The meaning of absolute value of a number?

Question

I have this doubt: by definition, absolute value of a reall number is the numerical value of the real number without regard to its sign. But is it really possible to deal with a quantity which has no sign? It seems to me that although the definition says abs(x)=()|x|, with no sign attached, we actually treat it as if it is +|x|. Otherwise how do people plot a function like y(x)=|x|? this plot is entirely on the positive side of Y-axis, which means we actually take |x|=+|x|. So I think the definition usually given for absolute function is not very accurate. A real number or quantity is either positive or negative. Please tell me what you think about this.

Answer 1

the absolute value of a number can be defined as simply the distance that a number has from the value of 0. It's really a question of definitions. In certain ways of thinking, distance can be regarded as negative or positive values. For example, you can say that a person moved -5 inches in the X direction, or you can say that negative values are impossible in distance measurement.

The plot of y(x) = |x| is entirely possible, and something that I have seen. it looks like the letter V, basically. What's odd is the derivative of this function(the graph of the slope of y(x)), it's -1 for all values less than zero, undefined at 0 and 1 for all values above zero.

So it's all a confusion about definitions. The absolute value of a number is not an innate property of the number, it's simply something that we humans define for convenience.

I think you'll be interested in number theory and discrete mathematics. You get into the theoretical basis of these definitions we've created and their inconsistencies.

Answer 2

Absolute Value Math Definition

Answer 3

The absolute value of a real number does have a sign and it's positive, we just don't write it down.

What is 7 - 5. The answer is 2, but do we need to say the answer is +2, no we don't. It's convention that if we write a number down with no sign next to it, we take it as a positive quantity.

A classic example of absolute values is when using distance, you cannot have a negative distance.

You wouldn't say that Blackpool is -40 miles away would you?

Answer 4

Technically, the definition of the absolute value is a piecewise function, defined as follows:

|x| = {x if x>=0
{-x if x<0

Essentially, if a number is positive, leave it be, and if it is negative, negate it again to make it positive. And yes, the graph of the absolute value of a function is a V. It has its base at (0,0), and then for x = -1 or 1, both take y value 1, x = -2 or 2, both take y value 2, and so on... The graph is symmetric with respect to the y axis.

Answer 5

You're really making things much more complicated than necessary. To quote you: by definition, absolute value of a reall number is the numerical value of the real number without regard to its sign. In other words it is the POSITIVE value of the real number. E.g., if x = 6, then lxl = 6. If x = -6, then lxl = 6.

The function y(x) = lxl on a graph would look like a sideways v. Try it.

Answer 6

Technically, of course, you're correct. BUt the convention has been in use for so long that it's probably not gonna change. You can think of the absolute value as the 'distance' along the number line to the point x so that |x| tells you haw far away from the origin it is. But negative distances don't make a lot of sense (except in a vector space) and so the + convention is used.

Doug

Answer 7

Absolute value of a real number represents the distance of the point from 0 on the number line, and hence cannot be negative.

Answer 8

By definition, the absolute value of a non-negative number is the number itself, and the absolute value of a negative number is the additive inverse of that number (the negative number multiplied by -1). The absolute value of a number can never be less than zero.

Answer 9

Absolute value shows the magnitude of a number.It's like the difference between distance and displacement.
For example,Distance-5km.Displacement- 5km towards east.
We are just observing the distance of the number from the zero on the number line, not the direction of the distance.

Answer 10

Absolute value is actually the distance of that perticular variable from origin whatever be the dimension of the variable and note distance can't be negative.

for example: if z = x + iy (if you don't know complex number then refer to the notation).
then absolute value = (x^2 + y^2)^(1/2)

hope this clarifies your doubt.