Technically you can't compare two countable sets using the Lebesgue measure, because they will both have measure 0.
EDIT: You could instead say something like 'the useful reals are an infinite-degree field extension of the rationals'. (Although as I mentioned elsewhere it's actually impossible to define the useful reals.)
EDIT: You could instead say something like 'the useful reals are an infinite-degree field extension of the rationals'. (Although as I mentioned elsewhere it's actually impossible to define the useful reals.)