Answered: 1. Prove that if f (n) ∼ A(n) as n→∞,…

1. Prove that if f (n) ∼ A(n) as n→∞, then A(n) ∼ f (n). 2. Prove that if f (n) ≤ g(n) ≤ h(n) and f (n) ∼ A(n) and h(n) ∼ A(n), then g(n) ∼ A(n).

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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Question

1. Prove that if f (n) ∼ A(n) as n→∞, then A(n) ∼ f (n).
2. Prove that if f (n) ≤ g(n) ≤ h(n) and f (n) ∼ A(n) and h(n) ∼ A(n), then g(n) ∼ A(n).

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