Contributions To The Founding Of The Theory Of Transfinite Numbers Classic Reprint
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Contributions To The Founding Of The Theory Of Transfinite Numbers
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Author : Georg Cantor
language : en
Publisher: Courier Corporation
Release Date : 1955-06-01
Contributions To The Founding Of The Theory Of Transfinite Numbers written by Georg Cantor and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1955-06-01 with Mathematics categories.
The famous articles, 1895–7, that founded a new branch of mathematics. Covers addition, multiplication and exponentiation of cardinal numbers, smallest transfinite cardinal numbers, ordinal types of simple ordered aggregates, more.
Contributions To The Founding Of The Theory Of Transfinite Numbers Classic Reprint
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Author : Georg Cantor
language : en
Publisher:
Release Date : 2015-06-29
Contributions To The Founding Of The Theory Of Transfinite Numbers Classic Reprint written by Georg Cantor and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-29 with History categories.
Excerpt from Contributions to the Founding of the Theory of Transfinite Numbers This volume contains a translation of the two very important memoirs of Georg Cantor on transfinite numbers which appeared in the Mathematische Annalen for 1895 i 1897 under the title: "Beitrage zur Begrundung der transfiniten Mengenlehre." It seems to me that, since these memoirs are chiefly occupied with the investigation of the various transfinite cardinal and ordinal numbers and not with investigations belonging to what is usually described as "the theory of aggregates" or "the theory of sets" (Mengenlehre, theorie des ensembles), - the elements of the sets being real or complex numbers which are imaged as geometrical "points" in space of one or more dimensions, - the title given to them in this translation is more suitable. These memoirs are the final and logically purified statement of many of the most important results of the long series of memoirs begun by Cantor in 1870. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works."
Contributions To The Founding Of The Theory Of Transfinite Numbers
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Author : George Cantor
language : en
Publisher: Cosimo, Inc.
Release Date : 2007-05-01
Contributions To The Founding Of The Theory Of Transfinite Numbers written by George Cantor and has been published by Cosimo, Inc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-01 with Cooking categories.
"In it, Jourdain outlines the contributions of many of Cantor?'s forerunners including Fourier, Dirichlet, Cauchy, Weierstrass, Riemann, Dedekind, and Hankel and then further contextualizes Cantor?'s groundbreaking theory by recounting and examining his earlier work. In this volume, Cantor addresses: the addition and multiplication of powers the exponentiation of powers the finite cardinal numbers the smallest transfinite cardinal number aleph-zero addition and multiplication of ordinal types well-ordered aggregates the ordinal numbers of well-ordered aggregates and much more.German mathematician GEORG CANTOR (1845-1918) is best remembered for formulating set theory. His work was considered controversial at the time, but today he is widely recognized for his important contributions to the field of mathematics."
Set Theory And The Continuum Hypothesis
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Author : Paul J. Cohen
language : en
Publisher: Courier Corporation
Release Date : 2008-12-09
Set Theory And The Continuum Hypothesis written by Paul J. Cohen and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-09 with Mathematics categories.
This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.
Kinetic Theory Of Gases The An Anthology Of Classic Papers With Historical Commentary
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Author : Stephen G Brush
language : en
Publisher: World Scientific
Release Date : 2003-07-28
Kinetic Theory Of Gases The An Anthology Of Classic Papers With Historical Commentary written by Stephen G Brush and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-28 with Science categories.
This book introduces physics students and teachers to the historical development of the kinetic theory of gases, by providing a collection of the most important contributions by Clausius, Maxwell and Boltzmann, with introductory surveys explaining their significance. In addition, extracts from the works of Boyle, Newton, Mayer, Joule, Helmholtz, Kelvin and others show the historical context of ideas about gases, energy and irreversibility. In addition to five thematic essays connecting the classical kinetic theory with 20th century topics such as indeterminism and interatomic forces, there is an extensive international bibliography of historical commentaries on kinetic theory, thermodynamics, etc. published in the past four decades.The book will be useful to historians of science who need primary and secondary sources to be conveniently available for their own research and interpretation, along with the bibliography which makes it easier to learn what other historians have already done on this subject.
Labyrinth Of Thought
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Author : Jose Ferreiros
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-01
Labyrinth Of Thought written by Jose Ferreiros 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 2001-11-01 with Mathematics categories.
"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)
The Philosophy Of Set Theory
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Author : Mary Tiles
language : en
Publisher: Courier Corporation
Release Date : 2004-01-01
The Philosophy Of Set Theory written by Mary Tiles and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.
A century ago, Georg Cantor demonstrated the possibility of a series of transfinite infinite numbers. His methods, unorthodox for the time, enabled him to derive theorems that established a mathematical reality for a hierarchy of infinities. Cantor's innovation was opposed, and ignored, by the establishment; years later, the value of his work was recognized and appreciated as a landmark in mathematical thought, forming the beginning of set theory and the foundation for most of contemporary mathematics. As Cantor's sometime collaborator, David Hilbert, remarked, "No one will drive us from the paradise that Cantor has created." This volume offers a guided tour of modern mathematics' Garden of Eden, beginning with perspectives on the finite universe and classes and Aristotelian logic. Author Mary Tiles further examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory; logical objects and logical types; and independence results and the universe of sets. She concludes with views of the constructs and reality of mathematical structure. Philosophers with only a basic grounding in mathematics, as well as mathematicians who have taken only an introductory course in philosophy, will find an abundance of intriguing topics in this text, which is appropriate for undergraduate-and graduate-level courses.
Cantorian Set Theory And Limitation Of Size
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Author : Michael Hallett
language : en
Publisher: Oxford University Press
Release Date : 1986
Cantorian Set Theory And Limitation Of Size written by Michael Hallett 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 1986 with Mathematics categories.
This volume presents the philosophical and heuristic framework Cantor developed and explores its lasting effect on modern mathematics. "Establishes a new plateau for historical comprehension of Cantor's monumental contribution to mathematics." --The American Mathematical Monthly
The National Union Catalog Pre 1956 Imprints
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Author : Library of Congress
language : en
Publisher:
Release Date : 1970
The National Union Catalog Pre 1956 Imprints written by Library of Congress and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Catalogs, Union categories.
Elements Of Set Theory
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Author : Herbert B. Enderton
language : en
Publisher: Gulf Professional Publishing
Release Date : 1977-04-28
Elements Of Set Theory written by Herbert B. Enderton and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-04-28 with Mathematics categories.
This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.