Some Notes on Game Bounds

Some Notes on Game Bounds

by Jorge-Nuno O. Silva
Some Notes on Game Bounds

Some Notes on Game Bounds

by Jorge-Nuno O. Silva

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Overview

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.


Product Details

ISBN-13: 9781581120219
Publisher: Dissertation.Com
Publication date: 05/19/1998
Pages: 108
Product dimensions: 5.50(w) x 8.50(h) x 0.26(d)

Table of Contents

Acknowledgmentii
Dedicationiii
Table of Contentsiv
Abstract1
Chapter 1Basic Definitions2
Chapter 2Birthdays4
Chapter 3Bounds for Numbers5
Chapter 4Bounds for Infinifesimals7
Bibliography11
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