(6) Suppose A CR is countable. Show that there exists a real number r such that An(r+ A) = 0. (Here, r+ A {r+ a : a € A}.)

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.2: Properties Of Group Elements
Problem 31E: 31. Prove statement of Theorem : for all integers and .
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(6) Suppose A C R is countable. Show that there exists a real number z such that
An (r+ A) = 0. (Here, z+ A = {r+ a : a € A}.)
Transcribed Image Text:(6) Suppose A C R is countable. Show that there exists a real number z such that An (r+ A) = 0. (Here, z+ A = {r+ a : a € A}.)
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