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The first kind of case derives simply from the fact that if you subtract a larger number from a smaller one, the result is a negative number. If you were to measure the indoor temperature as 293°K (about 68°F) and the outdoor temperature as 275°K (about 36°F), and then subtract the larger from the smaller, sure enough you would end up with —18°K. But this, of course, does not mean that there is any point in the physical universe where the temperature is 18 degrees below zero Kelvin. All it says is that the temperature difference between these two particular points is 18 degrees on the Kelvin scale. Looked at from one direction (larger minus smaller), it is +18°K; looked at from the other direction (smaller minus larger), it is —18°K. Similarly, 28 students in one class minus 30 students in another yields —2 students; 10 dollars in hand minus 12 dollars owed yields —2 dollars; and so on. In cases of this general type, the implication is not that there is any number of students or dollars, or whatever, smaller than zero. The negative sign in such cases is simply an indication that the difference between two numbers is being looked at from the direction of "smaller minus larger."
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The second kind of case involves instances where the polarity or directionality ("+" and "—") is not simply an artifact of the process of subtraction, but rather intrinsic to the phenomena that are being measured. In the realm of electricity, for example, there really are positive (+) and negative (—) electrical charges. Each proton possesses one unit of electrical charge, which by convention is spoken of as "positive," and each electron possesses an equal but opposite unit of "negative" electrical charge. Thus, a substance containing substantially more electrons than protons would have a net negative electrical charge, and any measure of voltage taken between that substance and "ground" (electrical zero) would also have a negative value. This, however, does not mean that a negative electrical charge is smaller than a zero electrical charge, nor that a negative value for voltage is smaller than zero voltage. In both cases, "zero" marks an absolute zero point on the scale. There is no electrical charge smaller than zero, and no voltage smaller than zero. It is simply a matter of whether a deviation from absolute zero goes off in one direction or the opposite direction.
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