> That's all very nice, but I prefer Peano's five, relatively succinct axioms as a starting point. You can probably derive some equivalent of all your "axioms" from them. And they have the pleasing property of describing the structure at least one subset of EVERY infinite set.
Except Peano's axioms are a joke, and you've been had. Sorry, you CANNOT derive my sound axioms from that rot. Please do show me how. You are talking nonsense!