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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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