Cartesian Product

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The Cartesian product produces a new set from two or more sets.
In set-builder notation the Cartesian product of A and B is:
    A × B = { (a, b) : a ∈ A, b ∈ B }

Example
For P = {x, y} and Q = {1, 2, 3} the Cartesian product P × Q is:

	{	(x, 1),		(x, 2),		(x, 3),
		(y, 1),		(y, 2),		(y, 3)	}

Note that (x, 1) is an ordered pair so (1, x) is not a member.
However the order of the members in the set is not important.
The set here has been spread over two lines for easier reading.