Discrete Mathematics with Applications (Epp) p.12
See also Mathematical sets and Ordered n-tuples
The Cartesian product of sets \(A_1, A_2..., A_n\) is the set of all ordered n-tuples \((a_1, a_2..., a_n)\) where \(a_1 \in A_1\), \(a_2 \in A_2\)…, \(a_n \in A_n\).
Symbolically:
$$A_1 \times A_2 \times ... \times A_n = \{(a_1, a_2..., a_n) | a_1 \in A_1, a_2 \in A_2..., a_3 \in A_3 \}$$
Therefore:
$$A_1 \times A_2 = \{(a_1, a_2) | a_1 \in A_1 \text{ and } a_2 \in A_2\}$$
Is the cartesian product of \(A_1\) and \(A_2\).