On the other hand, it is interesting to think about the fact that, say, the Avogadro number is usually represented as a real number; the problem with the number

On the other hand, it is interesting to think about the fact that, say, the Avogadro number is usually represented as a real number; the problem with the number of protons or other particles is that their number is unbounded: given enough energy, another particle can always jump into existence...