How To Measure The Infinite: Mathematics With Infinite And Infinitesimal Numbers
Language: English
Published by World Scientific Publishing Co Pte Ltd, SG, 2019
- Hardcover
- New
Seller: Rarewaves.com USA, London, London, United KingdomRarewaves.com USA
AbeBooks seller since June 11, 2025
Condition: New
£ 163.79
Quantity: Over 20 available
Add to basketItem description from seller
"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. …
Seller Inventory # LU-9789812836373
- Title
- How To Measure The Infinite: Mathematics With Infinite And Infinitesimal Numbers
- Author
- Mauro Di Nasso, Vieri Benci
- Publisher
- World Scientific Publishing Co Pte Ltd, SG
- Publication year
- 2019
- Condition
- New
- Binding
- Hardback
- Language
- English
- ISBN 10
- 9812836373
- ISBN 13
- 9789812836373
- Dimensions
- 16.99 x 2.06 x 24.41 cm
This 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.
"Synopsis" may belong to another edition of this title.
From the Back Cover
This book is the result of a scientific collaboration among different perspectives of mathematics. The first author is a leading figure in variational and topological methods in nonlinear analysis, and has cultivated a broad range of interests in applications of mathematics; while the second author is a specialist in mathematical logic and in the foundations of nonstandard analysis.
"About the title" may belong to another edition of this title.
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