You can't show me zero of something which is why you can't divide by it. Zero is a placeholder for what we can't show which is also why negative number exist on the opposite side of it. Zero isn't a number, it too is a name.

> You can't show me zero of something which is why you can't divide by it.

I've shown you zero fish. The number of fish I've shown you is zero. If I tracked you down, brought a fish with me and showed it to you, I'd have shown you 1 fish, but I haven't.

I did mention objects, not numbers. Maybe “symbols” representing concepts. I’d go with “name” for both zero and one — nonexistence and existence.