Use the Reflection Principle and analogous results about suprema to prove the following results. a) [APPROXIMATION PROPERTY FOR INFIMA] Prove that if a set E R has a finite infimum and > 0 is any positive number, then there is a point a E such that inf E + > a > inf E. b) [COMPLETENESS

Use the Reflection Principle and analogous results about suprema to prove the following results.
a) [APPROXIMATION PROPERTY FOR INFIMA] Prove that if a set E ⊂ R has a finite infimum and ε > 0 is any positive number, then there is a point a ∈ E such that inf E + ε > a > inf E.
b) [COMPLETENESS PROPERTY FOR INFIMA] If E ⊂ R is nonempty and bounded below, then E has a (finite) infimum.

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Related Book For answer-question

An Introduction to Analysis

4th edition

Authors: William R. Wade

ISBN: 978-0132296380