Is the definition correct? I'm writing a B.Sc. thesis in computer science and needed to include the definition of Cartesian product. I wrote it according to the following and wonder if it is correct:

Cartesian product - The set of all possible permutations of two other
  sets.

It sounds too simple and I didn't find it written exactly like that but when I look at definitions it seems to be the above meaning. Or did I misunderstand?
If A and B are two sets then the Cartesian product is the set of points $\big\{\{a1,b1\},\{a2,b2\},\dots\big\}$ excluding the points $\{b1,a1\}$ etc. 
Did I understand correctly?

remark
$$\{a,b\}=\{b,a\} $$
but
$$(a,b)\neq (b,a) $$
$$A\times B=\{(a,b)\;:\; a\in A , b\in B\} $$
