Thanks, but you may have misunderstood the definition I have for defining odd numbers, because that corresponds equally to the natural numbers as well.

So there is no better parity rule as you say, it is entirely arbitrary. It's not extending the same pattern, it's seeing that there are two ways of extending it and picking one arbitrarily.

In that case, if it were me, I'd call it something else. Not parity or even/odd. Because it's not the natural obvious extension. It's arbitrary.