Surreal Numbers - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Surreal Numbers write by Donald Ervin Knuth. This book was released on 1974. Surreal Numbers available in PDF, EPUB and Kindle. 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
An Introduction to the Theory of Surreal Numbers
An Introduction to the Theory of Surreal Numbers - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to the Theory of Surreal Numbers write by Harry Gonshor. This book was released on 1986-09-18. An Introduction to the Theory of Surreal Numbers available in PDF, EPUB and Kindle. These notes provide a formal introduction to the theory of surreal numbers in a clear and lucid style.
Mathematical Treks: From Surreal Numbers to Magic Circles
Mathematical Treks: From Surreal Numbers to Magic Circles - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mathematical Treks: From Surreal Numbers to Magic Circles write by Ivars Peterson. This book was released on 2020-08-03. Mathematical Treks: From Surreal Numbers to Magic Circles available in PDF, EPUB and Kindle.
On Numbers and Games
On Numbers and Games - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook On Numbers and Games write by John H. Conway. This book was released on 2000-12-11. On Numbers and Games available in PDF, EPUB and Kindle. Originally written to define the relation between the theories of transfinite numbers and mathematical games, the resulting work is a mathematically sophisticated but eminently enjoyable guide to game theory. By defining numbers as the strengths of positions in certain games, the author arrives at a new class that includes both real numbers and ordinal numbers: surreal numbers. The second edition presents developments in mathematical game theory, focusing on surreal numbers and the additive theory of partizan games.
Which Numbers Are Real?
Which Numbers Are Real? - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Which Numbers Are Real? write by Michael Henle. This book was released on 2012-12-31. Which Numbers Are Real? available in PDF, EPUB and Kindle. 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.
