On Numbers and Games (original) (raw)
On Numbers and Games (Sobre números y juegos) es un libro de John Horton Conway publicado por primera vez en 1976. Aunque el libro está dirigido a otros matemáticos, está desarrollado de una manera lúdica y sin pretensiones, y muchos capítulos son accesibles para los no matemáticos. Martin Gardner discutió el libro extensamente, particularmente la construcción de números surreales de Conway, en su columna Mathematical Games en Scientific American en septiembre de 1976.
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| dbo:abstract | On Numbers and Games (Sobre números y juegos) es un libro de John Horton Conway publicado por primera vez en 1976. Aunque el libro está dirigido a otros matemáticos, está desarrollado de una manera lúdica y sin pretensiones, y muchos capítulos son accesibles para los no matemáticos. Martin Gardner discutió el libro extensamente, particularmente la construcción de números surreales de Conway, en su columna Mathematical Games en Scientific American en septiembre de 1976. El libro está dividido aproximadamente en dos secciones: la primera mitad (o parte cero), sobre números, la segunda mitad (o primera parte), sobre juegos. En la primera sección, Conway proporciona una construcción axiomática de números y aritmética ordinal, a saber, los números enteros, reales, el infinito contable y torres enteras de infinitos ordinales, usando una notación que es esencialmente una variación casi trillada (pero críticamente importante) del corte Dedekind. Como tal, la construcción tiene sus raíces en la teoría axiomática de conjuntos y está estrechamente relacionada con los axiomas de Zermelo-Fraenkel. La sección también cubre lo que Conway (adoptando la nomenclatura de Knuth) denominó los "números surreales". Conway luego observa que, en esta notación, los números pertenecen de hecho a una clase más grande, la clase de todos los juegos de dos jugadores. Los axiomas de mayor que y menor que se consideran un orden natural en los juegos, correspondiente a cuál de los dos jugadores puede ganar. El resto del libro está dedicado a explorar una serie de juegos para dos jugadores diferentes (no tradicionales, inspirados matemáticamente), como Nim, Hackenbush y los juegos de colorear mapas Col y Snort. El desarrollo incluye su puntuación, una revisión del teorema de Sprague-Grundy y las interrelaciones con los números, incluida su relación con infinitesimales. (es) On Numbers and Games is a mathematics book by John Horton Conway first published in 1976. The book is written by a pre-eminent 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. Martin Gardner discussed the book at length, particularly Conway's construction of surreal numbers, in his Mathematical Games column in Scientific American in September 1976. 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 Zeroth Part, Conway provides axioms for arithmetic: addition, subtraction, multiplication, division and inequality. This allows an axiomatic construction of numbers and ordinal arithmetic, namely, the integers, reals, the countable infinity, and entire towers of infinite ordinals. The object to which these axioms apply takes the form {L|R}, which can be interpreted as a specialized kind of set; a kind of two-sided set. By insisting that LDedekind cut. The resulting construction yields a field, now called the surreal numbers. The ordinals are embedded in this field. The construction is rooted in axiomatic set theory, and is closely related to the Zermelo–Fraenkel axioms. In the original book, Conway simply refers to this field as "the numbers". The term "surreal numbers" is adopted later, at the suggestion of Donald Knuth. In the First Part, Conway notes that, by dropping the constraint that Lclass 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 the 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). (en) 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 zéroième et première partie. La zéroième 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. (fr) |
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| rdfs:comment | On Numbers and Games (Sobre números y juegos) es un libro de John Horton Conway publicado por primera vez en 1976. Aunque el libro está dirigido a otros matemáticos, está desarrollado de una manera lúdica y sin pretensiones, y muchos capítulos son accesibles para los no matemáticos. Martin Gardner discutió el libro extensamente, particularmente la construcción de números surreales de Conway, en su columna Mathematical Games en Scientific American en septiembre de 1976. (es) On Numbers and Games is a mathematics book by John Horton Conway first published in 1976. The book is written by a pre-eminent 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. Martin Gardner discussed the book at length, particularly Conway's construction of surreal numbers, in his Mathematical Games column in Scientific American in September 1976. (en) 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. (fr) |
| rdfs:label | On Numbers and Games (es) On Numbers and Games (fr) On Numbers and Games (en) |
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