How To Measure The Infinite: Mathematics With Infinite And Infinitesimal Numbers
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?-Theory
A01=Mauro Di Nasso
A01=Vieri Benci
Alpha-Theory
Author_Mauro Di Nasso
Author_Vieri Benci
AZA+--Theory
Calculus
Category=PBK
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Infinitesimal Numbers
Nonstandard Analysis
Nonstandard Models
Nonstandard Set Theories
Numerosities
Product details
- ISBN 9789812836373
- Publication Date: 28 Feb 2019
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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"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.
