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2) Let assume the set N = {1, 2, 3,...}. a) Show that the function d(x, y) = 1 X Y defined on N is a metric. b) Is the sequence (în) defined by în = n Cauchy sequence on the metric space (N, d) or not? Why? c) Is the metric space (N, d) complete? Why?

2) Let assume the set N = {1, 2, 3,...}. a) Show that the function d(x, y) = 1 X Y defined on N is a metric. b) Is the sequence (în) defined by în = n Cauchy sequence on the metric space (N, d) or not? Why? c) Is the metric space (N, d) complete? Why?

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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2) Let assume the set N = {1, 2, 3, ...}. 1 a) Show that the function d(x, y) = X Y defined on N is a metric. b) Is the sequence (xn) defined by n = n Cauchy sequence on the metric space (N, d) or not? Why? c) Is the metric space (N, d) complete? Why?
Transcribed Image Text:2) Let assume the set N = {1, 2, 3, ...}. 1 a) Show that the function d(x, y) = X Y defined on N is a metric. b) Is the sequence (xn) defined by n = n Cauchy sequence on the metric space (N, d) or not? Why? c) Is the metric space (N, d) complete? Why?
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