Suppose that SCR is a non-empty set which is bounded below. Define a set R by R= {bER| b is a lower bound for S}. Prove that sup R = inf S.
Suppose that SCR is a non-empty set which is bounded below. Define a set R by R= {bER| b is a lower bound for S}. Prove that sup R = inf S.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 18E: Let (A) be the power set of the nonempty set A, and let C denote a fixed subset of A. Define R on...
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Can you please provide a bit more details to the first part of the proof where L=SupR.
How do you know that sup R is a lower bound for S?
How do you know that it is greater than or equal to every other lower bound?
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