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- On_Numbers_and_Games abstract "On Numbers and Games is a mathematics book by John Horton Conway first published in 1976. The book is a mathematics book, written by a preeminent mathematician, and is directed at other mathematicians. The material is, however, developed in a playful and unpretentious manner and many chapters are accessible to non-mathematicians.The book is roughly divided into two sections: the first half (or Zeroth Part), on numbers, the second half (or First Part), on games. In the first section, Conway provides an axiomatic construction of numbers and ordinal arithmetic, namely, the integers, reals, the countable infinity, and entire towers of infinite ordinals, using a notation that is essentially an almost trite (but critically important) variation of the Dedekind cut. As such, the construction is rooted in axiomatic set theory, and is closely related to the Zermelo–Fraenkel axioms. The section also covers what Conway termed "surreal numbers".Conway then notes that, in this notation, the numbers in fact belong to a larger class, the class of all two-player games. The axioms for greater than and less than are seen to be a natural ordering on games, corresponding to which of the two players may win. The remainder of the book is devoted to exploring a number of different (non-traditional, mathematically inspired) two-player games, such as nim, hackenbush, and the map-coloring games col and snort. The development includes their scoring, a review of Sprague–Grundy theorem, and the inter-relationships to numbers, including their relationship to infinitesimals.The book was first published by Academic Press Inc in 1976, ISBN 0-12-186350-6, and re-released by AK Peters in 2000 (ISBN 1-56881-127-6).".
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- On_Numbers_and_Games wikiPageWikiLink Axiom.
- On_Numbers_and_Games wikiPageWikiLink Axiomatic.
- On_Numbers_and_Games wikiPageWikiLink Axiomatic_set_theory.
- On_Numbers_and_Games wikiPageWikiLink Category:1976_books.
- On_Numbers_and_Games wikiPageWikiLink Category:Combinatorial_game_theory.
- On_Numbers_and_Games wikiPageWikiLink Category:Mathematics_books.
- On_Numbers_and_Games wikiPageWikiLink Category:Systems_of_set_theory.
- On_Numbers_and_Games wikiPageWikiLink Class_(set_theory).
- On_Numbers_and_Games wikiPageWikiLink Col_(game).
- On_Numbers_and_Games wikiPageWikiLink Combinatorial_game_theory.
- On_Numbers_and_Games wikiPageWikiLink Countable_infinity.
- On_Numbers_and_Games wikiPageWikiLink Countable_set.
- On_Numbers_and_Games wikiPageWikiLink Dedekind_cut.
- On_Numbers_and_Games wikiPageWikiLink Empty_set.
- On_Numbers_and_Games wikiPageWikiLink Fuzzy_game.
- On_Numbers_and_Games wikiPageWikiLink Greater_than.
- On_Numbers_and_Games wikiPageWikiLink Hackenbush.
- On_Numbers_and_Games wikiPageWikiLink Inequality_(mathematics).
- On_Numbers_and_Games wikiPageWikiLink Infinitesimal.
- On_Numbers_and_Games wikiPageWikiLink Integer.
- On_Numbers_and_Games wikiPageWikiLink John_Horton_Conway.
- On_Numbers_and_Games wikiPageWikiLink Less_than.
- On_Numbers_and_Games wikiPageWikiLink Map-coloring_games.
- On_Numbers_and_Games wikiPageWikiLink Mathematics.
- On_Numbers_and_Games wikiPageWikiLink Nim.
- On_Numbers_and_Games wikiPageWikiLink Number.
- On_Numbers_and_Games wikiPageWikiLink Ordinal_arithmetic.
- On_Numbers_and_Games wikiPageWikiLink Ordinal_number.
- On_Numbers_and_Games wikiPageWikiLink Real_number.
- On_Numbers_and_Games wikiPageWikiLink Set_(mathematics).
- On_Numbers_and_Games wikiPageWikiLink Set_theory.
- On_Numbers_and_Games wikiPageWikiLink Sign_(mathematics).
- On_Numbers_and_Games wikiPageWikiLink Snort_(game).
- On_Numbers_and_Games wikiPageWikiLink Sprague–Grundy_theorem.
- On_Numbers_and_Games wikiPageWikiLink Star_(game_theory).
- On_Numbers_and_Games wikiPageWikiLink Surreal_number.
- On_Numbers_and_Games wikiPageWikiLink Winning_Ways_for_your_Mathematical_Plays.
- On_Numbers_and_Games wikiPageWikiLink Zermelo–Fraenkel_axioms.
- On_Numbers_and_Games wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- On_Numbers_and_Games wikiPageWikiLink Zero_game.
- On_Numbers_and_Games wikiPageWikiLinkText "(Conway, 1976)".
- On_Numbers_and_Games wikiPageWikiLinkText "John Horton Conway's book".
- On_Numbers_and_Games wikiPageWikiLinkText "On Numbers and Games".
- On_Numbers_and_Games hasPhotoCollection On_Numbers_and_Games.
- On_Numbers_and_Games wikiPageUsesTemplate Template:Italic_title.
- On_Numbers_and_Games subject Category:1976_books.
- On_Numbers_and_Games subject Category:Combinatorial_game_theory.
- On_Numbers_and_Games subject Category:Mathematics_books.
- On_Numbers_and_Games subject Category:Systems_of_set_theory.
- On_Numbers_and_Games hypernym Book.
- On_Numbers_and_Games type Book.
- On_Numbers_and_Games type Work.
- On_Numbers_and_Games type Book.
- On_Numbers_and_Games type Combinatoric.
- On_Numbers_and_Games type Work.
- On_Numbers_and_Games comment "On Numbers and Games is a mathematics book by John Horton Conway first published in 1976. The book is a mathematics book, written by a preeminent mathematician, and is directed at other mathematicians. The material is, however, developed in a playful and unpretentious manner and many chapters are accessible to non-mathematicians.The book is roughly divided into two sections: the first half (or Zeroth Part), on numbers, the second half (or First Part), on games.".
- On_Numbers_and_Games label "On Numbers and Games".
- On_Numbers_and_Games sameAs On_Numbers_and_Games.
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- On_Numbers_and_Games sameAs Q3352152.
- On_Numbers_and_Games sameAs Q3352152.
- On_Numbers_and_Games wasDerivedFrom On_Numbers_and_Games?oldid=621338540.
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