In the history of numbers, negative numbers as well as zero appear relatively late, possibly because the concepts represented are not really 'quantities' in a straightforward sense. However, even between these two, in many cultures $0$ seems to have been introduced as a number before the advent of negative numbers.
Question: Do you know of any culture that had negative numbers before they had zero?
Some thoughts of mine:
In the group theoretic formulation of arithmetic the concept of inverses doesn't even make sense without the notion of a neutral element. And for something to be a number, one should be able to calculate with it. One might therefore argue that if a culture had some negative number $-a$, they would need to have zero, because they would need some rule to add $-a$ and $a$.
However, the concept of negative numbers could have been more familiar because of financial debts (for instance), without there having to be a 'numerical' notion of zero.
The wikipedia page on negative numbers contains some information, but nothing conclusive. I am also aware that it is not perfectly clear what is meant here by 'number', but this should not prevent an answer to the question. Thank you.
