Definition b. Let \(A_1, \ldots, A_n\)A 1, , A n be sets. Then the Cartesian product \(A_1 \times \cdots \times A_n\)A 1 A n is the set of all ordered \(n\)n-tuples \(\left( a_1, \ldots, a_n \right)\) such that \(a_i \in A_i\)a i A i for \(1 \leq i \leq n\)1 i n.