James Propp <jamespropp@gmail.com> wrote:

(a) the blue points form a multiplicative group (the 2-adic units in the rationals, aka rational numbers of the form a/b where a and b are odd integers)

Right. Also just the positive blue numbers, as there's no way to get a negative by multiplying or dividing positives.

and (b) the blue and red points together form an additive group (rational numbers of the form a/b where b is odd).

Right. Also just the red numbers, as there's no way to get a blue number (odd/odd) by adding or subtracting red numbers (even/odd).