Why there is no negative absolute value of a number?

Answer 1

Imagine you are looking at a road map. You could view north or south as positive and negative, relatively. So let's say you want to travel one hundred miles. North or south, positive or negative - it doesn't matter. You would still be traveling one hundred miles, because you're car's rate of fuel consumption simply doesn't care, and your gas gauge would reflect that, absolutely. So absolute value simply relates a quantity of something, rather than whether that quantity is north or south, positive or negative, or some other directional value. It is simply a number without RELATIVITY. Without a frame of reference, a value becomes absolute.

For one last example, let's look at a financial situation. You just won $600 off a pick 3, and are now feeling confident. So you take your $600 and drop it at the nearest casino. Two hours later, you leave with a heavy heart because you're broke. Now, in your mind, you've just lost $600, which now gives it a negative value from your point of view. But from the casino's point of view, it has a positive value since it now belongs to them. Oddly enough, both perspectives are true. So now the $600 is both positive (profit) AND negative (deficit). But, in the end, $600 is still $600 (absolute); the only difference is perception - how it is viewed by different parties. This is what absolute value doesn't have to deal with. It removes all frames of reference so that ONLY the value itself remains.

So just remember, if you're almost out of gas, parked at some random greasy spoon in the middle of nowhere, all you really want to know is how far the nearest gas station is.