I googled all the way to Peano axioms too, but I was on my mobile, so I'd take some half an hour to reply with that...
Let's see the important ones for the 1+1=2 discussion.
Now, do the math!
Let's see the important ones for the 1+1=2 discussion.
Quote:1. 0 is a natural number.
6. For every natural number n, S(n) is a natural number.
Peano's original formulation of the axioms used 1 instead of 0 as the "first" natural number. This choice is arbitrary, as axiom 1 does not endow the constant 0 with any additional properties. However, because 0 is the additive identity in arithmetic, most modern formulations of the Peano axioms start from 0. Axioms 1 and 6 define a unary representation of the natural numbers: the number 1 can be defined as S(0), 2 as S(S(0)) (which is also S(1)), and, in general, any natural number n as Sn(0). The next two axioms define the properties of this representation.
7. For every natural number n, S(n) = 0 is false. That is, there is no natural number whose successor is 0.
[...]
Addition is the function + : N × N → N (written in the usual infix notation, mapping two elements of N to another element of N), defined recursively as:
a+0=a,
a+S(b) = S(a+b)
Now, do the math!
