# triangle inequality

### noun Mathematics.

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.

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.

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

## Origin of triangle inequality

First recorded in 1960–65

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Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019