# Was there a culture/number system with negative numbers but without zero?

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.

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