This is why people have brought up the successor function too: A + B, is, by definition B applications of Succ() on A: A + B = Succ(Succ(Succ(...Succ(A))))

This is why people have brought up the successor function too: A + B, is, by definition B applications of Succ() on A: A + B = Succ(Succ(Succ(...Succ(A)))) So using your own argument, we could say that using '+' is simply a convention on how we can write down the above — if we insist on spelling "conventional" things out, we must be able to use the underlying elementary function[]. Or isn't a factorial n! really n(n-1)...21, so all those numbers spelled out? The mathematical root probably first appeared as a square root and was later extended to support other exponents. But is there any fun in this? As noted elsewhere, the game is in finding the rules, and a solution within those rules. []Since all the natural numbers other than 1 are defined using a Succ() functions, there's a trivial solution. But if we only limit ourselves to this most elementary operation, we can't get a 1 because that's an axiom in itself ("There exists 1" or "There is a set of cardinality 1").