How To Measure The Infinite Mathematics With Infinite And Infinitesimal Numbers

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How To Measure The Infinite: Mathematics With Infinite And Infinitesimal Numbers

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Author : Vieri Benci
Publisher : World Scientific
ISBN 13 : 9813276606
Total Pages : 346 pages
Book Rating : 4.8/5 (132 download)

Book Synopsis How To Measure The Infinite: Mathematics With Infinite And Infinitesimal Numbers by : Vieri Benci

Download or read book How To Measure The Infinite: Mathematics With Infinite And Infinitesimal Numbers written by Vieri Benci and published by World Scientific. This book was released on 2019-02-19 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: '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.

Arithmetic of infinity

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Author : Yaroslav D. Sergeyev
Publisher : Yaroslav D. Sergeyev
ISBN 13 : 8889064013
Total Pages : 112 pages
Book Rating : 4.8/5 (89 download)

Book Synopsis Arithmetic of infinity by : Yaroslav D. Sergeyev

Download or read book Arithmetic of infinity written by Yaroslav D. Sergeyev and published by Yaroslav D. Sergeyev. This book was released on 2016-05-13 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first chapter of the book gives a brief description of the modern viewpoint on real numbers and presents the famous results of Georg Cantor regarding infinity. The second chapter has a preparative character and links the first and the third parts of the book. On the one hand, it shows that the commonly accepted point of view on numbers and infinity is not so clear as it seems at first sight (for example, it leads to numerous paradoxes). On the other hand, the chapter contains preliminary observations that will be used in the constructive introduction of a new arithmetic of infinity, given in the third chapter. This last part of the book contains the main results. It introduces notions of infinite and infinitesimal numbers, extended natural and real numbers, and operations with them. Surprisingly, the introduced arithmetical operations result in being very simple and are obtained as immediate extensions of the usual addition, multiplication, and division of finite numbers to infinite ones. This simplicity is a consequence of a newly developed positional numeral system used to express infinite numbers. Finally, the chapter contains solutions to a number of paradoxes regarding infinity (we can say that the new approach allows us to avoid paradoxes) and some examples of applications. In order to broaden the audience, the book was written as a popular one. The interested reader can find a number of technical articles of several researches that use the approach introduced here for solving a variety of research problems at the web page of the author. The author Yaroslav D. Sergeyev is Distinguished Professor and Head of Numerical Calculus Laboratory at the University of Calabria, Italy. He is also Professor (part-time contract) at Lobachevsky Nizhni Novgorod State University, Russia. His research interests include numerical analysis, global optimization, infinity computing, set theory, number theory, fractals, and parallel computing. He has been awarded several national and international prizes (Pythagoras International Prize in Mathematics, Italy; Lagrange Lecture, Turin University, Italy; MAIK Prize for the best scientific monograph published in Russian, Moscow, etc.). His list of scientific publications contains more than 200 items. He is a member of editorial boards of 5 international journals and has given more than 50 plenary and keynote lectures at prestigious international congresses.

The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics

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Author : John L. Bell
Publisher : Springer Nature
ISBN 13 : 3030187071
Total Pages : 313 pages
Book Rating : 4.0/5 (31 download)

Book Synopsis The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics by : John L. Bell

Download or read book The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics written by John L. Bell and published by Springer Nature. This book was released on 2019-09-09 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.

The History of Continua

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Author : Stewart Shapiro
Publisher : Oxford University Press, USA
ISBN 13 : 0198809646
Total Pages : 593 pages
Book Rating : 4.1/5 (988 download)

Book Synopsis The History of Continua by : Stewart Shapiro

Download or read book The History of Continua written by Stewart Shapiro and published by Oxford University Press, USA. This book was released on 2021 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical and philosophical thought about continuity has changed considerably over the ages, from Aristotle's insistence that a continuum is a unified whole, to the dominant account today, that a continuum is composed of infinitely many points. This book explores the key ideas and debates concerning continuity over more than 2500 years.

Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory

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Author : Mauro Di Nasso
Publisher : Springer
ISBN 13 : 3030179567
Total Pages : 206 pages
Book Rating : 4.0/5 (31 download)

Book Synopsis Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory by : Mauro Di Nasso

Download or read book Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory written by Mauro Di Nasso and published by Springer. This book was released on 2019-05-23 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent developments initially obtained in the nonstandard setting. This makes it the first combinatorics-focused account of nonstandard methods to be aimed at a general (graduate-level) mathematical audience. This book will provide a natural starting point for researchers interested in approaching the rapidly growing literature on combinatorial results obtained via nonstandard methods. The primary audience consists of graduate students and specialists in logic and combinatorics who wish to pursue research at the interface between these areas.

The Continuous and the Infinitesimal in Mathematics and Philosophy

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Author : John Lane Bell
Publisher : Polimetrica s.a.s.
ISBN 13 : 8876990151
Total Pages : 354 pages
Book Rating : 4.8/5 (769 download)

Book Synopsis The Continuous and the Infinitesimal in Mathematics and Philosophy by : John Lane Bell

Download or read book The Continuous and the Infinitesimal in Mathematics and Philosophy written by John Lane Bell and published by Polimetrica s.a.s.. This book was released on 2005 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Applications in Electronics Pervading Industry, Environment and Society

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Author : Francesco Bellotti
Publisher : Springer Nature
ISBN 13 : 3031481216
Total Pages : 523 pages
Book Rating : 4.0/5 (314 download)

Book Synopsis Applications in Electronics Pervading Industry, Environment and Society by : Francesco Bellotti

Download or read book Applications in Electronics Pervading Industry, Environment and Society written by Francesco Bellotti and published by Springer Nature. This book was released on 2024-01-12 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough overview of cutting-edge research on electronics applications relevant to industry, the environment, and society at large. It covers a broad spectrum of application domains, from automotive to space and from health to security, while devoting special attention to the use of embedded devices and sensors for imaging, communication, and control. The book is based on the 2023 ApplePies Conference, held in Genoa, Italy, in September 2023, which brought together researchers and stakeholders to consider the most significant current trends in the field of applied electronics and to debate visions for the future. Areas addressed by the conference included information communication technology; biotechnology and biomedical imaging; space; secure, clean, and efficient energy; the environment; and smart, green, and integrated transport. As electronics technology continues to develop apace, constantly meeting previously unthinkable targets, further attention needs to be directed toward the electronics applications and the development of systems that facilitate human activities. This book, written by industrial and academic professionals, represents a valuable contribution in this endeavor.

The Principles of Mathematics

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Author : Bertrand Russell
Publisher :
ISBN 13 :
Total Pages : 565 pages
Book Rating : 4.L/5 ( download)

Book Synopsis The Principles of Mathematics by : Bertrand Russell

Download or read book The Principles of Mathematics written by Bertrand Russell and published by . This book was released on 1903 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Principles of Mathematics

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Author : Bertrand Russell
Publisher : Routledge
ISBN 13 : 1135223114
Total Pages : 601 pages
Book Rating : 4.1/5 (352 download)

Book Synopsis Principles of Mathematics by : Bertrand Russell

Download or read book Principles of Mathematics written by Bertrand Russell and published by Routledge. This book was released on 2009-09-10 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: A precursor to Russell’s famous Principa Mathematica, this is one of the most original and comprehensive treatises on the logical foundation of mathematics available today.

Understanding Infinity

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Author : Anthony Gardiner
Publisher : Courier Corporation
ISBN 13 : 9780486425382
Total Pages : 324 pages
Book Rating : 4.4/5 (253 download)

Book Synopsis Understanding Infinity by : Anthony Gardiner

Download or read book Understanding Infinity written by Anthony Gardiner and published by Courier Corporation. This book was released on 2002-01-01 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conceived by the author as an introduction to "why the calculus works," this volume offers a 4-part treatment: an overview; a detailed examination of the infinite processes arising in the realm of numbers; an exploration of the extent to which familiar geometric notions depend on infinite processes; and the evolution of the concept of functions. 1982 edition.

Foundations of Infinitesimal Calculus

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Author : H. Jerome Keisler
Publisher : Prindle Weber & Schmidt
ISBN 13 : 9780871502155
Total Pages : 214 pages
Book Rating : 4.5/5 (21 download)

Book Synopsis Foundations of Infinitesimal Calculus by : H. Jerome Keisler

Download or read book Foundations of Infinitesimal Calculus written by H. Jerome Keisler and published by Prindle Weber & Schmidt. This book was released on 1976-01-01 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Principles of Mathematics

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Author : Bertrand Russell
Publisher : W. W. Norton & Company
ISBN 13 : 9780393314045
Total Pages : 580 pages
Book Rating : 4.3/5 (14 download)

Book Synopsis The Principles of Mathematics by : Bertrand Russell

Download or read book The Principles of Mathematics written by Bertrand Russell and published by W. W. Norton & Company. This book was released on 1996 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Russell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical--that what is commonly called mathematics is simply later deductions from logical premises.

On the Infinite and the Infinitesimal in Mathematical Analysis

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Author : Ernest William Hobson
Publisher :
ISBN 13 :
Total Pages : 48 pages
Book Rating : 4.F/5 ( download)

Book Synopsis On the Infinite and the Infinitesimal in Mathematical Analysis by : Ernest William Hobson

Download or read book On the Infinite and the Infinitesimal in Mathematical Analysis written by Ernest William Hobson and published by . This book was released on 1902 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Principles of Mathematics

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Author : Carl Barnett Allendoerfer
Publisher : CUP Archive
ISBN 13 :
Total Pages : 596 pages
Book Rating : 4./5 ( download)

Book Synopsis Principles of Mathematics by : Carl Barnett Allendoerfer

Download or read book Principles of Mathematics written by Carl Barnett Allendoerfer and published by CUP Archive. This book was released on 1953 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Forever Finite

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Author : Kip K. Sewell
Publisher : Rond Books
ISBN 13 :
Total Pages : 828 pages
Book Rating : 4.9/5 (881 download)

Book Synopsis Forever Finite by : Kip K. Sewell

Download or read book Forever Finite written by Kip K. Sewell and published by Rond Books. This book was released on 2023-08-01 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: INFINITY IS NOT WHAT IT SEEMS… Infinity is commonly assumed to be a logical concept, reliable for conducting mathematics, describing the Universe, and understanding the divine. Most of us are educated to take for granted that there exist infinite sets of numbers, that lines contain an infinite number of points, that space is infinite in expanse, that time has an infinite succession of events, that possibilities are infinite in quantity, and over half of the world’s population believes in a divine Creator infinite in knowledge, power, and benevolence. According to this treatise, such assumptions are mistaken. In reality, to be is to be finite. The implications of this assessment are profound: the Universe and even God must necessarily be finite. The author makes a compelling case against infinity, refuting its most prominent advocates. Any defense of the infinite will find it challenging to answer the arguments laid out in this book. But regardless of the reader’s position, Forever Finite offers plenty of thought-provoking material for anyone interested in the subject of infinity from the perspectives of philosophy, mathematics, science, and theology.

A Treatise on Algebra

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Author : James Edward Oliver
Publisher :
ISBN 13 :
Total Pages : 428 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis A Treatise on Algebra by : James Edward Oliver

Download or read book A Treatise on Algebra written by James Edward Oliver and published by . This book was released on 1887 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Mystery of the Aleph

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Author : Amir D. Aczel
Publisher : Simon and Schuster
ISBN 13 : 0743422996
Total Pages : 278 pages
Book Rating : 4.7/5 (434 download)

Book Synopsis The Mystery of the Aleph by : Amir D. Aczel

Download or read book The Mystery of the Aleph written by Amir D. Aczel and published by Simon and Schuster. This book was released on 2001-08-28 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: A compelling narrative that blends the story of infinity with the tragic tale of a tormented and brilliant mathematician.