In any case, zero is a different animal than any other number. It can't actually exist in the physical world like other numbers; it's definition is non-existenc

In any case, zero is a different animal than any other number. It can't actually exist in the physical world like other numbers; it's definition is non-existence. Zero is merely conceptual. Therefore, it can't easily fit into the picture of mathematics; at least not without requiring the definition of special cases.