> Give x < y, it's easy to construct x + (y-x)(sqrt(2))/2. That's only obviously irrational if x and y are rational. (But maybe you meant that, given an arbitr

> Give x < y, it's easy to construct x + (y-x)(sqrt(2))/2. That's only obviously irrational if x and y are rational. (But maybe you meant that, given an arbitrary interval a < b, you first shrink it to a rational interval a < x < y < b?)