Rationals are a strict subset of the reals. There are also the irrationals, and most of those cannot even be expressed (fortunately, since they cannot be expre

Rationals are a strict subset of the reals. There are also the irrationals, and most of those cannot even be expressed (fortunately, since they cannot be expressed, there's no chance of you bumping into them by accident - so it's somewhat of a moot point). The subset that you want to aim for is not the rationals, but the definable reals: https://en.wikipedia.org/wiki/Definable_real_number https://en.wikipedia.org/wiki/Definable_real_number.