Exercises on cluster points: (a) Let S(a, b) be an open interval with a, b € R and a < b. Show that [a, b] is the setof all cluster points of S.(b) Let S = Z. Show that S has no cluster points in R.(c) Let S = Q. Show that R is the set of all cluster points of S.-=

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Answered: (a) Let S = (a, b) be an open interval…

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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(a) Let S = (a, b) be an open interval with a, b = R and a < b. Show that [a, b] is the set of all cluster points of S. (b) Let S = Z. Show that S has no cluster points in R. (c) Let S Q. Show that R is the set of all cluster points of S.