please explain everything step by step 1.Prove that if A is infinite and a E A, then A – {a} is alsoinfinite.

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Answered: 1. Prove that if A is infinite and a e…

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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1. Prove that if A is infinite and a e A, then A – {a} is also - infinite.