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- Author: Donald E. Knuth
- Pages: 119
- Language: English
- ISBN/ASIN: 201038129
- ISBN13: 9780201038125
- Upload date: 27-12-2016, 12:32
- Category: Mathematics

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.

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Penrose Tiles to Trapdoor Ciphers Which Numbers Are Real? The Whole Truth About Whole Numbers: An Elementary Introduction to Number Theory The Structure of the Real Number System The Real Numbers: An Introduction to Set Theory and Analysis (Undergraduate Texts in Mathematics) The Real Numbers and Real Analysis The Magic Numbers of Dr. Matrix The Higher Arithmetic: An Introduction to the Theory of Numbers The Book of Numbers,1st edition Set Theory and Logic (Dover Books on Mathematics) Prime Numbers 101: A Primer on Number Theory On Numbers and Games (L.M.S. Monographs No. 6) Numbers: Rational and Irrational (New Mathematical Library) Numbers: A Very Short Introduction Number, Shape, & Symmetry: An Introduction to Number Theory, Geometry, and Group Theory Number Theory: An Introduction to Mathematics: Part B Number Story: From Counting to Cryptography Mathematical Games: The Entire Collection of His Scientific American Columns Elementary Number Theory with Programming Catalan Numbers Applications of Fibonacci Numbers: Volume 7 An Introduction to the Theory of Numbers, 6 Edition Algebra and Number Theory: An Integrated Approach A Concise Introduction to Pure Mathematics, Third Edition