>>11331885Assume is rational.
Then, for some we have , as you well know.
So for any set with , we have that satisfies and .
If is irrational, we consider some with . Then, unless I'm going clinically insane, , the closure of U, has nonempty interior, and .
Finally, because it's dense, and thus , and since , which gives
I'm sorry if there are any mistakes, it's two in the morning.