無限の数学 How to Measure the Infinite: Mathematics with Infinite and Infinitesimal Numbers

Benci, Vieri/ Di Nasso, Mauro

World Scientific Publishing Co Pte Ltd（2019/02発売）

• 製本 Hardcover:ハードカバー版／ページ数 348 p.
• 言語 ENG
• 商品コード 9789812836373
• DDC分類 515.24

Full Description

'This text shows that the study of the almost-forgotten, non-Archimedean mathematics deserves to be utilized more intently in a variety of fields within the larger domain of applied mathematics.'CHOICEThis book contains an original introduction to the use of infinitesimal and infinite numbers, namely, the Alpha-Theory, which can be considered as an alternative approach to nonstandard analysis.The basic principles are presented in an elementary way by using the ordinary language of mathematics; this is to be contrasted with other presentations of nonstandard analysis where technical notions from logic are required since the beginning. Some applications are included and aimed at showing the power of the theory.The book also provides a comprehensive exposition of the Theory of Numerosity, a new way of counting (countable) infinite sets that maintains the ancient Euclid's Principle: 'The whole is larger than its parts'. The book is organized into five parts: Alpha-Calculus, Alpha-Theory, Applications, Foundations, and Numerosity Theory.

Contents

Cardinal and Ordinal Numbers: An Overview; Numerosities of Infinite Sets; The -Calculus; The -Theory; Nonstandard Analysis; Foundational Aspects.