On Numbers and Games

Front Cover
CRC Press, Dec 11, 2000 - Mathematics - 256 pages
7 Reviews
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.
 

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Review: On Numbers and Games

User Review  - Goodreads

Conway's approach to foundations is frustratingly poorly ordered and I urge readers to look at the appendix to section 0 first. After skimming the book once it becomes extremely lucid and insightful if not haphazard. Truly a mathematical classic. Read full review

Review: On Numbers and Games

User Review  - David Hildebrand - Goodreads

Conway's approach to foundations is frustratingly poorly ordered and I urge readers to look at the appendix to section 0 first. After skimming the book once it becomes extremely lucid and insightful if not haphazard. Truly a mathematical classic. Read full review

Contents

The Class No is a Field
11
The Real and Ordinal Numbers
19
The Structure of the General Surreal Number
25
Algebra and Analysis of Numbers
35
Number Theory in the Land of Oz
41
The Curious Field On₂
46
Appendix to Part Zero
60
FIRST PART AND GAMES
65
Simplifying Games
105
Impartial Games and the Game of Nim
118
How to Lose when you Must
132
Animating Functions Welters Game and Hackenbush Unrestrained
149
How to Play Several Games at Once in a Dozen Different Ways
169
Ups Downs and Bynumbers
184
The Long and the Short and the Small
201
Epilogue
221

Playing Several Games at Once
67
Some Games are Already Numbers
77
On Games and Numbers
93
Appendix
225
Index
231
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