> Real numbers are discrete at the infinitesimal limit (grab your torch and pitchforks). I don't even know what that means. If you embed the real numbers in th

> Real numbers are discrete at the infinitesimal limit (grab your torch and pitchforks). I don't even know what that means. If you embed the real numbers in the hyperreals, where you do in fact have "infinitely close" numbers, those numbers aren't discrete either, as the hyperreal numbers are dense too. > Loops roughly = integrals I think this is the wrong way around. Loops loosely correspond to mathematical sums (finite or possibly countably infinite). We got integrals once people started asking themselves "what if you could have something like sums, but over intervals that are arbitrarily/infinitely small?". In that sense, integrals are an extension or generalisation of sums/loops - in the sense that sums are basically integrals with a discrete measure - but you don't need to more complicated, general concept to understand the simpler one. Of course, different areas of maths (and CS is basically a branch of maths) are inter-linked. That's the beauty of maths. Some people will see calculus everywhere, others will immediately see connections to category theory, logic, topology, etc. Maybe in 50 years we will discover a new branch of maths and suddenly see that it can be found everywhere, but that doesn't mean that we needed to know that branch to do all the things we were doing up until that point. But I don't think calculus is as fundamental to CS/programming as it is to, say, physics or much of the rest of the natural sciences. You do mention some examples (optimisation problems), but by and large I don't need to understand limits and Cauchy sequences to program a loop or even to prove statements about push-down automata or graphs or my favourite type system. (You mention topology. Topology is an abstraction over analysis which can be used in discrete settings too, it doesn't fundamentally require the real numbers.)