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    To prove given function is a metric

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    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 .

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    Solution Summary

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