Uses Of Infinity
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Author | : Leo Zippin |
Publisher | : Hassell Street Press |
Total Pages | : 162 |
Release | : 2021-09-09 |
Genre | : |
ISBN | : 9781014087102 |
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author | : Theodore G. Faticoni |
Publisher | : John Wiley & Sons |
Total Pages | : 361 |
Release | : 2012-04-23 |
Genre | : Mathematics |
ISBN | : 111824382X |
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.
Author | : Ian Stewart |
Publisher | : Oxford University Press |
Total Pages | : 161 |
Release | : 2017 |
Genre | : Mathematics |
ISBN | : 0198755236 |
Ian Stewart considers the concept of infinity and the profound role it plays in mathematics, logic, physics, cosmology, and philosophy. He shows that working with infinity is not just an abstract, intellectual exercise, and analyses its important practical everyday applications.
Author | : Haim Shapira |
Publisher | : Watkins |
Total Pages | : 256 |
Release | : 2019-04-16 |
Genre | : Mathematics |
ISBN | : 1786782340 |
A fun, non-technical and wonderfully engaging guide to that most powerful and mysterious of mathematical concepts: infinity.in this book, best-selling author and mathematician Haim Shapira presents an introduction to mathematical theories which deal with the most beautiful concept ever invented by humankind: infinity. In this book, best-selling author and mathematician Haim Shapira presents an introduction to mathematical theories which deal with the most beautiful concept ever invented by humankind: infinity. Written in clear, simple language and aimed at a lay audience, this book also offers some strategies that will allow readers to try their ability at solving truly fascinating mathematical problems. Infinity is a deeply counter-intuitive concept that has inspired many great thinkers. In this book we will meet many sages, both familiar and unfamiliar: Zeno and Pythagoras, Georg Cantor and Bertrand Russell, Sofia Kovalevskaya and Emmy Noether, al-Khwarizmi and Euclid, Sophie Germain and Srinivasa Ramanujan.The world of infinity is inhabited by many paradoxes, and so is this book: Zeno paradoxes, Hilbert's "Infinity Hotel", Achilles and the gods paradox, the paradox of heaven and hell, the Ross-Littlewood paradox involving tennis balls, the Galileo paradox and many more. Aimed at the curious but non-technical reader, this book refrains from using any fearsome mathematical symbols. It uses only the most basic operations of mathematics: adding, subtracting, multiplication, division, powers and roots – that is all. But that doesn’t mean that a bit of deep thinking won’t be necessary and rewarding. Writing with humour and lightness of touch, Haim Shapira banishes the chalky pallor of the schoolroom and offers instead a truly thrilling intellectual journey. Fasten your seatbelt – we are going to Infinity, and beyond!
Author | : Steven Henry Strogatz |
Publisher | : Houghton Mifflin Harcourt |
Total Pages | : 333 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 0547517653 |
A delightful tour of the greatest ideas of math, showing how math intersects with philosophy, science, art, business, current events, and everyday life, by an acclaimed science communicator and regular contributor to the "New York Times."
Author | : Barnaby Sheppard |
Publisher | : Cambridge University Press |
Total Pages | : 498 |
Release | : 2014-07-24 |
Genre | : Mathematics |
ISBN | : 1107058317 |
This book conveys to the novice the big ideas in the rigorous mathematical theory of infinite sets.
Author | : H. Chris Ransford |
Publisher | : Columbia University Press |
Total Pages | : 127 |
Release | : 2017-03-28 |
Genre | : Religion |
ISBN | : 3838270193 |
Drawing on the science and mathematics of infinity, H. Chris Ransford analyzes the traditional concept of godhood and reaches surprising conclusions. He addresses humankind's abiding core debate on the meaning of spirituality and God. Using mathematics, he explores key questions within this debate: for instance, why does evil exist if there is a God? The book fastidiously does not take sides nor proffers opinions, it only follows allowable mathematics wherever it leads. By doing so, it makes a major contribution to an understanding of the nature of reality.
Author | : Donald Ervin Knuth |
Publisher | : Stanford Univ Center for the Study |
Total Pages | : 257 |
Release | : 2001-01 |
Genre | : Science |
ISBN | : 9781575863276 |
How does a computer scientist understand infinity? What can probability theory teach us about free will? Can mathematical notions be used to enhance one's personal understanding of the Bible? Perhaps no one is more qualified to address these questions than Donald E. Knuth, whose massive contributions to computing have led others to nickname him "The Father of Computer Science"—and whose religious faith led him to understand a fascinating analysis of the Bible called the 3:16 project. In this series of six spirited, informal lectures, Knuth explores the relationships between his vocation and his faith, revealing the unique perspective that his work with computing has lent to his understanding of God. His starting point is the 3:16 project, an application of mathematical "random sampling" to the books of the Bible. The first lectures tell the story of the project's conception and execution, exploring its many dimensions of language translation, aesthetics, and theological history. Along the way, Knuth explains the many insights he gained from such interdisciplinary work. These theological musings culminate in a surprising final lecture tackling the ideas of infinity, free will, and some of the other big questions that lie at the juncture of theology and computation. Things a Computer Scientist Rarely Talks About, with its charming and user-friendly format—each lecture ends with a question and answer exchange, and the book itself contains more than 100 illustrations—is a readable and intriguing approach to a crucial topic, certain to edify both those who are serious and curious about their faiths and those who look at the science of computation and wonder what it might teach them about their spiritual world. Includes "Creativity, Spirituality, and Computer Science," a panel discussion featuring Harry Lewis, Guy L. Steele, Jr., Manuela Veloso, Donald E. Knuth, and Mitch Kapor.
Author | : David Deutsch |
Publisher | : Penguin UK |
Total Pages | : 571 |
Release | : 2011-03-31 |
Genre | : Science |
ISBN | : 0141969695 |
'Science has never had an advocate quite like David Deutsch ... A computational physicist on a par with his touchstones Alan Turing and Richard Feynman, and a philosopher in the line of his greatest hero, Karl Popper. His arguments are so clear that to read him is to experience the thrill of the highest level of discourse available on this planet and to understand it' Peter Forbes, Independent In our search for truth, how far have we advanced? This uniquely human quest for good explanations has driven amazing improvements in everything from scientific understanding and technology to politics, moral values and human welfare. But will progress end, either in catastrophe or completion - or will it continue infinitely? In this profound and seminal book, David Deutsch explores the furthest reaches of our current understanding, taking in the Infinity Hotel, supernovae and the nature of optimism, to instill in all of us a wonder at what we have achieved - and the fact that this is only the beginning of humanity's infinite possibility. 'This is Deutsch at his most ambitious, seeking to understand the implications of our scientific explanations of the world ... I enthusiastically recommend this rich, wide-ranging and elegantly written exposition of the unique insights of one of our most original intellectuals' Michael Berry, Times Higher Education Supplement 'Bold ... profound ... provocative and persuasive' Economist 'David Deutsch may well go down in history as one of the great scientists of our age' Scotsman
Author | : Paolo Mancosu |
Publisher | : Oxford University Press |
Total Pages | : 231 |
Release | : 2016 |
Genre | : Mathematics |
ISBN | : 0198746822 |
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.