Cartesian product

(Redirected from Product set)

The Cartesian product of two sets $A$ and $B$ is the set of all ordered pairs $(a,b)$ such that $a$ is an element of $A$ and $b$ is an element of $B$. More generally, the Cartesian product of an ordered family of sets $A_1, A_2, \dotsc$ is the set $A_1 \times A_2 \times \dotsb$ of ordered tuples $(a_1, a_2, \dotsb)$ such that $a_j$ is an element of $A_j$, for any positive integer $j$ for which we have specified a set $A_j$.

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