it's trivial to prove that (1+sqrt(5))/2 isn't covered, for example It could be, depending on how the rationals are enumerated. I think the flaw is that while

it's trivial to prove that (1+sqrt(5))/2 isn't covered, for example It could be, depending on how the rationals are enumerated. I think the flaw is that while it's true that every real is arbitrarily close to an infinite number of rationals, the size of the segment centered of each of those rationals keeps falling, so "most" reals never get reached.