About the Book
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 45. Chapters: Surreal number, Solved game, Nim, Sprague-Grundy theorem, Nimber, Impartial game, On Numbers and Games, Col, Shannon switching game, Game complexity, Go and mathematics, Angel problem, Jenga, Octal game, Domineering, Chomp, Genus theory, Map-coloring games, Shannon number, Game tree, Hackenbush, Kayles, Cram, Hot game, Subtract a square, Mis re, Pebble game, Toads and Frogs, Grundy's game, Star, Winning Ways for your Mathematical Plays, Maker-Breaker game, Sylver coinage, Sim, Tiny and miny, Variation, Indistinguishability quotient, Fuzzy game, Clobber, Disjunctive sum, Bulgarian solitaire, Branching factor, Positional game, Generalized game, Mex, Zero game, Partisan game, Null move, Sum of combinatorial games. Excerpt: In mathematics, the surreal number system is an arithmetic continuum containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share many properties with the reals, including a total order and the usual arithmetic operations (addition, subtraction, multiplication, and division); as such, they form an ordered field. In a rigorous set theoretic sense, the surreal numbers are the largest possible ordered field; all other ordered fields, such as the rationals, the reals, the rational functions, the Levi-Civita field, the superreal numbers, and the hyperreal numbers, are subfields of the surreals. The surreals also contain all transfinite ordinal numbers reachable in the set theory in which they are constructed. The definition and construction of the surreals is due to John Horton Conway. They were introduced in Donald Knuth's 1974 book Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness. This book is a mathematical novelette, and is notable as one of the...
