Some notes on Game Bounds (Adobe Reader) ebook download Jorge-Nuno Silva

Some notes on Game Bounds

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. In this work we establish some game bounds. 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.

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Title of ebook: Some notes on Game Bounds
ISBN: 9781599420219
parent-ISBN: 9781581120219
Publisher: Dissertation
Internet download file size: 126 kb
Pages: 19
Published: 10-2005
Released online for download: 10-31-2005
Author of eBook: Silva, Jorge-Nuno

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