The Nature Of Infinity
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A Brief History Of Infinity
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Author : Brian Clegg
language : en
Publisher: Hachette UK
Release Date : 2013-02-07
A Brief History Of Infinity written by Brian Clegg and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-07 with Mathematics categories.
'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.
What Is Infinity
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Author : Devesh Pratap Singh
language : en
Publisher: Independently Published
Release Date : 2023-06-14
What Is Infinity written by Devesh Pratap Singh and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-14 with categories.
Have you ever pondered over the enigmatic concept of infinity? While we are familiar with basic operations involving infinity, such as ∞ + n = ∞ or ∞ - n = ∞, we lack a concrete understanding of why these relationships hold true. The Nature of infinity remains elusive, existing as a mere abstract notion in our mathematical discourse. This book delves into the exploration of infinity, seeking to unravel its essence by examining the fundamental definition of numbers and their composition. By dissecting numbers into their constituents, we can shed light on the elusive nature of infinity and comprehend its role in three specific indeterminate forms: ∞ - ∞, ∞/∞ and 1^∞
The Infinite Book
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Author : John D. Barrow
language : en
Publisher: Random House
Release Date : 2010-03-30
The Infinite Book written by John D. Barrow and has been published by Random House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-30 with Science categories.
‘A delight. Popular science doesn’t come much better than this’ Independent Everything you might want to know about infinity - in history and all the way to today's cutting-edge science. Infinity is surely the strangest idea that humans have ever had. Where did it come from and what is it telling us about our Universe? Can there actually be infinities? Can you do an infinite number of things in a finite amount of time? Is the Universe infinite? Infinity is also the place where things happen that don't. What is it like to live in a Universe where nothing is original, where you can live forever, where anything that can be done, is done, over and over again? These are some of the deep questions that the idea of the infinite pushes us to ask. Throughout history, the infinite has been a dangerous concept. Many have lost their lives, their careers, or their freedom for talking about it. The Infinite Book will take you on a tour of these dangerous questions and the strange answers that scientists, mathematicians, philosophers and theologians have come up with to deal with its threats to our sanity.
The Beginning Of Infinity
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Author : David Deutsch
language : en
Publisher: Penguin
Release Date : 2011-07-21
The Beginning Of Infinity written by David Deutsch and has been published by Penguin this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-21 with Science categories.
The New York Times bestseller: A provocative, imaginative exploration of the nature and progress of knowledge “Dazzling.” – Steven Pinker, The Guardian In this groundbreaking book, award-winning physicist David Deutsch argues that explanations have a fundamental place in the universe—and that improving them is the basic regulating principle of all successful human endeavor. Taking us on a journey through every fundamental field of science, as well as the history of civilization, art, moral values, and the theory of political institutions, Deutsch tracks how we form new explanations and drop bad ones, explaining the conditions under which progress—which he argues is potentially boundless—can and cannot happen. Hugely ambitious and highly original, The Beginning of Infinity explores and establishes deep connections between the laws of nature, the human condition, knowledge, and the possibility for progress.
In Search Of Infinity
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Author : N.Ya. Vilenkin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
In Search Of Infinity written by N.Ya. Vilenkin 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 concept of infinity is one of the most important, and at the same time, one of the most mysterious concepts of science. Already in antiquity many philosophers and mathematicians pondered over its contradictory nature. In mathematics, the contradictions connected with infinity intensified after the creation, at the end of the 19th century, of the theory of infinite sets and the subsequent discovery, soon after, of paradoxes in this theory. At the time, many scientists ignored the paradoxes and used set theory extensively in their work, while others subjected set-theoretic methods in mathematics to harsh criticism. The debate intensified when a group of French mathematicians, who wrote under the pseudonym of Nicolas Bourbaki, tried to erect the whole edifice of mathematics on the single notion of a set. Some mathematicians greeted this attempt enthusiastically while others regarded it as an unnecessary formalization, an attempt to tear mathematics away from life-giving practical applications that sustain it. These differences notwithstanding, Bourbaki has had a significant influence on the evolution of mathematics in the twentieth century. In this book we try to tell the reader how the idea of the infinite arose and developed in physics and in mathematics, how the theory of infinite sets was constructed, what paradoxes it has led to, what significant efforts have been made to eliminate the resulting contradictions, and what routes scientists are trying to find that would provide a way out of the many difficulties.
Approaching Infinity
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Author : M. Huemer
language : en
Publisher: Springer
Release Date : 2016-05-23
Approaching Infinity written by M. Huemer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-23 with Philosophy categories.
Approaching Infinity addresses seventeen paradoxes of the infinite, most of which have no generally accepted solutions. The book addresses these paradoxes using a new theory of infinity, which entails that an infinite series is uncompletable when it requires something to possess an infinite intensive magnitude. Along the way, the author addresses the nature of numbers, sets, geometric points, and related matters. The book addresses the need for a theory of infinity, and reviews both old and new theories of infinity. It discussing the purposes of studying infinity and the troubles with traditional approaches to the problem, and concludes by offering a solution to some existing paradoxes.
God And The Mathematics Of Infinity
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Author : H. Chris Ransford
language : en
Publisher: Columbia University Press
Release Date : 2017-03-28
God And The Mathematics Of Infinity written by H. Chris Ransford and has been published by Columbia University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-28 with Religion categories.
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.
The Edge Of The Sky
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Author : Roberto Trotta
language : en
Publisher: Hachette UK
Release Date : 2014-09-23
The Edge Of The Sky written by Roberto Trotta and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-23 with Science categories.
From the big bang to black holes, from dark matter to dark energy, from the origins of the universe to its ultimate destiny, The Edge of the Sky tells the story of the most important discoveries and mysteries in modern cosmology -- with a twist. The book's lexicon is limited to the thousand most common words in the English language, excluding physics, energy, galaxy, or even universe. Through the eyes of a fictional scientist (Student-People) hunting for dark matter with one of the biggest telescopes (Big-Seers) on Earth (Home-World), cosmologist Roberto Trotta explores the most important ideas about our universe (All-there-is) in language simple enough for anyone to understand. A unique blend of literary experimentation and science popularization, this delightful book is a perfect gift for any aspiring astronomer. The Edge of the Sky tells the story of the universe on a human scale, and the result is out of this world.
Infinity And Truth
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Author : Chi Tat Chong
language : en
Publisher: World Scientific
Release Date : 2013-11-28
Infinity And Truth written by Chi Tat Chong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-28 with Mathematics categories.
This volume is based on the talks given at the Workshop on Infinity and Truth held at the Institute for Mathematical Sciences, National University of Singapore, from 25 to 29 July 2011. The chapters cover topics in mathematical and philosophical logic that examine various aspects of the foundations of mathematics. The theme of the volume focuses on two basic foundational questions: (i) What is the nature of mathematical truth and how does one resolve questions that are formally unsolvable within the Zermelo-Fraenkel Set Theory with the Axiom of Choice, and (ii) Do the discoveries in mathematics provide evidence favoring one philosophical view over others? These issues are discussed from the vantage point of recent progress in foundational studies.The final chapter features questions proposed by the participants of the Workshop that will drive foundational research. The wide range of topics covered here will be of interest to students, researchers and mathematicians concerned with issues in the foundations of mathematics.
Infinity
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Author : Ian Stewart
language : en
Publisher: Oxford University Press
Release Date : 2017
Infinity written by Ian Stewart 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 2017 with Infinite categories.
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.