Suppose that ACR is bounded below, and define B = {b € R | b is a lower bound for A}. Prove that sup B = inf A. Use (a) to explain why there is no need to assert that greatest upper bounds exist as part of the Axiom of Completeness.
Suppose that ACR is bounded below, and define B = {b € R | b is a lower bound for A}. Prove that sup B = inf A. Use (a) to explain why there is no need to assert that greatest upper bounds exist as part of the Axiom of Completeness.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 75E
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