EAN: 9783030647001

UNIVERSITEXT REAL ANALYSIS FOUNDATIONS - SERG...

This textbook explores the foundations of real analysis using the framework of general ordered
fields  demonstrating the multifaceted nature of the area. Focusing on the logical structure of
real analysis  the definitions and interrelations between core concepts are illustrated with
the use of numerous examples and counterexamples. Readers will learn of the equivalence between
various theorems and the completeness property of the underlying ordered field. These
equivalences emphasize the fundamental role of real numbers in analysis.Comprising six chapters
the book opens with a rigorous presentation of the theories of rational and real numbers in the
framework of ordered fields. This is followed by an accessible exploration of standard topics
of elementary real analysis  including continuous functions  differentiation  integration  and
infinite series. Readers will find this text conveniently self-contained  with three appendices
included after the main text  covering an overview of natural numbers and integers  Dedekind's
construction of real numbers  historical notes  and selected topics in algebra. Real Analysis:
Foundations is ideal for students at the upper-undergraduate or beginning graduate level who
are interested in the logical underpinnings of real analysis. With over 130 exercises  it is
suitable for a one-semester course on elementary real analysis  as well as independent study.

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