for cartesian product ordered pair, for example

[itex] A = \{a_1, a_{2}, a_{3}\} \\

B = \{b_{1}, b_{2}, b_{3}\} [/itex]

is the product [itex] A \times B = \{a_{1}b{1}, a_{1}b{2}, a_{1}b{3}, a_{2}b{1}, \\

a_{2}b{2}, a_{2}b{3}, a_{3}b{1}, a_{3}b{2}, a_{3}b{3},\} [/itex] ??

What does [itex] A \times B = \{(a,b)\mid a \in A and b \in B\} [/itex] mean in detail?

thanks.