High Quality Content by WIKIPEDIA articles! In mathematics, a Cartesian product (or product set) is the direct product of two sets. The Cartesian product is named after Rene Descartes,[1] whose formulation of analytic geometry gave rise to this concept.For example, the Cartesian product of the 13-element set of standard playing card ranks {Ace, King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2} and the four-element set of card suits {?, ?, ?, ?} is the 52-element set of all possible playing cards: ranks x suits = {(Ace, ?), (King, ?), ..., (2, ?), (Ace, ?), ..., (3, ?), (2, ?)}. The corresponding Cartesian product has 52 = 13 x 4 elements. The Cartesian product of the suits x ranks would still be the 52 pairings, but in the opposite order {(?, Ace), (?, King), ...}. Ordered pairs (a kind of tuple) have order, but sets are unordered. The order in which the elements of a set are listed is irrelevant; you can shuffle the deck and it's still the same set of cards.

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