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Which numbers are real?

Author: Michael Henle
Publisher: Washington, D.C. : Mathematical Association of America, ©2012.
Series: Classroom resource materials (Unnumbered)
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
The set of real numbers is one of the fundamental concepts of mathematics. This book surveys alternative number systems: systems that generalise the real numbers yet stay close to the properties that make the reals central to mathematics. There are many alternative number systems, such as multidimensional numbers (complex numbers, quarternions), infinitely small and infinitely large numbers (hyperreal numbers) and  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Michael Henle
ISBN: 9780883857779 0883857774 9781614441076 1614441073
OCLC Number: 806199380
Description: x, 219 pages : illustrations ; 23 cm.
Contents: [Pt.] I. The reals. Axioms for the reals --
Construction of the reals --
[pt.] II. Multi-dimensional numbers. The complex numbers --
The quaternions --
[pt.] III. Alternative lines. The constructive reals --
The hyperreals --
The surreals.
Series Title: Classroom resource materials (Unnumbered)
Responsibility: Michael Henle.
More information:

Abstract:

The set of real numbers is one of the fundamental concepts of mathematics. This book surveys alternative number systems: systems that generalise the real numbers yet stay close to the properties that make the reals central to mathematics. There are many alternative number systems, such as multidimensional numbers (complex numbers, quarternions), infinitely small and infinitely large numbers (hyperreal numbers) and numbers that represent positions in games (surreal numbers). Each system has a well-developed theory with applications in other areas of mathematics and science. They all feature in active areas of research and each has unique features that are explored in this book. Alternative number systems reveal the central role of the real numbers and motivate some exciting and eccentric areas of mathematics. What Numbers Are Real? will be an illuminating read for anyone with an interest in numbers, but specifically for advanced undergraduates, graduate students and teachers of university-level mathematics.

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