How to measure the infinite: mathematics with infinite and infinitesimal numbers
"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 mathemat...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Publishing Company Pte Limited
2019
|
| Schlagworte: | |
| Online-Zugang: | UBY01 Volltext |
| Zusammenfassung: | "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."-- |
| Beschreibung: | Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader |
| Beschreibung: | 1 online resource (348 pages) illustrations |
| ISBN: | 9789812836380 |
Internformat
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| 245 | 1 | 0 | |a How to measure the infinite |b mathematics with infinite and infinitesimal numbers |c Vieri Benci, Mauro di Nasso |
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| 505 | 8 | |a Includes bibliographical references and index | |
| 520 | |a "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."-- | ||
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Datensatz im Suchindex
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| contents | Includes bibliographical references and index |
| ctrlnum | (ZDB-124-WOP)00007081 (OCoLC)1190676781 (DE-599)BVBBV046808191 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Electronic eBook |
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| illustrated | Illustrated |
| index_date | 2024-07-03T14:58:09Z |
| indexdate | 2024-07-10T08:54:24Z |
| institution | BVB |
| isbn | 9789812836380 |
| language | English |
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| spelling | Benci, Vieri 1949- Verfasser (DE-588)1209642123 aut How to measure the infinite mathematics with infinite and infinitesimal numbers Vieri Benci, Mauro di Nasso Singapore World Scientific Publishing Company Pte Limited 2019 1 online resource (348 pages) illustrations txt rdacontent c rdamedia cr rdacarrier Mode of access: World Wide Web. - System requirements: Adobe Acrobat Reader Includes bibliographical references and index "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."-- Nonstandard mathematical analysis Calculus Series, Infinite Nichtarchimedische Analysis (DE-588)4171709-0 gnd rswk-swf Transfinite Zahl (DE-588)4471005-7 gnd rswk-swf Infinitesimalanalysis (DE-588)4161657-1 gnd rswk-swf Electronic books Nichtarchimedische Analysis (DE-588)4171709-0 s Infinitesimalanalysis (DE-588)4161657-1 s Transfinite Zahl (DE-588)4471005-7 s DE-604 Di Nasso, Mauro Sonstige oth Erscheint auch als Druck-Ausgabe 9789812836373 https://www.worldscientific.com/worldscibooks/10.1142/7081 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Benci, Vieri 1949- How to measure the infinite mathematics with infinite and infinitesimal numbers Includes bibliographical references and index Nonstandard mathematical analysis Calculus Series, Infinite Nichtarchimedische Analysis (DE-588)4171709-0 gnd Transfinite Zahl (DE-588)4471005-7 gnd Infinitesimalanalysis (DE-588)4161657-1 gnd |
| subject_GND | (DE-588)4171709-0 (DE-588)4471005-7 (DE-588)4161657-1 |
| title | How to measure the infinite mathematics with infinite and infinitesimal numbers |
| title_auth | How to measure the infinite mathematics with infinite and infinitesimal numbers |
| title_exact_search | How to measure the infinite mathematics with infinite and infinitesimal numbers |
| title_exact_search_txtP | How to measure the infinite mathematics with infinite and infinitesimal numbers |
| title_full | How to measure the infinite mathematics with infinite and infinitesimal numbers Vieri Benci, Mauro di Nasso |
| title_fullStr | How to measure the infinite mathematics with infinite and infinitesimal numbers Vieri Benci, Mauro di Nasso |
| title_full_unstemmed | How to measure the infinite mathematics with infinite and infinitesimal numbers Vieri Benci, Mauro di Nasso |
| title_short | How to measure the infinite |
| title_sort | how to measure the infinite mathematics with infinite and infinitesimal numbers |
| title_sub | mathematics with infinite and infinitesimal numbers |
| topic | Nonstandard mathematical analysis Calculus Series, Infinite Nichtarchimedische Analysis (DE-588)4171709-0 gnd Transfinite Zahl (DE-588)4471005-7 gnd Infinitesimalanalysis (DE-588)4161657-1 gnd |
| topic_facet | Nonstandard mathematical analysis Calculus Series, Infinite Nichtarchimedische Analysis Transfinite Zahl Infinitesimalanalysis |
| url | https://www.worldscientific.com/worldscibooks/10.1142/7081 |
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