An Introduction To The Theory Of Surreal Numbers
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An Introduction To The Theory Of Surreal Numbers
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Author : Harry Gonshor
language : en
Publisher: Cambridge University Press
Release Date : 1986-09-18
An Introduction To The Theory Of Surreal Numbers written by Harry Gonshor and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-09-18 with Mathematics categories.
These notes provide a formal introduction to the theory of surreal numbers in a clear and lucid style.
An Introduction To The Theory Of Surreal Numbers
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Author : Harry Gonshor
language : en
Publisher:
Release Date : 1987
An Introduction To The Theory Of Surreal Numbers written by Harry Gonshor and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
An Introduction To Surreal Numbers
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Author : Harry Gonshor
language : en
Publisher:
Release Date : 2014-05-14
An Introduction To Surreal Numbers written by Harry Gonshor and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.
These notes provide a formal introduction to the theory of surreal numbers in a clear and lucid style.
Surreal Numbers
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Author : Donald Ervin Knuth
language : en
Publisher: Addison-Wesley Professional
Release Date : 1974
Surreal Numbers written by Donald Ervin Knuth and has been published by Addison-Wesley Professional this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Computers categories.
Nearly 30 years ago, John Horton Conway introduced a new way to construct numbers. Donald E. Knuth, in appreciation of this revolutionary system, took a week off from work on The Art of Computer Programming to write an introduction to Conway's method. Never content with the ordinary, Knuth wrote this introduction as a work of fiction--a novelette. If not a steamy romance, the book nonetheless shows how a young couple turned on to pure mathematics and found total happiness. The book's primary aim, Knuth explains in a postscript, is not so much to teach Conway's theory as "to teach how one might go about developing such a theory." He continues: "Therefore, as the two characters in this book gradually explore and build up Conway's number system, I have recorded their false starts and frustrations as well as their good ideas. I wanted to give a reasonably faithful portrayal of the important principles, techniques, joys, passions, and philosophy of mathematics, so I wrote the story as I was actually doing the research myself."... It is an astonishing feat of legerdemain. An empty hat rests on a table made of a few axioms of standard set theory. Conway waves two simple rules in the air, then reaches into almost nothing and pulls out an infinitely rich tapestry of numbers that form a real and closed field. Every real number is surrounded by a host of new numbers that lie closer to it than any other "real" value does. The system is truly "surreal." quoted from Martin Gardner, Mathematical Magic Show, pp. 16--19 Surreal Numbers, now in its 13th printing, will appeal to anyone who might enjoy an engaging dialogue on abstract mathematical ideas, and who might wish to experience how new mathematics is created. 0201038129B04062001
An Introduction To The Theory Of Surreal Numbers
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Author : Harry Gonshor
language : en
Publisher: Cambridge University Press
Release Date : 1986-09-18
An Introduction To The Theory Of Surreal Numbers written by Harry Gonshor and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-09-18 with Mathematics categories.
The surreal numbers form a system which includes both the ordinary real numbers and the ordinals. Since their introduction by J. H. Conway, the theory of surreal numbers has seen a rapid development revealing many natural and exciting properties. These notes provide a formal introduction to the theory in a clear and lucid style. The the author is able to lead the reader through to some of the problems in the field. The topics covered include exponentiation and generalized e-numbers.
Number And Numbers
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Author : Alain Badiou
language : en
Publisher: John Wiley & Sons
Release Date : 2018-05-18
Number And Numbers written by Alain Badiou 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 2018-05-18 with Science categories.
The political regime of global capitalism reduces the world to an endless network of numbers within numbers, but how many of us really understand what numbers are? Without such an understanding, how can we challenge the regime of number? In Number and Numbers Alain Badiou offers an philosophically penetrating account with a powerful political subtext of the attempts that have been made over the last century to define the special status of number. Badiou argues that number cannot be defined by the multiform calculative uses to which numbers are put, nor is it exhausted by the various species described by number theory. Drawing on the mathematical theory of surreal numbers, he develops a unified theory of Number as a particular form of being, an infinite expanse to which our access remains limited. This understanding of Number as being harbours important philosophical truths about the structure of the world in which we live. In Badiou's view, only by rigorously thinking through Number can philosophy offer us some hope of breaking through the dense and apparently impenetrable capitalist fabric of numerical relations. For this will finally allow us to point to that which cannot be numbered: the possibility of an event that would deliver us from our unthinking subordination of number.
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.
Number And Numbers
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Author : Alain Badiou
language : en
Publisher: Polity
Release Date : 2008-05-19
Number And Numbers written by Alain Badiou and has been published by Polity this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-19 with Science categories.
The political regime of global capitalism reduces the world to an endless network of numbers within numbers, but how many of us really understand what numbers are? Without such an understanding, how can we challenge the regime of number? In Number and Numbers Alain Badiou offers an philosophically penetrating account with a powerful political subtext of the attempts that have been made over the last century to define the special status of number. Badiou argues that number cannot be defined by the multiform calculative uses to which numbers are put, nor is it exhausted by the various species described by number theory. Drawing on the mathematical theory of surreal numbers, he develops a unified theory of Number as a particular form of being, an infinite expanse to which our access remains limited. This understanding of Number as being harbours important philosophical truths about the structure of the world in which we live. In Badiou's view, only by rigorously thinking through Number can philosophy offer us some hope of breaking through the dense and apparently impenetrable capitalist fabric of numerical relations. For this will finally allow us to point to that which cannot be numbered: the possibility of an event that would deliver us from our unthinking subordination of number.
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Author :
language : zh-CN
Publisher:
Release Date : 2007
written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Number theory categories.
本书内容包括素数、无理数、同余、费马定理、连分数、不定方程、二次域、算术函数、分化等。
An Interpretive Introduction To Quantum Field Theory
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Author : Paul Teller
language : en
Publisher: Princeton University Press
Release Date : 2020-07-21
An Interpretive Introduction To Quantum Field Theory written by Paul Teller 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 2020-07-21 with Science categories.
Quantum mechanics is a subject that has captured the imagination of a surprisingly broad range of thinkers, including many philosophers of science. Quantum field theory, however, is a subject that has been discussed mostly by physicists. This is the first book to present quantum field theory in a manner that makes it accessible to philosophers. Because it presents a lucid view of the theory and debates that surround the theory, An Interpretive Introduction to Quantum Field Theory will interest students of physics as well as students of philosophy. Paul Teller presents the basic ideas of quantum field theory in a way that is understandable to readers who are familiar with non-relativistic quantum mechanics. He provides information about the physics of the theory without calculational detail, and he enlightens readers on how to think about the theory physically. Along the way, he dismantles some popular myths and clarifies the novel ways in which quantum field theory is both a theory about fields and about particles. His goal is to raise questions about the philosophical implications of the theory and to offer some tentative interpretive views of his own. This provocative and thoughtful book challenges philosophers to extend their thinking beyond the realm of quantum mechanics and it challenges physicists to consider the philosophical issues that their explorations have encouraged.