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There are lots of situations in the real world in which there are opposites, which can conveniently be expressed with positive/negative numbers. Here are some examples:
- Having money (positive), having a debt (negative)
- Getting a profit (positive) or a loss (negative) with a business venture
- An altitude above (positive) or below (negative) sea level
- Gaining points or losing points in a game
- Moving in one direction or in the opposite direction. In this case, it is quite arbitrary which direction is chosen as positive.
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