Comment by BoiledCabbage

Is there any notable difference between how it's presented in the post

> Thus, addition is a function P:NxN -> N such that for all numbers a, b,

> 1. P(a,0) = a

> 2. P(a,S(b)) = S(P(a,b))

And this alternate formulation?

1. P(a,0) = a

2. P(a,S(b)) = P(S(a),b)

Ie "decrease one from b and add it to a", instead of "decrease one from b and add it to the total".