Definition 5.18 (Cartesian Product)

#Definition

The $Cartesian Product$ of the 5.1 Sets $A_{1}, A_{2} \dots, A_{n}$ is denoted by
$A_{1} \times A_{2} \times \dots \times A_{n}$
and is the set of ordered $n$ -tuples $(a_{1}, a_{2}, \dots, a_{n})$ , where $a_{i}$ belongs to $A_{i}$ for $i = 1, 2, \dots, n$

A_{1} \times A_{2} \times \dots \times A_{n} : = {(a_{1}, a_{2}, \dots, a_{n}) | a_{1} \in A_{1}, \dots, a_{n} \in A_{n}}