{1 - - :n e N}. Find all cluster points of (a) Let A be the subset of R defined by A := (-1)" A and justify your answer. (b) Let S c R and let c e R be a cluster point of S. Prove that for each ɛ > 0 the set W := Sn (c – ɛ, c + e) has infinitely many elements.

{1 - - :n e N}. Find all cluster points of (a) Let A be the subset of R defined by A := (-1)" A and justify your answer. (b) Let S c R and let c e R be a cluster point of S. Prove that for each ɛ > 0 the set W := Sn (c – ɛ, c + e) has infinitely many elements.

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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Question

Let A be the subset of R defined by A := (1- (((-1)^n)/n)): n ∈ N.Find all cluster points of A and justify your answer

{1 -
- :n e N}. Find all cluster points of
(a) Let A be the subset of R defined by A :=
(-1)"
A and justify your answer.
(b) Let S c R and let c e R be a cluster point of S. Prove that for each ɛ > 0 the set
W := Sn (c – ɛ, c + e) has infinitely many elements.

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