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.
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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 3E
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6d34efb-714e-4109-86a1-c1e5ba7c23ed%2F838d2a77-eeb6-4abb-af4c-57dff2998e83%2Fys0dvvb_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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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