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Some Notes on Game Bounds

Name: Some Notes on Game Bounds
Brand: Dissertation.Com. - Do Not Use
SKU: 08743892
Price: 20.32 EUR
Availability: InStock
Author: Jorge Nuno Silva
ISBN: 9781581120219

Jorge Nuno Silva

Language

English

Book Paperback

Libristo code: 08743892

Publishers Dissertation.Com. - Do Not Use, May 1998

Combinatorial Games are a generalization of real numbers. Each game has a recursively defined comple... Full description

Libristo code: 08743892

49 b

20.32 €

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Combinatorial Games are a generalization of real numbers. Each game has a recursively defined complexity (birthday). In this paper we establish some game bounds. We find some limit cases for how big and how small a game can be, based on its complexity. For each finite birthday, N, we find the smallest positive number and the greatest game born by day N, as well as the smallest and the largest positive infinitesimals. As for each particular birthday we provide the extreme values for those types of games, these results extend those in [1, page 214]. The main references in the theory of combinatorial games are ONAG [1] and WW [2]. We'll use the notation and some fundamental results from WW---mainly from its first six chapters---to establish some bounds to the size of the games.