That is my point Halls. Numbers NEED units. The additive identity is a "property of zero". Not a description of what zero is.
If I asked you what a car was. You were to tell me "it gets you from (a) to (b)". You would be correct. Yet so to horses, bicycles, and scooters do the same thing. You cannot describe a "thing" by telling me what that thing does.
Also the "unit" applied to zero is not the same as a unit for concrete numbers. It is an abstract unit, not a concrete unit, and it is used differently.
