Arithmetic of infinity

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

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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 Mathematics of Infinity

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Author :
Publisher : John Wiley & Sons
ISBN 13 : 1118204484
Total Pages : 360 pages
Book Rating : 4.1/5 (182 download)

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Book Synopsis The Mathematics of Infinity by : Theodore G. Faticoni

Download or read book The Mathematics of Infinity written by Theodore G. Faticoni and published by John Wiley & Sons. This book was released on 2012-04-17 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Naming Infinity

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Author :
Publisher : Harvard University Press
ISBN 13 : 0674032934
Total Pages : 252 pages
Book Rating : 4.6/5 (74 download)

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Book Synopsis Naming Infinity by : Loren Graham

Download or read book Naming Infinity written by Loren Graham and published by Harvard University Press. This book was released on 2009-03-31 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :
Publisher : Oxford University Press, USA
ISBN 13 : 0198523947
Total Pages : 264 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis The Invention of Infinity by : Judith Veronica Field

Download or read book The Invention of Infinity written by Judith Veronica Field and published by Oxford University Press, USA. This book was released on 1997 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fully illustrated, this story brings together the histories of arts and mathematics and shows how infinity at last acquired a precise mathematical meaning.

Roads to Infinity

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Author :
Publisher : CRC Press
ISBN 13 : 1439865507
Total Pages : 202 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Roads to Infinity by : John Stillwell

Download or read book Roads to Infinity written by John Stillwell and published by CRC Press. This book was released on 2010-07-13 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Winner of a CHOICE Outstanding Academic Title Award for 2011!This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is h

Beyond Infinity

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Publisher : Profile Books
ISBN 13 : 1782830812
Total Pages : 204 pages
Book Rating : 4.7/5 (828 download)

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Book Synopsis Beyond Infinity by : Eugenia Cheng

Download or read book Beyond Infinity written by Eugenia Cheng and published by Profile Books. This book was released on 2017-03-09 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Playing with Infinity

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Author :
Publisher :
ISBN 13 : 9780844652351
Total Pages : pages
Book Rating : 4.6/5 (523 download)

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Book Synopsis Playing with Infinity by : Rozsa Peter

Download or read book Playing with Infinity written by Rozsa Peter and published by . This book was released on 1986-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Popular account ranges from counting to mathematical logic and covers many concepts related to infinity: graphic representation of functions; pairings, other combinations; prime numbers; logarithms, circular functions; more. 216 illustrations.

Infinity

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Publisher : Oxford University Press
ISBN 13 : 0198755236
Total Pages : 161 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis Infinity by : Ian Stewart

Download or read book Infinity written by Ian Stewart and published by Oxford University Press. This book was released on 2017 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinity is an intriguing topic, with connections to religion, philosophy, metaphysics, logic, and physics as well as mathematics. Its history goes back to ancient times, with especially important contributions from Euclid, Aristotle, Eudoxus, and Archimedes. The infinitely large (infinite) isintimately related to the infinitely small (infinitesimal). Cosmologists consider sweeping questions about whether space and time are infinite. Philosophers and mathematicians ranging from Zeno to Russell have posed numerous paradoxes about infinity and infinitesimals. Many vital areas ofmathematics rest upon some version of infinity. The most obvious, and the first context in which major new techniques depended on formulating infinite processes, is calculus. But there are many others, for example Fourier analysis and fractals.In this Very Short Introduction, Ian Stewart discusses infinity in mathematics while also drawing in the various other aspects of infinity and explaining some of the major problems and insights arising from this concept. He argues that working with infinity is not just an abstract, intellectualexercise but that it is instead a concept with important practical everyday applications, and considers how mathematicians use infinity and infinitesimals to answer questions or supply techniques that do not appear to involve the infinite.ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, andenthusiasm to make interesting and challenging topics highly readable.

The Logic of Infinity

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Author :
Publisher : Cambridge University Press
ISBN 13 : 1107058317
Total Pages : 498 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis The Logic of Infinity by : Barnaby Sheppard

Download or read book The Logic of Infinity written by Barnaby Sheppard and published by Cambridge University Press. This book was released on 2014-07-24 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book conveys to the novice the big ideas in the rigorous mathematical theory of infinite sets.

The Mathematics of Infinity

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Author :
Publisher : John Wiley & Sons
ISBN 13 : 111824382X
Total Pages : 361 pages
Book Rating : 4.1/5 (182 download)

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Book Synopsis The Mathematics of Infinity by : Theodore G. Faticoni

Download or read book The Mathematics of Infinity written by Theodore G. Faticoni and published by John Wiley & Sons. This book was released on 2012-04-23 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Math Without Numbers

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Author :
Publisher : Penguin
ISBN 13 : 1524745561
Total Pages : 225 pages
Book Rating : 4.5/5 (247 download)

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Book Synopsis Math Without Numbers by : Milo Beckman

Download or read book Math Without Numbers written by Milo Beckman and published by Penguin. This book was released on 2022-01-11 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: An illustrated tour of the structures and patterns we call "math" The only numbers in this book are the page numbers. Math Without Numbers is a vivid, conversational, and wholly original guide to the three main branches of abstract math—topology, analysis, and algebra—which turn out to be surprisingly easy to grasp. This book upends the conventional approach to math, inviting you to think creatively about shape and dimension, the infinite and infinitesimal, symmetries, proofs, and how these concepts all fit together. What awaits readers is a freewheeling tour of the inimitable joys and unsolved mysteries of this curiously powerful subject. Like the classic math allegory Flatland, first published over a century ago, or Douglas Hofstadter's Godel, Escher, Bach forty years ago, there has never been a math book quite like Math Without Numbers. So many popularizations of math have dwelt on numbers like pi or zero or infinity. This book goes well beyond to questions such as: How many shapes are there? Is anything bigger than infinity? And is math even true? Milo Beckman shows why math is mostly just pattern recognition and how it keeps on surprising us with unexpected, useful connections to the real world. The ambitions of this book take a special kind of author. An inventive, original thinker pursuing his calling with jubilant passion. A prodigy. Milo Beckman completed the graduate-level course sequence in mathematics at age sixteen, when he was a sophomore at Harvard; while writing this book, he was studying the philosophical foundations of physics at Columbia under Brian Greene, among others.

Abstraction and Infinity

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Publisher : Oxford University Press
ISBN 13 : 0198746822
Total Pages : 231 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis Abstraction and Infinity by : Paolo Mancosu

Download or read book Abstraction and Infinity written by Paolo Mancosu and published by Oxford University Press. This book was released on 2016 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Brief History of Infinity

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Author :
Publisher : Robinson
ISBN 13 : 1472107640
Total Pages : 185 pages
Book Rating : 4.4/5 (721 download)

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Book Synopsis A Brief History of Infinity by : Brian Clegg

Download or read book A Brief History of Infinity written by Brian Clegg and published by Robinson. This book was released on 2013-02-07 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space.' Douglas Adams, Hitch-hiker's Guide to the Galaxy We human beings have trouble with infinity - yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity - yet it is a concept routinely used by schoolchildren. Exploring the infinite is a journey into paradox. Here is a quantity that turns arithmetic on its head, making it feasible that 1 = 0. Here is a concept that enables us to cram as many extra guests as we like into an already full hotel. Most bizarrely of all, it is quite easy to show that there must be something bigger than infinity - when it surely should be the biggest thing that could possibly be. Brian Clegg takes us on a fascinating tour of that borderland between the extremely large and the ultimate that takes us from Archimedes, counting the grains of sand that would fill the universe, to the latest theories on the physical reality of the infinite. Full of unexpected delights, whether St Augustine contemplating the nature of creation, Newton and Leibniz battling over ownership of calculus, or Cantor struggling to publicise his vision of the transfinite, infinity's fascination is in the way it brings together the everyday and the extraordinary, prosaic daily life and the esoteric. Whether your interest in infinity is mathematical, philosophical, spiritual or just plain curious, this accessible book offers a stimulating and entertaining read.

The Arithmetic of Infinitesimals

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Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1475743122
Total Pages : 226 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis The Arithmetic of Infinitesimals by : John Wallis

Download or read book The Arithmetic of Infinitesimals written by John Wallis and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: John Wallis (1616-1703) was the most influential English mathematician prior to Newton. He published his most famous work, Arithmetica Infinitorum, in Latin in 1656. This book studied the quadrature of curves and systematised the analysis of Descartes and Cavelieri. Upon publication, this text immediately became the standard book on the subject and was frequently referred to by subsequent writers. This will be the first English translation of this text ever to be published.

From 0 to Infinity in 26 Centuries

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Publisher : Michael O'Mara Books
ISBN 13 : 1843179210
Total Pages : 170 pages
Book Rating : 4.8/5 (431 download)

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Book Synopsis From 0 to Infinity in 26 Centuries by : Chris Waring

Download or read book From 0 to Infinity in 26 Centuries written by Chris Waring and published by Michael O'Mara Books. This book was released on 2012-09-06 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: We may remember their equations and discoveries from school, but do we remember who the men behind the maths were? From the theories of Pythagoras (did you know he ran a secret brotherhood that studied maths, music and gymnastics?) to coining the term 'Googol', From 0 to Infinity in 26 Centuries: The extraordinary story of maths is packed full of fascinating facts and surprising stories from ancient times to the modern day. Do you want to know why the Ancient Greeks knew so much maths? Or, why there was so little maths studied in the Dark Ages? Read this fascinating book to uncover the mysteries of maths...

Infinity and the Mind

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Author :
Publisher : Princeton University Press
ISBN 13 : 0691191255
Total Pages : pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Infinity and the Mind by : Rudy Rucker

Download or read book Infinity and the Mind written by Rudy Rucker and published by Princeton University Press. This book was released on 2019-07-23 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A dynamic exploration of infinity In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the “Mindscape,” where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Using cartoons, puzzles, and quotations to enliven his text, Rucker acquaints us with staggeringly advanced levels of infinity, delves into the depths beneath daily awareness, and explains Kurt Gödel’s belief in the possibility of robot consciousness. In the realm of infinity, mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise, we gain profound insights into the human mind, its powers, and its limitations. This Princeton Science Library edition includes a new preface by the author.

The End of Infinity

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Author :
Publisher : Algora Publishing
ISBN 13 : 1628943416
Total Pages : 200 pages
Book Rating : 4.6/5 (289 download)

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Book Synopsis The End of Infinity by : Anthony C. Patton

Download or read book The End of Infinity written by Anthony C. Patton and published by Algora Publishing. This book was released on 2018-07-01 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: