It might be better to conceptualize negative numbers as numbers in a different direction or along a different axis. If I cover lunch for you, you would owe me

It might be better to conceptualize negative numbers as numbers in a different direction or along a different axis. If I cover lunch for you, you would owe me $5. In a way, you now have -$5. You won't have $0 until you pay me back the $5 you owe. We can also say you have $5 of debt. That makes the number positive while still representing the amount. But when reconciling your books, it'll be subtracted from your total.