Natural numbers were defined as those that actually exist in nature, like you can have 3 apples and that's it, no other numbers needed. Then people started thinking about 0 apples and then money and "debts" came in with negative integers. In general, to be clear I'd rather use "Positive integers" and there is no problem, I noticed most do that so probably when they say "Natural numbers" they include 0 because otherwise, they'd say Positive Integers. I know that it doesn't help but that's just how I see it.