Subzero Temperatures

Natural Numbers Are Pretty Great, But They Are Also Quite Limited.

To start with, it is not always possible to subtract two naturals and get another natural. If all I have to work with are these counting numbers, I have no idea how to parse a statement like 3 - 8.

One of the wonderful things about maths is that, when we are confronted with a limitation like this, we can just expand the system we are working with to remove the limitation. To allow for subtraction, we add -1 to our growing number line. -1 brings with it all the other negative whole numbers, since multiplying a positive number by -1 gives the negative version of that number: -3 is just -1 x 3. By bringing in negative numbers, we have solved our subtraction problem. 3 - 8 is just -5. Putting together the positive numbers, zero, and our new negative numbers, we get the integers, and we can always subtract two integers from each other and get an integer as the result. The integers provide the anchor points for the number line.

The negative numbers are useful in representing deficits -- if I owe the bank $US500, I can think of my bank balance as being -500. We also use negative numbers when we have some scaled quantity where values below zero are possible, such as temperature. In the frozen wasteland of my hometown of Buffalo, we would get a few winter days each year down in the -20° range.