> But at the lowest level, isn’t everything (time, space, energy etc) basically discrete, so the reals aren’t really real? That literally doesn't matter one wa

> But at the lowest level, isn’t everything (time, space, energy etc) basically discrete, so the reals aren’t really real? That literally doesn't matter one way or the other in the slightest, for two huge reasons: 1. No mathematics is exactly the same as reality itself, and cannot be, even in principle. Mathematics can be used to useful model certain limited aspects of reality, but of course models aren't the same as reality. 2. The mathematics of the reals and of continuity in general are essential for a vast number of kinds of practical computation that sometimes (not always!) turn out to be vastly harder to do without the assumption of continuity. We often want to bring to bear the whole apparatus of established mathematics to solve problems in order to get answers, and no one trying to get answers cares whether the mathematics used is "real", only whether the final answers are useful (accurate etc). Actually there's a third reason that is even more important to some people: this is usually merely about word definitions. Words like "real" and "exist" have sharply defined unambiguous technical definitions in mathematics that are only indirectly related to the loosely defined vague non-technical definitions of the same words that we use in natural languages like English. It is ultimately irrelevant whether e.g. the real numbers "exist" in the physical universe, because whether they do or not, they provably exist in (most) formal mathematics -- the word "exist" does not have the same meaning in the two realms. It's still interesting to ask whether the physical universe has reals or continuity or infinities or infinitesimals etc., it just shouldn't be confused with the issue of their technical existence (or "reality") in mathematics.