**Convergence of Sequences in a Metric Space**Let \((X, d)\) be a metric space. Suppose that \((x_n)\) is a sequence of points in \(X\) which converges to a point \(x \in X\), and \((y_n)\) is a sequence of points in \(X\) which converges to a point \(y \in X\). Prove that the sequence of real numbers, \(d(x_n, y_n)\) converges to \(d(x, y)\).

Name: **Convergence of Sequences in a Metric Space**Let \((X, d)\) be a met
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Description: **Convergence of Sequences in a Metric Space**Let \((X, d)\) be a metric space. Suppose that \((x_n)\) is a sequence of points in \(X\) which converges to a point \(x \in X\), and \((y_n)\) is a sequence of points in \(X\) which converges to a point

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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).

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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