[Harmattan]

So dt cannot be a real number? Interesting. Fine. Yet it works. So it's just that mathematics cannot explain why. By the way, I see the infinite appearing here and there under mathematicians' pens even though it is not a real either.

See? I have no problem going there. Physics is right: there are only real numbers. And nature does not use infinitesimal numbers actually, see Heisenberg. Physicists only use them to model and calculate derivatives.

Huh, suddenly I wonder if derivatives in nature are conform to the analytical results or rather to numerical approximations with a granularity tied to Heisenberg's constants. I bet for the latter.

[Besoeker]

There are obviously no "infinitesimal real numbers". For instance, there is no positive real number x such that x < 1/n for all positive integers n.

But we don't deal with just integers in real life.