Arithmetic Of Infinity
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Arithmetic Of Infinity
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Author : Yaroslav D. Sergeyev
language : en
Publisher: Yaroslav D. Sergeyev
Release Date : 2016-05-13
Arithmetic Of Infinity written by Yaroslav D. Sergeyev and has been published by Yaroslav D. Sergeyev this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-13 with Science categories.
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.
Naming Infinity
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Author : Loren Graham
language : en
Publisher: Harvard University Press
Release Date : 2009-03-31
Naming Infinity written by Loren Graham and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-31 with Science categories.
In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity.
The Invention Of Infinity
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Author : Judith Veronica Field
language : en
Publisher: Oxford University Press, USA
Release Date : 1997
The Invention Of Infinity written by Judith Veronica Field and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Art categories.
Fully illustrated, this story brings together the histories of arts and mathematics and shows how infinity at last acquired a precise mathematical meaning.
Understanding Infinity
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Author : Anthony Gardiner
language : en
Publisher: Courier Corporation
Release Date : 2002-01-01
Understanding Infinity written by Anthony Gardiner and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
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.
Beyond Infinity
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Author : Eugenia Cheng
language : en
Publisher: Profile Books
Release Date : 2017-03-09
Beyond Infinity written by Eugenia Cheng and has been published by Profile Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-09 with Mathematics categories.
SHORTLISTED FOR THE 2017 ROYAL SOCIETY SCIENCE BOOK PRIZE Even small children know there are infinitely many whole numbers - start counting and you'll never reach the end. But there are also infinitely many decimal numbers between zero and one. Are these two types of infinity the same? Are they larger or smaller than each other? Can we even talk about 'larger' and 'smaller' when we talk about infinity? In Beyond Infinity, international maths sensation Eugenia Cheng reveals the inner workings of infinity. What happens when a new guest arrives at your infinite hotel - but you already have an infinite number of guests? How does infinity give Zeno's tortoise the edge in a paradoxical foot-race with Achilles? And can we really make an infinite number of cookies from a finite amount of cookie dough? Wielding an armoury of inventive, intuitive metaphor, Cheng draws beginners and enthusiasts alike into the heart of this mysterious, powerful concept to reveal fundamental truths about mathematics, all the way from the infinitely large down to the infinitely small.
Abstraction And Infinity
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Author : Paolo Mancosu
language : en
Publisher: Oxford University Press
Release Date : 2016
Abstraction And Infinity written by Paolo Mancosu and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.
Mancosu offers an original investigation of key notions in mathematics: abstraction and infinity, and their interaction. He gives a historical analysis of the theorizing of definitions by abstraction, and explores a novel approach to measuring the size of infinite sets, showing how this leads to deep mathematical and philosophical problems.
The Mathematics Of Infinity
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Author : Theodore G. Faticoni
language : en
Publisher: John Wiley & Sons
Release Date : 2012-04-17
The Mathematics Of Infinity written by Theodore G. Faticoni and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-17 with Mathematics categories.
Praise for the First Edition ". . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity."—Computing Reviews ". . . a very well written introduction to set theory . . . easy to read and well suited for self-study . . . highly recommended."—Choice The concept of infinity has fascinated and confused mankind for centuries with theories and ideas that cause even seasoned mathematicians to wonder. The Mathematics of Infinity: A Guide to Great Ideas, Second Edition uniquely explores how we can manipulate these ideas when our common sense rebels at the conclusions we are drawing. Continuing to draw from his extensive work on the subject, the author provides a user-friendly presentation that avoids unnecessary, in-depth mathematical rigor. This Second Edition provides important coverage of logic and sets, elements and predicates, cardinals as ordinals, and mathematical physics. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun readers' intuitive view of the world. With an accessible and balanced treatment of both concepts and theory, the book focuses on the following topics: Logic, sets, and functions Prime numbers Counting infinite sets Well ordered sets Infinite cardinals Logic and meta-mathematics Inductions and numbers Presenting an intriguing account of the notions of infinity, The Mathematics of Infinity: A Guide to Great Ideas, Second Edition is an insightful supplement for mathematics courses on set theory at the undergraduate level. The book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the world of counterintuitive mathematics.
Aristotle On Mathematical Infinity
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Author : Theokritos Kouremenos
language : en
Publisher: Franz Steiner Verlag
Release Date : 1995
Aristotle On Mathematical Infinity written by Theokritos Kouremenos and has been published by Franz Steiner Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with History categories.
Aristotle was the first not only to distinguish between potential and actual infinity but also to insist that potential infinity alone is enough for mathematics thus initiating an issue still central to the philosophy of mathematics. Modern scholarship, however, has attacked Aristotle's thesis because, according to the received doctrine, it does not square with Euclidean geometry and it also seems to contravene Aristotle's belief in the finitude of the physical universe. This monograph, the first thorough study of the issue, puts Aristotle's views on infinity in the proper perspective. Through a close study of the relevant Aristotelian passages it shows that the Stagirite's theory of infinity forms a well argued philosophical position which does not bear on his belief in a finite cosmos and does not undermine the Euclidean nature of geometry. The monograph draws a much more positive picture of Aristotle's views and reaffirms his disputed stature as a serious philosopher of mathematics. This innovative and stimulating contribution will be essential reading to a wide range of scholars, including classicists, philosophers of science and mathematics as well as historians of ideas.
The Arithmetic Of Infinitesimals
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Author : John Wallis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
The Arithmetic Of Infinitesimals written by John Wallis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
The book is the first English translation of John Wallis's Arithmetica Infinitorum (1656), a key text on the seventeenth-century development of the calculus. Accompanied with annotations and an introductory essay, the translation makes Wallis's work fully available for the first time to modern readers. It shows how Wallis drew on some of the most important new ideas from the preceding twenty years, and took them forward to lay the foundations on which Newton was to build. Above all, the book displays the crucial mid-seventeenth-century shift from geometry to arithmetic and algebra as the primary language of mathematics.
Roads To Infinity
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Author : John Stillwell
language : en
Publisher: A K PETERS
Release Date : 2024-10-14
Roads To Infinity written by John Stillwell and has been published by A K PETERS this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-14 with Mathematics categories.
This book unifies ideas from set theory and mathematical logic and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. Ideas are shown to evolve from natural mathematical questions about the nature of infinity and the nature of proof, set against a background of broader questions and developm