On Numbers And Games
John Conway
ONAG, as the book is 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.
"ONAG is a unique and wonderful book, certainly one of the top mathematical creations of the 20th century. Warning: It is essentially as addictive as the Internet, because you will think of fascinating new things to explore as you examine every page." - Donald E Knuth, Stanford University | "Conway's fertile imagination, unconventional notation, and whimsical vocabulary produce an exotic mix of mathematics and mystery." - American Mathematical Monthly |
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