Answered: Let A and B be non-empty and bounded…

Let A and B be non-empty and bounded subsets of R such that inf A < inf B. Prove the following: ∃a ∈ A ∀b ∈ B : a < b Hint: Show first that there exists a ∈ A such that a < inf B.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 28E: 28. Let where and are nonempty. Prove that has the property that for every subset of if...

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Question

Let A and B be non-empty and bounded subsets of R such that inf A < inf B. Prove the following:

∃a ∈ A ∀b ∈ B : a < b

Hint: Show first that there exists a ∈ A such that a < inf B.

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