Surreal Numbers

Author : Donald Ervin Knuth
Publisher : Addison-Wesley Professional
ISBN 13 : 9780201038125
Total Pages : 130 pages
Book Rating : 4.29/5 ( download)

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Download or read book Surreal Numbers written by Donald Ervin Knuth and published by Addison-Wesley Professional. This book was released on 1974 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nearly 30 years ago, John Horton Conway introduced a new way to construct numbers. Donald E. Knuth, in appreciation of this revolutionary system, took a week off from work on The Art of Computer Programming to write an introduction to Conway's method. Never content with the ordinary, Knuth wrote this introduction as a work of fiction--a novelette. If not a steamy romance, the book nonetheless shows how a young couple turned on to pure mathematics and found total happiness. The book's primary aim, Knuth explains in a postscript, is not so much to teach Conway's theory as "to teach how one might go about developing such a theory." He continues: "Therefore, as the two characters in this book gradually explore and build up Conway's number system, I have recorded their false starts and frustrations as well as their good ideas. I wanted to give a reasonably faithful portrayal of the important principles, techniques, joys, passions, and philosophy of mathematics, so I wrote the story as I was actually doing the research myself."... It is an astonishing feat of legerdemain. An empty hat rests on a table made of a few axioms of standard set theory. Conway waves two simple rules in the air, then reaches into almost nothing and pulls out an infinitely rich tapestry of numbers that form a real and closed field. Every real number is surrounded by a host of new numbers that lie closer to it than any other "real" value does. The system is truly "surreal." quoted from Martin Gardner, Mathematical Magic Show, pp. 16--19 Surreal Numbers, now in its 13th printing, will appeal to anyone who might enjoy an engaging dialogue on abstract mathematical ideas, and who might wish to experience how new mathematics is created. 0201038129B04062001

Author : Harry Gonshor
Publisher : Cambridge University Press
ISBN 13 : 0521312051
Total Pages : 205 pages
Book Rating : 4.59/5 ( download)

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Download or read book An Introduction to the Theory of Surreal Numbers written by Harry Gonshor and published by Cambridge University Press. This book was released on 1986-09-18 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes provide a formal introduction to the theory of surreal numbers in a clear and lucid style.

Author : Ivars Peterson
Publisher : American Mathematical Soc.
ISBN 13 : 1470458519
Total Pages : 170 pages
Book Rating : 4.15/5 ( download)

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Download or read book Mathematical Treks: From Surreal Numbers to Magic Circles written by Ivars Peterson and published by American Mathematical Soc.. This book was released on 2020-08-03 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : John H. Conway
Publisher : CRC Press
ISBN 13 : 1439864152
Total Pages : 253 pages
Book Rating : 4.59/5 ( download)

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Download or read book On Numbers and Games written by John H. Conway and published by CRC Press. This book was released on 2000-12-11 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: ONAG, as the book is commonly known, is one of those rare publications that sprang to life in a moment of creative energy and has remained influential for over a quarter of a century. Originally written to define the relation between the theories of transfinite numbers and mathematical games, the resulting work is a mathematically sophisticated but

Author : N.L. Alling
Publisher : Elsevier
ISBN 13 : 9780080872520
Total Pages : 372 pages
Book Rating : 4.22/5 ( download)

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Download or read book Foundations of Analysis over Surreal Number Fields written by N.L. Alling and published by Elsevier. This book was released on 1987-04-01 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, a tower of surreal number fields is defined, each being a real-closed field having a canonical formal power series structure and many other higher order properties. Formal versions of such theorems as the Implicit Function Theorem hold over such fields. The Main Theorem states that every formal power series in a finite number of variables over a surreal field has a positive radius of hyper-convergence within which it may be evaluated. Analytic functions of several surreal and surcomplex variables can then be defined and studied. Some first results in the one variable case are derived. A primer on Conway's field of surreal numbers is also given. Throughout the manuscript, great efforts have been made to make the volume fairly self-contained. Much exposition is given. Many references are cited. While experts may want to turn quickly to new results, students should be able to find the explanation of many elementary points of interest. On the other hand, many new results are given, and much mathematics is brought to bear on the problems at hand.

Author : Gary Rimmer
Publisher : Red Wheel Weiser
ISBN 13 : 1609259041
Total Pages : 244 pages
Book Rating : 4.44/5 ( download)

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Download or read book Number Freaking written by Gary Rimmer and published by Red Wheel Weiser. This book was released on 2006-01-01 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This isn’t a book of statistics and it isn’t a book of science. It has nothing whatsoever to do with actuaries or accountants. Number Freaking is a book of surreal sums and absurd arithmetic: it’s doodling with numbers, doing sums in your head just for fun, playing dice with the universe. It’s the art of putting numbers where none existed before to take an off-the-wall peek behind the curtains at how numbers rule our lives. It’s about taking numbers that were never meant to be in the same room, crashing them together and seeing what comes out the other end. Number Freaking reveals the low drama of life, the unexpected realities and unforeseen truths that emerge only when numbers are tested to destruction. How long would it take to drive your car to the moon? How many people on Earth are drunk right now? If you were falling from the world’s tallest building, would you have time to phone a friend to say goodbye? Which is more crowded: Jakarta, an IKEA store or Hell? How long will it take for America to eventually collide with Japan? What's a decent boyfriend worth… in chocolate? Discover for yourself how far you walk in a lifetime, how many people have ever lived and how to cure world debt in this essential guide to modern life.

Author : Michael Henle
Publisher : American Mathematical Soc.
ISBN 13 : 0883857774
Total Pages : 231 pages
Book Rating : 4.79/5 ( download)

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Download or read book Which Numbers Are Real? written by Michael Henle and published by American Mathematical Soc.. This book was released on 2012-12-31 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : John H. Conway
Publisher : CRC Press
ISBN 13 : 1439864896
Total Pages : 442 pages
Book Rating : 4.90/5 ( download)

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Download or read book The Symmetries of Things written by John H. Conway and published by CRC Press. This book was released on 2016-04-05 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Start with a single shape. Repeat it in some way—translation, reflection over a line, rotation around a point—and you have created symmetry. Symmetry is a fundamental phenomenon in art, science, and nature that has been captured, described, and analyzed using mathematical concepts for a long time. Inspired by the geometric intuition of Bill Thurston and empowered by his own analytical skills, John Conway, with his coauthors, has developed a comprehensive mathematical theory of symmetry that allows the description and classification of symmetries in numerous geometric environments. This richly and compellingly illustrated book addresses the phenomenological, analytical, and mathematical aspects of symmetry on three levels that build on one another and will speak to interested lay people, artists, working mathematicians, and researchers.

Author : Alain Badiou
Publisher : John Wiley & Sons
ISBN 13 : 1509534067
Total Pages : 240 pages
Book Rating : 4.67/5 ( download)

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Download or read book Number and Numbers written by Alain Badiou and published by John Wiley & Sons. This book was released on 2018-05-18 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The political regime of global capitalism reduces the world to an endless network of numbers within numbers, but how many of us really understand what numbers are? Without such an understanding, how can we challenge the regime of number? In Number and Numbers Alain Badiou offers an philosophically penetrating account with a powerful political subtext of the attempts that have been made over the last century to define the special status of number. Badiou argues that number cannot be defined by the multiform calculative uses to which numbers are put, nor is it exhausted by the various species described by number theory. Drawing on the mathematical theory of surreal numbers, he develops a unified theory of Number as a particular form of being, an infinite expanse to which our access remains limited. This understanding of Number as being harbours important philosophical truths about the structure of the world in which we live. In Badiou's view, only by rigorously thinking through Number can philosophy offer us some hope of breaking through the dense and apparently impenetrable capitalist fabric of numerical relations. For this will finally allow us to point to that which cannot be numbered: the possibility of an event that would deliver us from our unthinking subordination of number.

Author : John H. Conway
Publisher : Springer Science & Business Media
ISBN 13 : 1461240727
Total Pages : 313 pages
Book Rating : 4.23/5 ( download)

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Download or read book The Book of Numbers written by John H. Conway and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: "...the great feature of the book is that anyone can read it without excessive head scratching...You'll find plenty here to keep you occupied, amused, and informed. Buy, dip in, wallow." -IAN STEWART, NEW SCIENTIST "...a delightful look at numbers and their roles in everything from language to flowers to the imagination." -SCIENCE NEWS "...a fun and fascinating tour of numerical topics and concepts. It will have readers contemplating ideas they might never have thought were understandable or even possible." -WISCONSIN BOOKWATCH "This popularization of number theory looks like another classic." -LIBRARY JOURNAL