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Real Analysis: Foundations

Name: Real Analysis: Foundations
Brand: Springer Nature Switzerland AG
SKU: 36216037
Price: 52.69 EUR
Availability: InStock
Author: Sergei Ovchinnikov
ISBN: 9783030647001

Sergei Ovchinnikov

Language

English

Book Paperback

Libristo code: 36216037

Publishers Springer Nature Switzerland AG, February 2021

This textbook explores the foundations of real analysis using the framework of general ordered field... Full description

Libristo code: 36216037

129 b

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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.