Part of the definition of a metric space is that the metricobeys commutativity and this other statement, and this statement is used to define the norm of avector space.
The generalization of this statement to Lp spaces is called the Minkowski inequality, and thisstatement is reversed in Minkowski spaces. Part of the definition of a metric space is that the metricobeys commutativity and this other statement, and this statement is used to define the norm of avector space. It can be proven by reduction from the Cauchy-Schwarz inequality on an inner productspace, or by considering the Law of Cosines and (*) removing the cosine term. This statement can beused to show that the shortest distance between two points in Euclidian space is a straight line. For 10points, name this inequality, which states that the sum of the lengths of two sides of the namesake figure isgreater than the length of the third side.
The generalization of this statement to Lp spaces is called the Minkowski inequality, and thisstatement is reversed in Minkowski spaces.
triangle inequality [prompt on "Cauchy-Schwarz inequality" due to ambiguities]