Prove the following, unofficially known as the Awesome Lemma or Awesome Theorem: Suppose {an} is a sequence that converges to a real number a. (a) If a < b, then there exists an NEN such that, if n > N, then an < b. (b) If a > b, then there exists an NEN such that, if n > N, then an > b. (You may omit the proof of part (b) and simply state that it follows from part (a) “by symmetric argument.")

Prove the following, unofficially known as the Awesome Lemma or Awesome Theorem: Suppose {an} is a sequence that converges to a real number a. (a) If a < b, then there exists an NEN such that, if n > N, then an < b. (b) If a > b, then there exists an NEN such that, if n > N, then an > b. (You may omit the proof of part (b) and simply state that it follows from part (a) “by symmetric argument.")

Name: Prove the following, unofficially known as the Awesome Lemma or Aweso
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Description: Prove the following, unofficially known as the Awesome Lemma or Awesome Theorem:Suppose {a,} is a sequence that converges to a real number a.(a) If a N, then an b, then there exists an N

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.2: Mathematical Induction

Problem 55E: The Fibonacci sequence fn=1,1,2,3,5,8,13,21,... is defined recursively by f1=1,f2=1,fn+2=fn+1+fn for...

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