Why is it impossible for the absolute value of a number to be negative?

Answer 1

because absolute value is defined as the distance from zero and you can't have negative distances.

Answer 2

The absolute value of a number is its distance from 0 on a number line. For example, the number 9 is 9 units away from 0. Therefore its absolute value is 9.

Negative numbers are more interesting, because the number -4 is still 4 units away from 0. The absolute value of -4 is therefore positive 4.

Answer 3

By its definition. The absolute value is the distance a number is to 0. Since a distance cannot be negative, absolute value cannot be negative. Why can't distance be negative? Because it is the length of a segment between 2 points.

Answer 4

Simply because that is the definition of an absolute value.
It is based on the concept of distance, which, in mathematics, is a function which must always be positive (unless it is exactly zero). When mathematicians want to make real sure that they mean the mathematical concpet, they may use the noun "metric". As in, what is the metric in this field? (the manner in which distance is calculated).

In real numbers, the absolute value represents the distance between two numbers. ABS(x-y) return the distance between x and y, regardless of the direction you take (therefore, always positive).

In other fields, it is often seen as the length of a vector. In vector spaces, the equivalent concept is called a "norm" (also length or magnitude).

It is sometimes called modulus (although the word modulus can mean other things in physics and in other branches of mathematics). The use of "modulus" instead of "absolute" is normally reserved to complex numbers.

There too, the value is always non-negative.
if z = x + yi, then the absolute value of z =
SQRT(x^2 + y^2) defined as positive only (NOT "plus or minus")

Answer 5

The absolute value of a number |n|
is always positive because it represents
only the magnitude of the value with
absolutely no regard to sign.

Answer 6

The absolute value of a number is defined to be always positive. It represents the magnitude of the number without regard as to its sign.

If you owe someone $10 or someone owes you $10 the amount in either case is + $10. If you walk 10 miles due West or walk 10 miles due East, in both cases you have walked +10 miles. You did not walk 10 miles in one direction and -10 miles in the other.

Answer 7

becuz it is the rule of the absolute value. the absolute value measures distance. and since in reality, you cannot have negative distances, whatever is in between the brackets becomes positive weather or not it was originally positive.

Answer 8

absolute value is a way we define "distance.."

how far is it from Washington DC to New York City?
(325 miles)

so is it -325 miles from NY to DC ?

we represent distance as a positive number.... absolute value does that for us!

Answer 9

beacuse negetive number only makes sence in mathematics
i belive the negetive number doesnt exist.

Answer 10

because it is by necessity whatever value it has is a value greater than zero.