Example: In the Euclidean metric space (R, I-1), we have the following:1.The closed interval (a , b] is compact because it closed and bounded.2.The interval [0, 00) is not compact because it not bounded.3.The open interval (0, 1) is not compact because it is not closed and there is an open covering of the form{(0, 1-):n = 2,3,.) of (0, 1) but has no finite subcovering.4.Z is not compact because it is not bounded.R is not compact because there is an open cover of the form { (-n, n) : n € Z* } but it has no finite subcovering.5.6.Every finite set in R is compact. Why?

The given question is related to real analysis. We have to show that every finite set in ℝ is…

Answered: 6. Every finite set in R is compact.…

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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6. Every finite set in R is compact. Why?