The Other Side of Zero
Subtracting as adding the inverse
Use an infinite lift to see subtraction as adding the inverse.
Imagine an 'infinite lift' that goes up forever and down forever from Level 0. To work out (+2000) - (-200), think: Target Level - Starting Level = Movement needed. From -200 to +2000, you press +200 to reach zero and then +2000 more, so +2200 in all. So (+2000) - (-200) = +2200.
Notice that (+2000) + (+200) is also +2200. Subtracting a negative number is the same as adding the corresponding positive number. So we can always replace 'subtract -200' with 'add +200'.
This works for every subtraction: the number being subtracted can be replaced by its inverse and then added. For example:
- (+7) - (+5) = (+7) + (-5) = +2.
- (-3) - (+8) = (-3) + (-8) = -11.
- (+8) - (-2) = (+8) + (+2) = +10.
- (+6) - (-9) = (+6) + (+9) = +15.
The book shows why with a journey from 2 to -3. Directly, the movement is -3 - 2 = -5. In two parts, from 2 to 0 is -2 and from 0 to -3 is -3, and the total is -3 + (-2) = -5. The second way has no subtraction at all!
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