Introduction to Real Numbers - Problem 1 3,373 views

The absolute value is probably something that you have seen before, and basically what it is is, the distance of whatever number, is in the absolute value is from zero. You probably think of it as, just the magical little bars that make something positive, which is one way of looking at it. But really, the technical definition is the distance of this number from zero.

How we can write that is, the number inside is just the number, if your number is positive, and it’s the opposite, if your number is negative. The way you can sort of think about that is, the distance between two things is always positive. You don’t say, I’m 5feet away from you no matter where you, you say, you’re 5 feet away from something no matter where you are. You don’t say I’m negative 5 feet if you’re behind. The distance is always positive, so what you’re really doing is, taking the distance between 2 points; the point you’re looking at, and the origin. The absolute value say of 4, is 4 units. You’re 4 units from zero and the absolute value of negative 7, is just 7, because you’re really 7 units away.

Technically, it does make everything positive, but if you really want to know the formal definition, it’s the distance form zero.