# The Real Numbers and Real Analysis

## Ethan D. Bloch

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This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus.

The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.

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From the Back Cover:

This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs.  The choice of material and the flexible organization, including three different entryways into the study of the real numbers, making it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus.  The Real Numbers and Real Analysis is accessible to students who have prior experience with mathematical proofs and who have not previously studied real analysis. The text includes over 350 exercises.

Key features of this textbook:

- provides an unusually thorough treatment of the real numbers, emphasizing their importance as the basis of real analysis

- presents material in an order resembling that of standard calculus courses, for the sake of student familiarity, and for helping future teachers use real analysis to better understand calculus

- emphasizes the direct role of the Least Upper Bound Property in the study of limits, derivatives and integrals, rather than relying upon sequences for proofs; presents the equivalence of various important theorems of real analysis with the Least Upper Bound Property

- includes a thorough discussion of some topics, such as decimal expansion of real numbers, transcendental functions, area and the number p, that relate to calculus but that are not always treated in detail in real analysis texts

- offers substantial historical material in each chapter

This book will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.

Dr. Ethan D. Bloch of Bard College is the author of two Springer publications "A First Course in Geometric Topology and Differential Geometry," and the first and second editions of, "Proofs and Fundamentals: A First Course in Abstract Mathematics." More information about Dr. Ethan D. Bloch can be found on his person web page: http://math.bard.edu/bloch

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## 1.The Real Numbers and Real Analysis (Hardback)

Editorial: Springer-Verlag New York Inc., United States (2011)
ISBN 10: 0387721762 ISBN 13: 9780387721767
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(London, Reino Unido)
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Descripción Springer-Verlag New York Inc., United States, 2011. Hardback. Estado de conservación: New. 2011 ed.. Language: English . Brand New Book. This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus. Nº de ref. de la librería AAU9780387721767

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## 2.The Real Numbers and Real Analysis

Editorial: Springer (2011)
ISBN 10: 0387721762 ISBN 13: 9780387721767
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Descripción Springer, 2011. Estado de conservación: New. 2011. 2011th Edition. Hardcover. . . . . . . Nº de ref. de la librería V9780387721767

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## 3.The Real Numbers and Real Analysis

Editorial: Springer New York 2011-05-27, New York (2011)
ISBN 10: 0387721762 ISBN 13: 9780387721767
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Descripción Springer New York 2011-05-27, New York, 2011. hardback. Estado de conservación: New. Nº de ref. de la librería 9780387721767

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## 4.The Real Numbers and Real Analysis

Editorial: Springer
ISBN 10: 0387721762 ISBN 13: 9780387721767
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Descripción Springer. Hardcover. Estado de conservación: New. New copy - Usually dispatched within 2 working days. Nº de ref. de la librería B9780387721767

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## 5.The Real Numbers and Real Analysis (Hardback)

Editorial: Springer-Verlag New York Inc., United States (2011)
ISBN 10: 0387721762 ISBN 13: 9780387721767
Librería
The Book Depository US
(London, Reino Unido)
Valoración

Descripción Springer-Verlag New York Inc., United States, 2011. Hardback. Estado de conservación: New. 2011 ed.. Language: English . Brand New Book. This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus. Nº de ref. de la librería AAU9780387721767

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## 6.The Real Numbers and Real Analysis

Editorial: Springer-Verlag New York Inc. (2011)
ISBN 10: 0387721762 ISBN 13: 9780387721767
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Descripción Springer-Verlag New York Inc., 2011. HRD. Estado de conservación: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. de la librería BB-9780387721767

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## 7.The Real Numbers and Real Analysis

Editorial: Springer
ISBN 10: 0387721762 ISBN 13: 9780387721767
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Descripción Springer. Estado de conservación: New. 2011. 2011th Edition. Hardcover. . . . . . Books ship from the US and Ireland. Nº de ref. de la librería V9780387721767

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## 8.The Real Numbers and Real Analysis

Editorial: Springer-Verlag New York Inc. (2011)
ISBN 10: 0387721762 ISBN 13: 9780387721767
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Descripción Springer-Verlag New York Inc., 2011. HRD. Estado de conservación: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería IP-9780387721767

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## 9.The Real Numbers and Real Analysis

Editorial: Springer (2011)
ISBN 10: 0387721762 ISBN 13: 9780387721767
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Descripción Springer, 2011. Estado de conservación: New. Nº de ref. de la librería EH9780387721767

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## 10.The Real Numbers and Real Analysis

Editorial: Springer (2016)
ISBN 10: 0387721762 ISBN 13: 9780387721767
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Descripción Springer, 2016. Paperback. Estado de conservación: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Nº de ref. de la librería ria9780387721767_lsuk

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