There are multiple proofs for this, but my favorite simple, yet informal proof, is that there is no real number you can add to 0.999 infinitely repeating to make it 1. So mathematically, they are equal.
If spheres have theoretically zero contact area, and they stack in a tube, is there zero contact area between the spheres?
We say that the limits of 1/x and 2/x are equal, but they have different slopes approaching said asymptotic limit