Georg Cantor
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Georg Cantor
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Author : Joseph Warren Dauben
language : en
Publisher: Princeton University Press
Release Date : 1990
Georg Cantor written by Joseph Warren Dauben 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 1990 with Biography & Autobiography categories.
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.
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."
Mathematics And The Divine
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Author : Teun Koetsier
language : en
Publisher: Elsevier
Release Date : 2004-12-09
Mathematics And The Divine written by Teun Koetsier and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-09 with Mathematics categories.
Mathematics and the Divine seem to correspond to diametrically opposed tendencies of the human mind. Does the mathematician not seek what is precisely defined, and do the objects intended by the mystic and the theologian not lie beyond definition? Is mathematics not Man's search for a measure, and isn't the Divine that which is immeasurable ?The present book shows that the domains of mathematics and the Divine, which may seem so radically separated, have throughout history and across cultures, proved to be intimately related. Religious activities such as the building of temples, the telling of ritual stories or the drawing of enigmatic figures all display distinct mathematical features. Major philosophical systems dealing with the Absolute and theological speculations focussing on our knowledge of the Ultimate have been based on or inspired by mathematics. A series of chapters by an international team of experts highlighting key figures, schools and trains of thought is presented here. Chinese number mysticism, the views of Pythagoras and Plato and their followers, Nicholas of Cusa's theological geometry, Spinozism and intuitionism as a philosophy of mathematics are treated side by side among many other themes in an attempt at creating a global view on the relation of mathematics and Man's quest for the Absolute in the course of history.·Mathematics and man's quest for the Absolute·A selective history highlighting key figures, schools and trains of thought ·An international team of historians presenting specific new findings as well as general overviews·Confronting and uniting otherwise compartmentalized information
Georg Cantor
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Author : Joseph Warren Dauben
language : en
Publisher: Princeton University Press
Release Date : 1990-10-10
Georg Cantor written by Joseph Warren Dauben 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 1990-10-10 with Mathematics categories.
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.
The History Of Continua
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Author : Stewart Shapiro
language : en
Publisher: Oxford University Press (UK)
Release Date : 2021
The History Of Continua written by Stewart Shapiro and has been published by Oxford University Press (UK) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematics categories.
Mathematical and philosophical thought about continuity has changed considerably over the ages, from Aristotle's insistence that a continuum is a unified whole, to the dominant account today, that a continuum is composed of infinitely many points. This book explores the key ideas and debates concerning continuity over more than 2500 years.
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.
The Mystery Of The Aleph
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Author : Amir D. Aczel
language : en
Publisher: Simon and Schuster
Release Date : 2001-08-28
The Mystery Of The Aleph written by Amir D. Aczel and has been published by Simon and Schuster this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-28 with Mathematics categories.
A compelling narrative that blends the story of infinity with the tragic tale of a tormented and brilliant mathematician.
Remarkable Mathematicians
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Author : Ioan James
language : en
Publisher: Mathematical Association of America
Release Date : 2003-02-06
Remarkable Mathematicians written by Ioan James and has been published by Mathematical Association of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-02-06 with Mathematics categories.
Ioan James introduces and profiles sixty mathematicians from the era when mathematics was freed from its classical origins to develop into its modern form. The subjects, all born between 1700 and 1910, come from a wide range of countries, and all made important contributions to mathematics, through their ideas, their teaching, and their influence. James emphasizes their varied life stories, not the details of their mathematical achievements. The book is organized chronologically into ten chapters, each of which contains biographical sketches of six mathematicians. The men and women James has chosen to portray are representative of the history of mathematics, such that their stories, when read in sequence, convey in human terms something of the way in which mathematics developed. Ioan James is a professor at the Mathematical Institute, University of Oxford. He is the author of Topological Topics (Cambridge, 1983), Fibrewise Topology (Cambridge, 1989), Introduction to Uniform Spaces (Cambridge, 1990), Topological and Uniform Spaces (Springer-Verlag New York, 1999), and co-author with Michael C. Crabb of Fibrewise Homotopy Theory (Springer-Verlag New York, 1998). James is the former editor of the London Mathematical Society Lecture Note Series and volume editor of numerous books. He is the organizer of the Oxford Series of Topology symposia and other conferences, and co-chairman of the Task Force for Mathematical Sciences of Campaign for Oxford.
Understanding The Infinite
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Author : Shaughan Lavine
language : en
Publisher: Harvard University Press
Release Date : 2009-06-30
Understanding The Infinite written by Shaughan Lavine and has been published by Harvard University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-30 with Mathematics categories.
An accessible history and philosophical commentary on our notion of infinity. How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge. Praise for Understanding the Infinite “Understanding the Infinite is a remarkable blend of mathematics, modern history, philosophy, and logic, laced with refreshing doses of common sense. It is a potted history of, and a philosophical commentary on, the modern notion of infinity as formalized in axiomatic set theory . . . An amazingly readable [book] given the difficult subject matter. Most of all, it is an eminently sensible book. Anyone who wants to explore the deep issues surrounding the concept of infinity . . . will get a great deal of pleasure from it.” —Ian Stewart, New Scientist “How, in a finite world, does one obtain any knowledge about the infinite? Lavine argues that intuitions about the infinite derive from facts about the finite mathematics of indefinitely large size . . . The issues are delicate, but the writing is crisp and exciting, the arguments original. This book should interest readers whether philosophically, historically, or mathematically inclined, and large parts are within the grasp of the general reader. Highly recommended.” —D. V. Feldman, Choice
Reader S Guide To The History Of Science
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Author : Arne Hessenbruch
language : en
Publisher: Routledge
Release Date : 2013-12-16
Reader S Guide To The History Of Science written by Arne Hessenbruch and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-16 with History categories.
The Reader's Guide to the History of Science looks at the literature of science in some 550 entries on individuals (Einstein), institutions and disciplines (Mathematics), general themes (Romantic Science) and central concepts (Paradigm and Fact). The history of science is construed widely to include the history of medicine and technology as is reflected in the range of disciplines from which the international team of 200 contributors are drawn.