triangle inequality

American  

noun

Mathematics.

1. the theorem that the absolute value of the sum of two quantities is less than or equal to the sum of the absolute values of the quantities.

2. the related theorem that the magnitude of the sum of two vectors is less than or equal to the sum of the magnitudes of the vectors.

3. (for metric spaces) the related theorem that the distance between two points does not exceed the sum of their distances from any third point.

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Etymology

Origin of triangle inequality

First recorded in 1960–65

Example Sentences

The triangle inequality is used at a key point of the proof, so we first review this key property of absolute value.

From Textbooks • Mar. 30, 2016

Verify that the vectors a, b, and a + b, and, respectively, a, b, and a − b satisfy the triangle inequality.

From Textbooks • Mar. 30, 2016

This is known more generally as the triangle inequality.

From Textbooks • Mar. 30, 2016