Question 1.3] Given a metric space < X, p >.(a) If x, y E X and p(x, y) < ɛ for all e > 0, prove that x = y.(b) Prove that a sequence (xm)neN C X can have at most one limit.

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Answered: Question 1. 5] Given a metric space <…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 55E

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Question 1. 5] Given a metric space < X, p>. (a) If r, y E X and p(x, y) < ɛ for all e > 0, prove that r = y. (b) Prove that a sequence (xn)neN CX can have at most one limit.