Density has to do with the order structure of Q and R. If r and q are real numbers such that r q, then there exists a rational number j such that r j q. Actually, it seems clear to me that there exist "infinitely many" rationals between any two reals. We can just take (r*+q*)/2, where r* and q* indicate rationals such that r r* q* q. I've digressed, but this should make it clear that the density property concerns the ordering of the rationals and reals which talks about how the rationals and reals relate to other rationals and reals. In other words, the order property concerns elements of the sets. Countability and un-countability concern the entire sets themselves, not relations between their elements.