The problem with computables is that equivalence between them is only semi-decidable. (If the two numbers are different, it is decidable, but if they are not, it isn't. The problem is that you don't know if they are different a priori, so you might get lucky and find difference, but you might as well not.)

We know for sure that algebraic numbers behave nicely in terms of equivalence, and there are other, bigger number systems that are conjectured to behave nicely ( https://en.wikipedia.org/wiki/Period_(algebraic_geometry) ), but the problem with these and computers is that they are hard to represent.

Yeah, all these types have problems, we've decided to put up with the IEEE floating point numbers, we could have chosen to have the big rationals, or drawn any other line. I don't disagree that there's no satisfying "correct" answer but it's a little disappointing that programmers so easily accept the status quo as though nothing else could be in its place.

Maybe Python having automatic big numbers like Lisps often did will help introduce new programmers to the idea that the 32-bit two's complement integer provided on all modern computers isn't somehow "really" how numbers work.