It was my understanding that it's like velocity vs speed. Positive/Negative numbers have a directional component, that is that they are above or below zero. Absolute values, however, lack a direction. They're a value, but they don't tell you if the value is positive or negative.
Absolute value shows only distance from the 0 value on the number line without the direction. All distances are positive when viewed without direction.
I don't understand this argument. I've heard high school teachers decree it as a mathematical truth before.
Do we all agree absolute value is a function from reals to reals? If so, the absolute value of any real number is nonnegative. It can be zero or any positive numbers.
