It is because you mean two different things by "natural numbers", even though the same words are used for things that are not the same things. I prefer to star

It is because you mean two different things by "natural numbers", even though the same words are used for things that are not the same things. I prefer to start by zero; I think it is more useful in general, and makes more sense mathematically for many (although not all) purposes, and systems that you will find objects and operations that have these properties too.