But the infinitesimals invite treating them as "quantities" in an algebraic "game". That's a drill-lesson in abstraction when they're teaching you ( usually pre

But the infinitesimals invite treating them as "quantities" in an algebraic "game". That's a drill-lesson in abstraction when they're teaching you ( usually pre)Calculus, before you learn the dF(x)/dt transforms in derivative and integral tables. They also turn up in engineering contexts, which is pretty cool when it happens - it's not all just slide rule and look-up - you get to play with first principles some times when you're lucky... Wasn't me, but I got to watch. I still suspect the generators are infinite sets in the Cantor sense, just stated more politely. We're more of a habit to think in terms of ... series in that way. I recall being exhilarated by the sheer ... hubris of Cantor's approach. So I am probably biased. And as strange as it may sound, if I use infinite sets to derive the Diagonalization, then use that to assist in Godel's Theorem, it feels less like there's a tangled hierarchy when reasoning about Turing machines. That could easily be an elegance that I'm am stubborn about missing.