Let be irrational. For each positive integer there is a least integer such that , and then this number is rational. You need to prove that this sequence tends to . Now let be rational, and repeat the above argument with something like instead of . [You'll also need to prove that is irrational whenever , and cook up a way of avoiding having in the sequence.] Edit: Or consider or something like that, as Cameron Buie suggests in the comments. The moral of the story is that and are dense in .