Let (X, d) be a metric space. Suppose that (xn) is a sequence of points in X which converges to a point x E X, and (yn) is a sequence of points in X which converges to a point y E X. Prove that the sequence of real numbers, d(xn, Yn) coverges to d(x, y).

Let (X, d) be a metric space. Suppose that (xn) is a sequence of points in X which converges to a point x E X, and (yn) is a sequence of points in X which converges to a point y E X. Prove that the sequence of real numbers, d(xn, Yn) coverges to d(x, y).

Name: Let (X, d) be a metric space. Suppose that (xn) is a sequence ofpoint
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Description: Let (X, d) be a metric space. Suppose that (xn) is a sequence ofpoints in X which converges to a point x E X, and (yn) is a sequenceof points in X which converges to a point y E X. Prove that thesequence of real numbers, d(xn, Yn) coverges to d(x, y

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 16E: Prove that if a subring R of an integral domain D contains the unity element of D, then R is an...

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