There is a fundamental difference between conventions of notation, and properties of the thing being notated, in this case arithmetic. I'm frankly surprised tha

There is a fundamental difference between conventions of notation, and properties of the thing being notated, in this case arithmetic. I'm frankly surprised that someone with a mathematical background keeps mixing up the two. There are a dozen people in this thread of comments posting different notations - prefix, postfix, what have you. Do you think these define a different arithmetic? Now of course it's stupid to ask people a question without defining what you mean by your notation - you might as well mumble something and expect them to decipher it. But that is in no way equivalent to asking a question which is undecidable in mathematical logic (which is not necessarily a stupid thing to do). And features of some particular notation do not in any way, shape, or form, or by any stretch of semantics, constitute axioms, or properties, or anything else which belongs to arithmetic itself. Do you really disagree with that?