we have 2 sets which are subsets of Q, A, where p^2<2 and B where p^2>2. how are the members of B the upper bounds of A? aren't the rationals close to the sqrt(2) the upper bounds of A and not the members of B? I can see that members of A can't be the upper bounds of A because then there would be members of A outside of that upper bound and there is no rational number sqrt(2) so that A has no least upper bound in Q?