That famous paradox is interesting, because it shows in its own way that Mathematics can’t always produce for a Physicist a good description of reality.

When in reality the race between Achilles and the Tortoise occurs, physically there is no difficulty and no paradox whatsoever. But when Zeno starts to think about it in his own terms, then he sees infinitely many steps for Achilles. But those infinite steps don’t exist anywhere, except in Zeno’s model.

Simply put, today when we see an infinity appearing in our computations in Physics, we know that something is wrong in the model, so the model has to be dropped. We do that because we know that <<infinity does not exist>>. And to be more accurate on that statement, we can even add “<<infinity does not exist>> as a thing”, but it was implicit.