We know that cartesian product of two sets and is:

and

the integer quotient obtained when is divided by

the integer remainder obtained when is divided by

I'm reading a Discrete math book and I am on Functions chapter. It has a line in it that says:

" and are really functions defined on Cartesian products of integers."

For what reason is this statement true? I know it's true but I've no idea why.

I don't see the connection between Cartesian product and the , functions.

Can anyone kindly tell me when I use and functions how is that they are really functions on Cartesian products of integers?