You cannot achieve all of mathematics from Peano arithmetic (PA). But, you can achieve all (or almost all) of math from set theory (including PA).

Regardless, zero is still treated as an object in PA and this is especially apparent since you need to treat zero as an object to arrive at any other number.

Alex, give up the ghost. You are swimming against a huge current of knowledge established by people like Hilbert, Peano, Zermelo, Russell, Whiteside, etc.

Warm regards, Harv

• Harvey, why should I give up what works (science)? - alexander - November 8, 2001 - 23:05 UTC