Contributions to the Founding of the Theory of Transfinite Numbers PDF Download

Author: Georg Cantor
Publisher:
ISBN:
Category : Arithmetic
Languages : en
Pages : 236

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Author: George Cantor
Publisher: Cosimo, Inc.
ISBN: 1602064423
Category : Cooking
Languages : en
Pages : 225

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"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."

Author: Georg Cantor
Publisher:
ISBN:
Category : Number theory
Languages : en
Pages : 236

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Author: Georg Cantor
Publisher:
ISBN: 9780758131690
Category :
Languages : en
Pages : 211

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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. Translated with introduction by P. Jourdain.

Author: T. H. Hildebrandt
Publisher:
ISBN:
Category :
Languages : en
Pages : 382

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Author: Georg Cantor
Publisher: Hardpress Publishing
ISBN: 9781313358941
Category :
Languages : en
Pages : 236

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Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Author: Joseph Warren Dauben
Publisher: Princeton University Press
ISBN: 9780691085838
Category : Infinite..
Languages : en
Pages : 422

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One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets. This revolution is the subject of Joseph Dauben's important studythe most thorough yet writtenof the philosopher and mathematician who was once called a "corrupter of youth" for an innovation that is now a vital component of elementary school curricula. Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great interest. Cantor's own faith in his theory was partly theological. His religious beliefs led him to expect paradoxes in any concept of the infinite, and he always retained his belief in the utter veracity of transfinite set theory. Later in his life, he was troubled by recurring attacks of severe depression. Dauben shows that these played an integral part in his understanding and defense of set theory.

Author: Georg Cantor
Publisher:
ISBN: 9781330493045
Category : History
Languages : en
Pages : 228

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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."

Author: Jose Ferreiros
Publisher: Springer Science & Business Media
ISBN: 9783764357498
Category : Mathematics
Languages : en
Pages : 472

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"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)

Author: Georg 1845-1918 Cantor
Publisher: Wentworth Press
ISBN: 9781374627871
Category : History
Languages : en
Pages : 236

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