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Let (Xd) be a metric space and suppose that a sequence (a.} has a subsequence that converges to an element LEX. One of these statements is 5. correct: 1. The sequence {an} itself must converge. 2. The sequence (a.} may not converge. Use your intuition to think of which is true. Then, prove it.

Let (Xd) be a metric space and suppose that a sequence (a.} has a subsequence that converges to an element LEX. One of these statements is 5. correct: 1. The sequence {an} itself must converge. 2. The sequence (a.} may not converge. Use your intuition to think of which is true. Then, prove it.

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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5. Let (Xd) be a metric space and suppose that a sequence {a,} has a subsequence that converges to an element LEX. One of these statements is correct: 1. The sequence {a.} itself must converge. 2. The sequence {an} may not converge. Use your intuition to think of which is true. Then, prove it.
Transcribed Image Text:5. Let (Xd) be a metric space and suppose that a sequence {a,} has a subsequence that converges to an element LEX. One of these statements is correct: 1. The sequence {a.} itself must converge. 2. The sequence {an} may not converge. Use your intuition to think of which is true. Then, prove it.
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