Along with symmetry and nonnegativityrestriction, this statement must be true for a distance function to be a metric.
A very strong form of this statement holds in spaces like the p-adics. Along with symmetry and nonnegativityrestriction, this statement must be true for a distance function to be a metric. Thegeneralization of this statement to the p-norm is named for Minkowski, and it can also be derived from astatement named for (*) Cauchy and Schwarz. One reformulation of it states that absolute value of quantity x plusy is less than or equal to absolute value of x plus absolute value of y. This statement follows from the law of cosines,because the magnitude of cosine in the namesake shapes is less than one. For 10 points, identify this statementwhich says that, for a certain three-sided figure, a plus b is greater than c.
A very strong form of this statement holds in spaces like the p-adics.
 triangle inequality [prompt on ultrametric inequality before the word metric is said, do not accept "Cauchy-Schwarz" inequality at any point] 