On Numbers and Games est un livre de mathématiques, en anglais, écrit par John Horton Conway en 1976. Il introduit notamment le concept de nombre surréel et pose les bases de la théorie des jeux partisans.

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  • On Numbers and Games est un livre de mathématiques, en anglais, écrit par John Horton Conway en 1976. Il introduit notamment le concept de nombre surréel et pose les bases de la théorie des jeux partisans. Avec Winning Ways for your Mathematical Plays, ce livre est considéré comme fondateur de la théorie des jeux combinatoires.Conway indique dans le prologue de la seconde édition (2001) qu'il a écrit ce livre principalement parce que la théorie des nombres surréels commençait à gêner le développement de Winning Ways for your Mathematical Plays, qu'il était alors en train de coécrire avec Elwyn Berlekamp et Richard Guy. En cachette des autres coauteurs, il décida alors d'écrire un livre séparé, et après une semaine de rédaction ininterrompue, On Numbers and Games était prêt.Le livre est découpé en deux grandes parties, numérotées de façon humoristique zéro-ième et première partie. La zéro-ième partie traite des nombres surréels, puis la première partie traite des jeux partisans. Les chapitres de chaque partie sont également numérotés à partir du nombre zéro.
  • 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 est un livre de mathématiques, en anglais, écrit par John Horton Conway en 1976. Il introduit notamment le concept de nombre surréel et pose les bases de la théorie des jeux partisans.
  • 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.
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  • On Numbers and Games
  • On Numbers and Games
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