If you can debate whether or not zero is a number then you haven't invented it. If zero might not be a number then you can't state that 0 * n = 0 and 0 + n = n

If you can debate whether or not zero is a number then you haven't invented it. If zero might not be a number then you can't state that 0 * n = 0 and 0 + n = n and n - n = 0, etc