On Numbers and Games

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 eminently enjoyable guide to game theory. By defining numbers as the strengths of positions in certain games, the author arrives at a new class, the surreal numbers, that includes both real numbers and ordinal numbers. These surreal numbers are applied in the author's mathematical analysis of game strategies. The additions to the Second Edition present recent developments in the area of mathematical game theory, with a concentration on surreal numbers and the additive theory of partizan games.

ISBN 1568811276   Pages 256 ISBN13 9781568811277 (What's this?)   Volumes 001 Publisher Taylor & Francis Inc   Weight (grammes) 476 Imprint A K Peters   Published in Natick Format Hardback   Previous ISBN 9780121863500 Publication date 01 Dec 2000   Height (mm) 235 Library of Congress QA241.C69   Width (mm) 185 DEWEY 519.3   Spine width (mm) 19 DEWEY edition DC21   Academic level Undergraduate, Postgraduate, Professional / Scholarly

		Prologue
		Preface
Ch. 0		All Numbers Great and Small		3
Ch. 1		The Class No is a Field		15
Ch. 2		The Real and Ordinal Numbers		23
Ch. 3		The Structure of the Genral Surreal Number		29
Ch. 4		Algebra and Analysis of Numbers		39
Ch. 5		Number Theory in the Land of Oz		45
Ch. 6		The Curious Field On[subscript 2]		50
		Appendix to Part Zero		64
Ch. 7		Playing Several Games at Once		71
Ch. 8		Some Games are Already Numbers		81
Ch. 9		On Games and Numbers		97
Ch. 10		Simplifying Games		109
Ch. 11		Impartial Games and the Game of Nim		122
Ch. 12		How to Lose when you Must		122
Ch. 13		Animating Functions, Welter's Game and Hackenbush Unrestrained		153
Ch. 14		How to Play Several Games at Once in a Dozen Different Ways		173
Ch. 15		Ups, Downs and Bynumbers		188
Ch. 16		The Long and the Short and the Small		205
		Epilogue		225
		Appendix		229
		Index		235

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