Let S be a non-empty subset of R that is bounded below. Prove that a lower bound m of S is the infimum of S if and only if for every ε > 0 there exists tε ∈S such that tε

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.5: Permutations And Inverses
Problem 5E: Let f:AA, where A is nonempty. Prove that f a has right inverse if and only if f(f1(T))=T for every...
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Let S be a non-empty subset of R that is bounded below. Prove that a lower bound m of S is the infimum of S if and only if for every ε > 0 there exists tε ∈S such that tε <m+ε.

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