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Contributions to the Founding of the Theory of Transfinite Numbers
Author: George Cantor
Publisher: Cosimo, Inc.
Published: 2007-05-01
Total Pages: 225
ISBN-13: 1602064423
DOWNLOAD EBOOK →"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."
Contributions to the Founding of the Theory of Transfinite Numbers
Author: Georg Cantor
Publisher: Courier Corporation
Published: 1955-06-01
Total Pages: 229
ISBN-13: 0486600459
DOWNLOAD EBOOK →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
Contributions to the Founding of the Theory of Transfinite Numbers
Author: Georg Cantor
Publisher:
Published: 2003-01
Total Pages: 211
ISBN-13: 9780758131690
DOWNLOAD EBOOK →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.
CONTRIBUTIONS TO THE FOUNDING OF THE THEORY OF TRANSFINITE NUMBERS
Author: GEORG. CANTOR
Publisher:
Published: 2018
Total Pages: 0
ISBN-13: 9781033269688
DOWNLOAD EBOOK →Georg Cantor
Author: Joseph Warren Dauben
Publisher: Princeton University Press
Published: 1990
Total Pages: 422
ISBN-13: 9780691085838
DOWNLOAD EBOOK →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.
Labyrinth of Thought
Author: Jose Ferreiros
Publisher: Springer Science & Business Media
Published: 2001-11-01
Total Pages: 472
ISBN-13: 9783764357498
DOWNLOAD EBOOK →"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
Author: Mary Tiles
Publisher: Courier Corporation
Published: 2012-03-08
Total Pages: 258
ISBN-13: 0486138550
DOWNLOAD EBOOK →DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. /div
Set Theory and the Continuum Hypothesis
Author: Paul J. Cohen
Publisher: Courier Corporation
Published: 2008-12-09
Total Pages: 196
ISBN-13: 0486469212
DOWNLOAD EBOOK →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.
