If by "discrete" you mean rejecting the continuum, then I don't think it's as scary as it sounds. The rationals do not form a continuum, but they are "effectiv

If by "discrete" you mean rejecting the continuum, then I don't think it's as scary as it sounds. The rationals do not form a continuum, but they are "effectively" continuous -- between any two of them there is another. There are no "leaps" between them, and no concept of consecutive numbers. Computable numbers are similarly countable but allow the expression of numbers that can only be approximated by rationals. It's the reals that require "bold" assumptions -- numbers exist which are not possible to compute even approximately?