# To prove given function is a metric

This problem from Methods of Real Analysis, 2nd edition, by Richard Goldberg.

For P<x_1,y_1> and Q<x_2, y_2>

define σ(P,Q)=| x_1- x_2 |+|y_1+y_2 |

Show that σ is a metric for the set of ordered pairs of real numbers.

Also, if:

τ(P,Q)=max(| x_1- x_2 |,|y_1+y_2 |)

show that τ defines a metric for the same set .

https://brainmass.com/math/real-analysis/satisfying-the-properties-of-a-metric-570416

#### Solution Summary

This document contains two problems on showing that two given functions satisfy the properties of a metric on a given set.

$2.19