A symbol being arbitrary doesn't influence the reality of the meaning behind a thing. I've always thought about `zero` while counting, it never was about `0`.

I observe zero.

I don't think zero is an absence of quantity. I don't think zero is the null set.

You can write types in a programming language, but there are other type theory books that do include zero in the natural numbers. And type theory comes from number/set theory. So it's ok if you decide to exclude it, but this is just as arbitrary.

In fact I'd be happy to write `>=0` or `>0` or `=0` any day instead of mangling the idea of zero representing 0 and zero representing something like `None`, `null` or any other tag of that sort. I don't think the natural world has anything like "nothing" it just has logical fallacies.