[tsimionescu]

Even if accuracy is finite, the fact that, for example, circles aren't polygons is definitely relevant to physics. You might be able to get all of the relevant physics you need without the continuum by working with several disjoint sets of numbers (the rationals, the rationals-multiplied-by-pi, the rationals-multiplied-by-e, etc) but I'm not even sure of that.

[rbanffy]

If you look close enough, from the physics point of view, all circles are polygons, and, also, they aren’t really flat.

Zeroes and infinities are problematic in physics. Physics and math aren’t the same discipline, and it’s dangerous to conflate them.

I’m pretty sure there will be a point where you’ll have a light-emitting superconductor on your way to an infinite current.