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

In his annual letter to investors, the outspoken venture capitalist wrote about how rising interest rates caused “absolute value destruction” among money-losing start-ups, like the ones he had invested in.

From New York Times

“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 Literature

However, China’s transaction volume with illicit addresses has fallen drastically over the two-year period in terms of absolute value and relative to other countries, Chainalysis said.

From Reuters

From the standpoint of the absolute value of secularism, “it doesn’t conform to his obligation to be neutral,” Ms. Lorcerie said.

From New York Times

For that particular problem, any solution has an absolute value lower than the square root of a given n.

From Scientific American