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An introduction to Conway’s games and numbers

Title data

Schleicher, Dierk ; Stoll, Michael:
An introduction to Conway’s games and numbers.
In: Moscow Mathematical Journal. Vol. 6 (2006) Issue 2 . - pp. 359-388.
ISSN 1609-3321

Official URL: Volltext

Abstract in another language

This note attempts to furnish John H. Conway's combinatorial game theory with an introduction that is easily accessible and yet mathematically precise and self-contained and which provides complete statements and proofs for some of the folklore in the subject.
Conway's theory is a fascinating and rich theory based on a simple and intuitive recursive definition of games, which yields a very rich algebraic structure. Games form an abelian GROUP in a very natural way. A certain subgroup of games, called numbers, is a FIELD that contains both the real numbers and the ordinal numbers. Conway's theory is deeply satisfying from a theoretical point of view, and at the same time it has useful applications to specific games such as Go.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: Conway game, surreal number, combinatorial game theory
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II > Chair Mathematics II - Univ.-Prof. Dr. Michael Stoll
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 22 Jan 2015 12:10
Last Modified: 12 Feb 2015 12:08
URI: https://eref.uni-bayreuth.de/id/eprint/5829