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.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.2: Norms And Distance Functions
Problem 14EQ
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