Which Numbers Are Real?

Michael Henle

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Language: English

Published by Mathematical Association Of America (MAA) Sep 2012, 2012

0883857774 / 9780883857779

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Neuware - Everyone knows the real numbers, those fundamental quantities that make possible all of mathematics from high school algebra and Euclidean geometry through the Calculus and beyond; and also serve as the basis for measurement in science, industry, and ordinary life. This book surveys alternative real number systems: systems that generalize and extend the real numbers yet stay close to these properties that make the reals central to mathematics. Alternative real numbers include many different kinds of numbers, for example multidimensional numbers (the complex numbers, the quaternions and others), infinitely small and infinitely large numbers (the hyperreal numbers and the surreal numbers), and numbers that represent positions in games (the surreal numbers). Each system has a well-developed theory, including applications to other areas of mathematics and science, such as physics, the theory of games, multi-dimensional geometry, and formal logic. They are all active areas of current mathematical research and each has unique features, in particular, characteristic methods of proof and implications for the philosophy of mathematics, both highlighted in this book. Alternative real number systems illuminate the central, unifying role of the real numbers and include some exciting and eccentric parts of mathematics.Which Numbers Are Real Will be of interest to anyone with an interest in numbers, but specifically to upper-level undergraduates, graduate students, and professional mathematicians, particularly college mathematics teachers.…

Seller Inventory # 9780883857779

Title
Which Numbers Are Real?
Author
Michael Henle
Publisher
Mathematical Association Of America (MAA) Sep 2012
Publication year
2012
Condition
Neu
Binding
Buch
Language
English
ISBN 10
0883857774
ISBN 13
9780883857779
Item weight
431 grams
Dimensions
231x155x18 mm

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