The set of natural numbers should have zero, otherwise it's not a ring. However, from the perspective of Peano's axioms, it doesn't matter as far as I am concer

The set of natural numbers should have zero, otherwise it's not a ring. However, from the perspective of Peano's axioms, it doesn't matter as far as I am concerned what the symbols are called, as long as you have a successor function. Apart from that, I agree that it depends whether you are counting [1] or doing something else. [1] That's why I do HN references like this.