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SECTION 1.2 emphasizes the principleof mathematical induction. SECTION 1.3 introduces basic ideas of set theory in the context of sets of real num- bers. In this section we prove two fundamental theorems: the Heine–Borel and Bolzano– Weierstrass theorems.
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Library of Congress Cataloging-in-PublicationData Trench, William F. Introduction to real analysis / William F. Trench p. cm. ISBN 0-13-045786-8 1. MathematicalAnalysis. I. Title.
What does section 1.1 of real analysis begin with?
Section 1.1 begins with a brief dis- cussion of the axioms for a complete ordered field, but no attempt is made to develop the reals from them; rather, it is assumed that the student is familiar with the consequences of these axioms, except for one: completeness.
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