For example, an altitude above sea-level can be expressed as a positive number; below sea-level is negative.
Or: If you have money, you have a positive amount of money; if you owe money, that goes against you, you have "less than nothing", so it can be expressed as a negative amount.
In technology and science - would you classify that as "real-world"? - negative numbers are used all the time. For example, if you decide that moving in a certain direction (e.g., "up") is positive, a movement in the opposite direction is negative.
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