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

How does the graph of the absolute value function compare to the graph of the quadratic function, in terms of increasing and decreasing intervals?

From Textbooks • Sep. 23, 2020

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

The steps for solving an absolute value equation are summarized here.

From Textbooks • May 6, 2020

The absolute value of the energy difference is used, since frequencies and wavelengths are always positive.

From Textbooks • Feb. 14, 2019

“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