Are Numbers Real
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Are Numbers Real
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Author : Brian Clegg
language : en
Publisher: Hachette UK
Release Date : 2017-02-02
Are Numbers Real 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 2017-02-02 with Science categories.
Have you ever wondered what humans did before numbers existed? How they organized their lives, traded goods, or kept track of their treasures? What would your life be like without them? Numbers began as simple representations of everyday things, but mathematics rapidly took on a life of its own, occupying a parallel virtual world. In Are Numbers Real? Brian Clegg explores the way that maths has become more and more detached from reality, yet despite this is driving the development of modern physics. From devising a new counting system based on goats, through the weird and wonderful mathematics of imaginary numbers and infinity to the debate over whether mathematics has too much influence on the direction of science, this fascinating and accessible book opens the reader's eyes to the hidden reality of the strange yet familiar world of numbers.
Which Numbers Are Real
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Author : Michael Henle
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-12-31
Which Numbers Are Real written by Michael Henle and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-31 with Mathematics categories.
Everyone knows the real numbers, those fundamental quantities that make possible all of mathematics from high school algebra and Euclidean geometry through the Calculus and beyond; and also serve as the basis for measurement in science, industry, and ordinary life. This book surveys alternative real number systems: systems that generalize and extend the real numbers yet stay close to these properties that make the reals central to mathematics. Alternative real numbers include many different kinds of numbers, for example multidimensional numbers (the complex numbers, the quaternions and others), infinitely small and infinitely large numbers (the hyperreal numbers and the surreal numbers), and numbers that represent positions in games (the surreal numbers). Each system has a well-developed theory, including applications to other areas of mathematics and science, such as physics, the theory of games, multi-dimensional geometry, and formal logic. They are all active areas of current mathematical research and each has unique features, in particular, characteristic methods of proof and implications for the philosophy of mathematics, both highlighted in this book. Alternative real number systems illuminate the central, unifying role of the real numbers and include some exciting and eccentric parts of mathematics. Which Numbers Are Real? Will be of interest to anyone with an interest in numbers, but specifically to upper-level undergraduates, graduate students, and professional mathematicians, particularly college mathematics teachers.
Exploring The Real Numbers
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Author : Frederick W. Stevenson
language : en
Publisher:
Release Date : 2000
Exploring The Real Numbers written by Frederick W. Stevenson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Exploring the Real Numbers helps readers understand the real number system. Stevenson brings readers up to date with the study of the nature of real numbers, and provides a sense of the historical journey that has led to our current knowledge of the subject. Presents many interesting topics that arise during study of the real numbers. Offers 21 exploratory projects, encouraging readers to pursue concepts beyond the book. Includes over 100 carefully worked examples. Features abundant exercises throughout. For anyone interested in learning more about some of the very different and often beautiful aspects of mathematics.
The Irrationals
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Author : Julian Havil
language : en
Publisher: Princeton University Press
Release Date : 2014-09-22
The Irrationals written by Julian Havil and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-22 with Mathematics categories.
The first popular history of irrational numbers and their discoverers, from ancient Greece to the twenty-first century The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational numbers are surprisingly difficult to define—and why so many questions still surround them. Fascinating and illuminating, this is a book for everyone who loves math and the history behind it.
Real Numbers Generalizations Of The Reals And Theories Of Continua
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Author : P. Ehrlich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Real Numbers Generalizations Of The Reals And Theories Of Continua written by P. Ehrlich 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.
Since their appearance in the late 19th century, the Cantor--Dedekind theory of real numbers and philosophy of the continuum have emerged as pillars of standard mathematical philosophy. On the other hand, this period also witnessed the emergence of a variety of alternative theories of real numbers and corresponding theories of continua, as well as non-Archimedean geometry, non-standard analysis, and a number of important generalizations of the system of real numbers, some of which have been described as arithmetic continua of one type or another. With the exception of E.W. Hobson's essay, which is concerned with the ideas of Cantor and Dedekind and their reception at the turn of the century, the papers in the present collection are either concerned with or are contributions to, the latter groups of studies. All the contributors are outstanding authorities in their respective fields, and the essays, which are directed to historians and philosophers of mathematics as well as to mathematicians who are concerned with the foundations of their subject, are preceded by a lengthy historical introduction.
The Real Numbers And Real Analysis
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Author : Ethan D. Bloch
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-27
The Real Numbers And Real Analysis written by Ethan D. Bloch 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 2011-05-27 with Mathematics categories.
This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.
A Dictionary Of Real Numbers
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Author : Jonathan Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Dictionary Of Real Numbers written by Jonathan Borwein 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 2012-12-06 with Mathematics categories.
How do we recognize that the number . 93371663 . . . is actually 2 IoglQ(e + 7r)/2 ? Gauss observed that the number 1. 85407467 . . . is (essentially) a rational value of an elliptic integral-an observation that was critical in the development of nineteenth century analysis. How do we decide that such a number is actually a special value of a familiar function without the tools Gauss had at his disposal, which were, presumably, phenomenal insight and a prodigious memory? Part of the answer, we hope, lies in this volume. This book is structured like a reverse telephone book, or more accurately, like a reverse handbook of special function values. It is a list of just over 100,000 eight-digit real numbers in the interval [0,1) that arise as the first eight digits of special values of familiar functions. It is designed for people, like ourselves, who encounter various numbers computationally and want to know if these numbers have some simple form. This is not a particularly well-defined endeavor-every eight-digit number is rational and this is not interesting. However, the chances of an eight digit number agreeing with a small rational, say with numerator and denominator less than twenty-five, is small. Thus the list is comprised primarily of special function evaluations at various algebraic and simple transcendental values. The exact numbers included are described below. Each entry consists of the first eight digits after the decimal point of the number in question.
From Numbers To Analysis
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Author : Inder K. Rana
language : en
Publisher: World Scientific
Release Date : 1998
From Numbers To Analysis written by Inder K. Rana and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
"This book is recommended to students and instructors looking for a very well-organized introduction to the foundations of analysis".Acta Sci. Math., 1999
The Book Of Numbers
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Author : John H. Conway
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-03-16
The Book Of Numbers written by John H. Conway 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 1998-03-16 with Mathematics categories.
"...the great feature of the book is that anyone can read it without excessive head scratching...You'll find plenty here to keep you occupied, amused, and informed. Buy, dip in, wallow." -IAN STEWART, NEW SCIENTIST "...a delightful look at numbers and their roles in everything from language to flowers to the imagination." -SCIENCE NEWS "...a fun and fascinating tour of numerical topics and concepts. It will have readers contemplating ideas they might never have thought were understandable or even possible." -WISCONSIN BOOKWATCH "This popularization of number theory looks like another classic." -LIBRARY JOURNAL
The Real Numbers
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Author : John Stillwell
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-16
The Real Numbers written by John Stillwell 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 2013-10-16 with Mathematics categories.
While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory—uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis—the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor–Schröder–Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions.