On Friday, May 2, 2014 11:37:10 AM UTC-4, Peter Percival wrote: > Dan Christensen wrote: > > > > > After over a century of intensive scrutiny, no one has been able to > > > demonstrate any inconsistency arising from that the Peano's Axioms > > > for the infinite set of natural numbers. And no one, not even you WM, > > > has been able to successfully develop number theory on any other > > > formal basis. > > > > Are you saying that no one has successfully developed number theory > > other than on the basis of Peano's axioms? >
Number theory was already well developed before Peano, but to formally develop number theory from first principles, I think you have to start with a set N and an unary operator S on N that satisfy Peano's axioms.