absolute value

American  

[ab-suh-loot val-yoo] / ˈæb səˌlut ˈvæl yu /

noun

Mathematics.

1. Also called numerical value.  the magnitude of a quantity, irrespective of sign; the distance of a quantity from zero. The absolute value of a number is symbolized by two vertical lines, as |3| or |−3| is equal to 3.

2. the square root of the sum of the squares of the real and imaginary parts of a given complex number, as |a + b i | is equal to .

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absolute value British  

noun

1. the positive real number equal to a given real but disregarding its sign. Written | x |. Where r is positive, | r | = r = | – r |

2. Also called: modulus.  a measure of the magnitude of a complex number, represented by the length of a line in the Argand diagram: | x + i y | = √( x ² + y ²), so | 4 + 3i | = 5

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absolute value Scientific  

1. The value of a number without regard to its sign. For example, the absolute value of +3 (written ‖+3‖) and the absolute value of −3 (written ‖−3‖) are both 3.

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Etymology

Origin of absolute value

First recorded in 1905–10

Example Sentences

The graph of the absolute value function does not cross the -axis, so the graph is either completely above or completely below the -axis.

From Textbooks • Dec. 21, 2021

The absolute value function is often thought of as providing the distance the number is from zero on a number line.

From Textbooks • Sep. 23, 2020

Since they have the same distance from zero, they have the same absolute value.

From Textbooks • May 6, 2020

We can generalize this to the following property for absolute value equations.

From Textbooks • May 6, 2020

“Oh, really? Well, if x is greater than or equal to zero, then x to the fourth power minus six times x squared plus nine equals the absolute value of x squared minus three.”

From "The Smartest Kid in the Universe" by Chris Grabenstein