Well, it's easy to find the equivalence classes.

Start with, say, (1, 1).

For another point (x, y) to be equivalent to this we require that 1 + y = 1 + x. So solve this for y and you get the equation y = x. Thus all the points in A X A that are equivalent to (1, 1) are in the form (a, a), where .

Now pick the point (2, 1), etc.

-Dan