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why? is this just a computer science problem , or is this a mathematical property.

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up vote 4 down vote accepted

I'm not sure what level of answer you're looking for, so (at the risk of appearing stupid) here's my explanation:

0 is nothing. A negative number is the absence of something, a deficit. Subtraction is the removal of one quantity from another quantity. Therefore subtracting something from nothing results in a deficit, and absence, a negative number.

Put visually:

-5  -4  -3  -2  -1   0   1   2   3   4   5

If I want to make 3 a negative number, I can subtract 3 from 0.

As a bonus, you can also make a number negative by multiplying it by -1.

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