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

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

Elements Of Modern Algebra

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Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.5: Normal Subgroups

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Question

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

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