Originally Posted by

**Hartlw** so 1+1 = 1+1?

You haven't defined the successor function. You only defined it for 1 and 2. What is your definiton of the successor function. All you have said so far is 2 is the successor of 1 by definition.

1 and 2 is a notation convention for the natural numbers which is independent of the Peano Postulates.

Having defined the natuaral numbers, you can then define a notation convention such as binary, decimal, hexadecimal, etc. But informally it's ok.

Edit: To save some back and forth, my definition of the successor function for the natural numbers is S(n)=n+1. What's yours?

Edit: Peano's potulates don't define addition. But if you want to assume it's been defined somewhere, informally that's ok.