), (b, 2), (c, 0), (c, 1), (c, 2)}.
If set A includes m elements and set B includes n elements, then the Cartesian product A ☓ B includes m ☓ n elements.