On Numbers and Games

I read the first edition of this book as an undergraduate student of mathematics and, like many of my peers, was astonished at the effortless way in which an entire new class of numbers was defined, and then extended again to embrace the world of mathematical games. It's deep, yet playful (anything which deals with 'surreal numbers' is OK by me) and accessible, although not to someone without some knowledge of algebra. Conway is an inventive genius and nowhere is that more obvious than in this book.
(The copy catalogued here is the second edition of 2001; the original dates from 1976, when I first read it.)
This ranks with "Mathematics made difficult" and most of Martin Gardner's mathematical diversions as essential reading for show more enthusiasts of mathematics. It reminds you why it's fun. show less

Cet ouvrage traite de l'aspect mathématique d'une démarche qui existait parallèlement dans les deux ouvrages, Winning Ways : tome 1 et 2
Knuth a voulu faire un récit autour d'une genèse de ces notions dans Surreal Numbers
J'ai retrouvé dans la démarche de Conway la manière dont, dans les années 60, on m'avait présenté les réels à travers les coupures, avant la présentation par les suites de Cauchy

On s'approche des réels dont je reste convaincu que nous n'avons, à l'heure actuelle, qu'une approche assez réduite. Comme un voyageur parcourant les océans le long de routes balisées.
On peut s'en apercevoir à travers le peu de parcours possibles dans l'ensemble des transcendants (j'ai l'impression qu'on n'en connaît que show more quelques familles algébriques) ou dans l'émergence des nombres Ω show less

Indeholder "Preface", "Zeroth Part ... On Numbers", " Chapter 0: All Numbers Great and Small", " Chapter 1: The Class No is a Field", " Chapter 2: The Real and Ordinal Numbers", " Chapter 3: The Structure of the General Number", " Chapter 4: Algebra and Analysis of Numbers", " Chapter 5: Number Theory in the Land of Oz", " Chapter 6: The Curious Field On2", " Appendix to Part Zero", "First Part ... and Games", " Chapter 7: Playing Several Games at Once", " Chapter 8: Some Games are Already Numbers", " Chapter 9: On Games and Numbers", " Chapter 10: Simplifying Games", " Chapter 11: Impartial Games and the Game of Nim", " Chapter 12: How to Lose when you Must", " Chapter 13: Animated Functions, Welter's Game and Hackenbush Unrestrained", show more " Chapter 14: How to Play Several Games at Once in a Dozen Different Ways", " Chapter 15: Ups, Downs and Bynumbers", " Chapter 16: The Long and the Short and the Small", "Appendix", "Index".

"Preface" handler om ???
"Zeroth Part ... On Numbers" handler om ???
" Chapter 0: All Numbers Great and Small" handler om ???
" Chapter 1: The Class No is a Field" handler om ???
" Chapter 2: The Real and Ordinal Numbers" handler om ???
" Chapter 3: The Structure of the General Number" handler om ???
" Chapter 4: Algebra and Analysis of Numbers" handler om ???
" Chapter 5: Number Theory in the Land of Oz" handler om ???
" Chapter 6: The Curious Field On2" handler om ???
" Appendix to Part Zero" handler om ???
"First Part ... and Games" handler om ???
" Chapter 7: Playing Several Games at Once" handler om ???
" Chapter 8: Some Games are Already Numbers" handler om ???
" Chapter 9: On Games and Numbers" handler om ???
" Chapter 10: Simplifying Games" handler om ???
" Chapter 11: Impartial Games and the Game of Nim" handler om ???
" Chapter 12: How to Lose when you Must" handler om ???
" Chapter 13: Animated Functions, Welter's Game and Hackenbush Unrestrained" handler om ???
" Chapter 14: How to Play Several Games at Once in a Dozen Different Ways" handler om ???
" Chapter 15: Ups, Downs and Bynumbers" handler om ???
" Chapter 16: The Long and the Short and the Small" handler om ???
"Appendix" handler om ???
"Index" handler om ???

Conway, alias J. H. Conway alias John Horton Conway, er genial. Denne gamle bog fra 1976 er historien om hvordan man kan definere tal på en måde, så snart sagt alle mulige udvidelser springer frem af panden af sig selv. Surreal Numbers er et forsøg fra Donald Knuth på at lave en lille roman ud af disse tal.

Theorem 100: This is the last theorem in this book. (The proof is obvious). show less