Actually, digital computers can compute over the real numbers. They can compute quite a lot over the real numbers, even. See https://en.wikipedia.org/wiki/Compu

Actually, digital computers can compute over the real numbers. They can compute quite a lot over the real numbers, even. See https://en.wikipedia.org/wiki/Computable_analysis#Basic_results https://en.wikipedia.org/wiki/Computable_analysis#Basic_resu... This even has some concrete applications. See this: https://icfp19.sigplan.org/details/icfp-2019-papers/15/Sound-and-robust-solid-modeling-via-exact-real-arithmetic-and-continuity https://icfp19.sigplan.org/details/icfp-2019-papers/15/Sound... Finally, saying that digital computers can't compute functions of the form Real -> Real is like saying that a computer can't compute functions of the form (Int -> Int) -> (Int -> Int). In other words, it's like saying that higher order functions are impossible.