| 书目名称 | Real Analysis: Foundations | | 编辑 | Sergei Ovchinnikov | | 视频video | | | 概述 | Explores the foundations of real analysis using the framework of general ordered fields, demonstrating the multifaceted nature of the area.Illustrates the definitions and logical interrelations betwee | | 丛书名称 | Universitext | | 图书封面 |  | | 描述 | .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 o | | 出版日期 | Textbook 2021 | | 关键词 | Real analysis ordered fields; Real analysis rational numbers; Real analysis textbook; Real analysis fou | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-64701-8 | | isbn_softcover | 978-3-030-64700-1 | | isbn_ebook | 978-3-030-64701-8Series ISSN 0172-5939 Series E-ISSN 2191-6675 | | issn_series | 0172-5939 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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发表于 2025-3-21 16:25:31
