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Exercise. Suppose that X is a non-empty set, and that a function p : X x X R satisfies the following two conditions: a) For every r, y E X, we have p(x, y) = 0 if and only if r = y. b) For every x, Y, z E X, we have p(x, y) < p(x, z) + p(y, z). Prove that p is a metric on X.

Exercise. Suppose that X is a non-empty set, and that a function p : X x X R satisfies the following two conditions: a) For every r, y E X, we have p(x, y) = 0 if and only if r = y. b) For every x, Y, z E X, we have p(x, y) < p(x, z) + p(y, z). Prove that p is a metric on X.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 18E: In Exercises , prove the statements concerning the relation on the set of all integers. 18. If ...
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Exercise. Suppose that X is a non-empty set, and that a function p : X x X - R satisfies the following two conditions: a) For every r, y E X, we have p(x, y) = 0 if and only if r = y. b) For every r, y, z E X, we have p(x, y) < p(x, z) + p(y, z). Prove that p is a metric on X.
Transcribed Image Text:Exercise. Suppose that X is a non-empty set, and that a function p : X x X - R satisfies the following two conditions: a) For every r, y E X, we have p(x, y) = 0 if and only if r = y. b) For every r, y, z E X, we have p(x, y) < p(x, z) + p(y, z). Prove that p is a metric on X.
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