are we finished with f(a).b and when a is odd f(a)=-(a+1)/2 and when a is even f(a)=a/2 ?
Thanks emakarov - I didn't remember which direction was technically called the pairing function.
gutnedawg, you essentially got my idea right. The bijection is given by where is the function you described and , where is the pairing function.
(Here is the set of rational numbers with terminating decimal expansions.)