EAN: 9783030647001

Bilder-Quelle: discount24.de - Sport-Freizeit

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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