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Negative numbers can be introduced by means of temperature, but it does not make sense to multiply two negative temperatures. Moreover, it is even objectionable to say 20°C is twice as hot as 10°C. A negative number may also represent a quantity with an opposite direction, but under such circumstances it is tempting to think that negative numbers should be compared in terms of their absolute values.

Positive numbers can be perfectly conceived of as lengths of line segments. Real numbers that are greater than or equal to 0 and less than or equal to 1 can be conceived of as probabilities. What about negative numbers?

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  • $\begingroup$ What is this for? I guess for application purposes, money may be a good indicator (negative balance/debt). $\endgroup$
    – Paul Ash
    Commented Apr 7 at 5:11

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If you're trying to introduce negative numbers by a real-world scenario, the first thing that comes to mind is debt, i.e., the amount of money owed.

Addition makes sense:

Bob owes Janet $\$20$ dollars (corresponding to a debt of $-\$20$) and owes Mike $\$35$ dollars (corresponding to a debt of $-\$35)$. Thus, his total debt is $-\$20 + -\$35 = -\$55$.

Subtraction makes sense:

Bob just paid Janet the $\$20$. Hence, his debt is now $-\$55 - (-\$20) = -\$35$.

and etc.

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