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| georg cantor: Georg Cantor Joseph Warren Dauben, 1990 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. |
| georg cantor: Georg Cantor Joseph Warren Dauben, 1990-10-10 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. |
| georg cantor: Contributions to the Founding of the Theory of Transfinite Numbers Georg Cantor, 1915 |
| georg cantor: The Philosophy of Set Theory Mary Tiles, 2012-03-08 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 |
| georg cantor: The Continuum, and Other Types of Serial Order, With an Introduction to Cantor's Transfinite Numbers Edward V. Huntington, 2022-10-27 This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. |
| georg cantor: Contributions to the Founding of the Theory of Transfinite Numbers Georg Cantor, 1911 |
| georg cantor: Labyrinth of Thought Jose Ferreiros, 2001-11-01 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) |
| georg cantor: Mathematics and the Divine Teun Koetsier, Luc Bergmans, 2004-12-09 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: Cantorian Set Theory and Limitation of Size Michael Hallett, 1986 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 |
| georg cantor: Naming Infinity Loren Graham, Jean-Michel Kantor, 2009-03-31 In 1913, Russian imperial marines stormed an Orthodox monastery at Mt. Athos, Greece, to haul off monks engaged in a dangerously heretical practice known as Name Worshipping. Exiled to remote Russian outposts, the monks and their mystical movement went underground. Ultimately, they came across Russian intellectuals who embraced Name Worshipping—and who would achieve one of the biggest mathematical breakthroughs of the twentieth century, going beyond recent French achievements. Loren Graham and Jean-Michel Kantor take us on an exciting mathematical mystery tour as they unravel a bizarre tale of political struggles, psychological crises, sexual complexities, and ethical dilemmas. At the core of this book is the contest between French and Russian mathematicians who sought new answers to one of the oldest puzzles in math: the nature of infinity. The French school chased rationalist solutions. The Russian mathematicians, notably Dmitri Egorov and Nikolai Luzin—who founded the famous Moscow School of Mathematics—were inspired by mystical insights attained during Name Worshipping. Their religious practice appears to have opened to them visions into the infinite—and led to the founding of descriptive set theory. The men and women of the leading French and Russian mathematical schools are central characters in this absorbing tale that could not be told until now. Naming Infinity is a poignant human interest story that raises provocative questions about science and religion, intuition and creativity. |
| georg cantor: Satan, Cantor & Infinity Raymond M. Smullyan, 2009-01-01 Honorable knights, lying knaves, and other fanciful characters populate this unusual survey of the principles underlying the works of Georg Cantor. Created by a renowned mathematician, these engaging puzzles apply logical precepts to issues of infinity, probability, time, and change. They require a strong mathematics background and feature complete solutions. |
| georg cantor: People, Problems, and Proofs Richard J. Lipton, Kenneth W. Regan, 2013-12-11 People, problems, and proofs are the lifeblood of theoretical computer science. Behind the computing devices and applications that have transformed our lives are clever algorithms, and for every worthwhile algorithm there is a problem that it solves and a proof that it works. Before this proof there was an open problem: can one create an efficient algorithm to solve the computational problem? And, finally, behind these questions are the people who are excited about these fundamental issues in our computational world. In this book the authors draw on their outstanding research and teaching experience to showcase some key people and ideas in the domain of theoretical computer science, particularly in computational complexity and algorithms, and related mathematical topics. They show evidence of the considerable scholarship that supports this young field, and they balance an impressive breadth of topics with the depth necessary to reveal the power and the relevance of the work described. Beyond this, the authors discuss the sustained effort of their community, revealing much about the culture of their field. A career in theoretical computer science at the top level is a vocation: the work is hard, and in addition to the obvious requirements such as intellect and training, the vignettes in this book demonstrate the importance of human factors such as personality, instinct, creativity, ambition, tenacity, and luck. The authors' style is characterize d by personal observations, enthusiasm, and humor, and this book will be a source of inspiration and guidance for graduate students and researchers engaged with or planning careers in theoretical computer science. |
| georg cantor: The Continuum, and Other Types of Serial Order Edward Vermilye Huntington, 1917 |
| georg cantor: Imaginary Philosophical Dialogues Kenneth Binmore, 2020-12-23 How would Plato have responded if his student Aristotle had ever challenged his idea that our senses perceive nothing more than the shadows cast upon a wall by a true world of perfect ideals? What would Charles Darwin have said to Karl Marx about his claim that dialectical materialism is a scientific theory of evolution? How would Jean-Paul Sartre have reacted to Simone de Beauvoir’s claim that the Marquis de Sade was a philosopher worthy of serious attention? This light-hearted book proposes answers to such questions by imagining dialogues between thirty-three pairs of philosophical sages who were alive at the same time. Sometime famous sages get a much rougher handling than usual, as when Adam Smith beards Immanuel Kant in his Konigsberg den. Sometimes neglected or maligned sages get a chance to say what they really believed, as when Epicurus explains that he wasn’t epicurean. Sometimes the dialogues are about the origins of modern concepts, as when Blaise Pascal and Pierre de Fermat discuss their invention of probability, or when John Nash and John von Neumann discuss the creation of game theory. Even in these scientific cases, the intention is that the protagonists come across as fallible human beings like the rest of us, rather than the intellectual paragons of philosophical textbooks. |
| georg cantor: The Mystery of the Aleph Amir D. Aczel, 2001-08-28 A compelling narrative that blends the story of infinity with the tragic tale of a tormented and brilliant mathematician. |
| georg cantor: The Logic of Infinity Barnaby Sheppard, 2014-07-24 This book conveys to the novice the big ideas in the rigorous mathematical theory of infinite sets. |
| georg cantor: Revolutions in Mathematics Donald Gillies, 1995 The essays in this book provide the first comprehensive treatment of the concept of revolution in mathematics. In 1962 an exciting discussion of revolutions in the natural sciences was prompted by the publication of Kuhn's The Structure of Scientific Revolutions. A fascinating but little knownoffshoot of this debate was begun in the USA in the mid-1970s: can the concept of revolutions be applied to mathematics as well as science? Michael Crowe declared that revolutions never occur in mathematics, while Joseph Dauben argued that there have been mathematical revolutions and gave someexamples.The original papers of Crowe, Dauben, and Mehrtens are reprinted in this book, together with additional chapters giving their current views. To this are added new contributions from nine further experts in the history of mathematics who each discuss an important episode and consider whether it was arevolution.This book is an excellent reference work and an ideal course text for both graduate and undergraduate courses in the history and philosophy of science and mathematics. |
| georg cantor: Everything and More: A Compact History of Infinity David Foster Wallace, 2010-10-04 A gripping guide to the modern taming of the infinite. —New York Times Part history, part philosophy, part love letter to the study of mathematics, Everything and More is an illuminating tour of infinity. With his infectious curiosity and trademark verbal pyrotechnics, David Foster Wallace takes us from Aristotle to Newton, Leibniz, Karl Weierstrass, and finally Georg Cantor and his set theory. Through it all, Wallace proves to be an ideal guide—funny, wry, and unfailingly enthusiastic. Featuring an introduction by Neal Stephenson, this edition is a perfect introduction to the beauty of mathematics and the undeniable strangeness of the infinite. |
| georg cantor: Classic Set Theory D.C. Goldrei, 2017-09-06 Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbersDefining natural numbers in terms of setsThe potential paradoxes in set theoryThe Zermelo-Fraenkel axioms for set theoryThe axiom of choiceThe arithmetic of ordered setsCantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory. |
| georg cantor: Foundations of Constructive Mathematics M.J. Beeson, 2012-12-06 This book is about some recent work in a subject usually considered part of logic and the foundations of mathematics, but also having close connec tions with philosophy and computer science. Namely, the creation and study of formal systems for constructive mathematics. The general organization of the book is described in the User's Manual which follows this introduction, and the contents of the book are described in more detail in the introductions to Part One, Part Two, Part Three, and Part Four. This introduction has a different purpose; it is intended to provide the reader with a general view of the subject. This requires, to begin with, an elucidation of both the concepts mentioned in the phrase, formal systems for constructive mathematics. Con structive mathematics refers to mathematics in which, when you prove that l a thing exists (having certain desired properties) you show how to find it. Proof by contradiction is the most common way of proving something exists without showing how to find it - one assumes that nothing exists with the desired properties, and derives a contradiction. It was only in the last two decades of the nineteenth century that mathematicians began to exploit this method of proof in ways that nobody had previously done; that was partly made possible by the creation and development of set theory by Georg Cantor and Richard Dedekind. |
| georg cantor: The History of Continua Stewart Shapiro, Geoffrey Hellman, 2021 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. |
| georg cantor: The Higher Infinite Akihiro Kanamori, 2008-11-28 Over the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research, with open questions and speculations throughout. |
| georg cantor: A Brief History of Infinity Brian Clegg, 2013-02-07 'Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space.' Douglas Adams, Hitch-hiker's Guide to the Galaxy We human beings have trouble with infinity - yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity - yet it is a concept routinely used by schoolchildren. Exploring the infinite is a journey into paradox. Here is a quantity that turns arithmetic on its head, making it feasible that 1 = 0. Here is a concept that enables us to cram as many extra guests as we like into an already full hotel. Most bizarrely of all, it is quite easy to show that there must be something bigger than infinity - when it surely should be the biggest thing that could possibly be. Brian Clegg takes us on a fascinating tour of that borderland between the extremely large and the ultimate that takes us from Archimedes, counting the grains of sand that would fill the universe, to the latest theories on the physical reality of the infinite. Full of unexpected delights, whether St Augustine contemplating the nature of creation, Newton and Leibniz battling over ownership of calculus, or Cantor struggling to publicise his vision of the transfinite, infinity's fascination is in the way it brings together the everyday and the extraordinary, prosaic daily life and the esoteric. Whether your interest in infinity is mathematical, philosophical, spiritual or just plain curious, this accessible book offers a stimulating and entertaining read. |
| georg cantor: Bridges to Infinity Michael Guillen, 1983 This book is an endlessly fascinating journey through a mathematician's looking glass. |
| georg cantor: Vita Mathematica Ronald Calinger, 1996 Enables teachers to learn the history of mathematics and then incorporate it in undergraduate teaching. |
| georg cantor: The Mathematics of Infinity Theodore G. Faticoni, 2012-04-17 Praise for the First Edition . . . an enchanting book for those people in computer science or mathematics who are fascinated by the concept of infinity.—Computing Reviews . . . a very well written introduction to set theory . . . easy to read and well suited for self-study . . . highly recommended.—Choice The concept of infinity has fascinated and confused mankind for centuries with theories and ideas that cause even seasoned mathematicians to wonder. The Mathematics of Infinity: A Guide to Great Ideas, Second Edition uniquely explores how we can manipulate these ideas when our common sense rebels at the conclusions we are drawing. Continuing to draw from his extensive work on the subject, the author provides a user-friendly presentation that avoids unnecessary, in-depth mathematical rigor. This Second Edition provides important coverage of logic and sets, elements and predicates, cardinals as ordinals, and mathematical physics. Classic arguments and illustrative examples are provided throughout the book and are accompanied by a gradual progression of sophisticated notions designed to stun readers' intuitive view of the world. With an accessible and balanced treatment of both concepts and theory, the book focuses on the following topics: Logic, sets, and functions Prime numbers Counting infinite sets Well ordered sets Infinite cardinals Logic and meta-mathematics Inductions and numbers Presenting an intriguing account of the notions of infinity, The Mathematics of Infinity: A Guide to Great Ideas, Second Edition is an insightful supplement for mathematics courses on set theory at the undergraduate level. The book also serves as a fascinating reference for mathematically inclined individuals who are interested in learning about the world of counterintuitive mathematics. |
| georg cantor: Hausdorff on Ordered Sets Felix Hausdorff, 2005 Georg Cantor, the founder of set theory, published his last paper on sets in 1897. In 1900, David Hilbert made Cantor's Continuum Problem and the challenge of well-ordering the real numbers the first problem in his famous Paris lecture. It was time for the appearance of the second generation of Cantorians. They emerged in the decade 1900-1909, and foremost among them were Ernst Zermelo and Felix Hausdorff. Zermelo isolated the Choice Principle, proved that every set could be well-ordered, and axiomatized the concept of set. He became the father of abstract set theory. Hausdorff eschewed foundations and pursued set theory as part of the mathematical arsenal. He was recognized as the era's leading Cantorian. From 1901-1909, Hausdorff published seven articles in which he created a representation theory for ordered sets and investigated sets of real sequences partially ordered by eventual dominance, together with their maximally ordered subsets. These papers are translated and appear in this volume. Each is accompanied by an introductory essay. These highly accessible works are of historical significance, not only for set theory, but also for model theory, analysis and algebra. |
| georg cantor: Galileo Unbound David D. Nolte, 2018-07-12 Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once -- setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world. |
| georg cantor: Everything and More: A Compact History of Infinity David Foster Wallace, 2010-09-21 The period from the 5th to the 7th century AD was characterised by far-reaching structural changes that affected the entire west of the Roman Empire. This process used to be regarded by scholars aspart of the dissolution of Roman order, but in current discussions it is nowexamined more critically. The contributions to this volume of conference papers combine approaches from history and literature studies in order to review the changing forms and fields of the establishment of collective identities, and to analyse them in their mutual relationships. |
| georg cantor: Reader's Guide to the History of Science Arne Hessenbruch, 2013-12-16 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. |
| georg cantor: Mathematical Fallacies and Paradoxes Bryan Bunch, 2012-10-16 Stimulating, thought-provoking analysis of the most interesting intellectual inconsistencies in mathematics, physics, and language, including being led astray by algebra (De Morgan's paradox). 1982 edition. |
| georg cantor: Mathematical Apocrypha Steven G. Krantz, 2002-09-12 Collection of stories about famous contemporary mathematicians, with illustrations. |
| georg cantor: Badiou and Indifferent Being William Watkin, 2017-09-21 The first critical work to attempt the mammoth undertaking of reading Badiou's Being and Event as part of a sequence has often surprising, occasionally controversial results. Looking back on its publication Badiou declared: “I had inscribed my name in the history of philosophy”. Later he was brave enough to admit that this inscription needed correction. The central elements of Badiou's philosophy only make sense when Being and Event is read through the corrective prism of its sequel, Logics of Worlds, published nearly twenty years later. At the same time as presenting the only complete overview of Badiou's philosophical project, this book is also the first to draw out the central component of Badiou's ontology: indifference. Concentrating on its use across the core elements Being and Event-the void, the multiple, the set and the event-Watkin demonstrates that no account of Badiou's ontology is complete unless it accepts that Badiou's philosophy is primarily a presentation of indifferent being. Badiou and Indifferent Being provides a detailed and lively section by section reading of Badiou's foundational work. It is a seminal source text for all Badiou readers. |
| georg cantor: Remarkable Mathematicians Ioan James, 2003-02-06 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. |
| georg cantor: The Elements of Cantor Sets Robert W. Vallin, 2013-07-30 A systematic and integrated approach to Cantor Sets and their applications to various branches of mathematics The Elements of Cantor Sets: With Applications features a thorough introduction to Cantor Sets and applies these sets as a bridge between real analysis, probability, topology, and algebra. The author fills a gap in the current literature by providing an introductory and integrated perspective, thereby preparing readers for further study and building a deeper understanding of analysis, topology, set theory, number theory, and algebra. The Elements of Cantor Sets provides coverage of: Basic definitions and background theorems as well as comprehensive mathematical details A biography of Georg Ferdinand Ludwig Philipp Cantor, one of the most significant mathematicians of the last century Chapter coverage of fractals and self-similar sets, sums of Cantor Sets, the role of Cantor Sets in creating pathological functions, p-adic numbers, and several generalizations of Cantor Sets A wide spectrum of topics from measure theory to the Monty Hall Problem An ideal text for courses in real analysis, topology, algebra, and set theory for undergraduate and graduate-level courses within mathematics, computer science, engineering, and physics departments, The Elements of Cantor Sets is also appropriate as a useful reference for researchers and secondary mathematics education majors. |
| georg cantor: Peirce and Contemporary Thought Kenneth Laine Ketner, 1995 A distinguished panel of essayists address many key issues in Peirce's thought. |
| georg cantor: Understanding the Infinite Shaughan Lavine, 2009-06-30 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 |
| georg cantor: Georg Cantor Abraham Adolf Fraenkel, 1930 |
| georg cantor: Richard Dedekind Stefan Müller-Stach, 2024-12-06 The two works titled What Are and What Should the Numbers Be? (1888) and Continuity and Irrational Numbers (1872) are Dedekind's contributions to the foundations of mathematics; therein, he laid the groundwork for set theory and the theory of real and natural numbers. These writings are indispensable in modern mathematics. However, Dedekind's achievements have not always been adequately acknowledged, and the content of these books is still little known to many mathematicians today. This volume contains not only the original texts but also a detailed analysis of the two writings and an interpretation in modern language, as well as a brief biography and a transcript of the famous letter to H. Keferstein. The extensive commentary offers a fascinating insight into the life and work of Dedekind's pioneering work and relates the latter to great contemporaries such as Cantor, Dirichlet, Frege, Hilbert, Kronecker, and Riemann. Researchers and students alike will find this work a valuable reference in the history of mathematics. |
| georg cantor: Handbook of Philosophical Logic Dov M. Gabbay, Franz Guenthner, 2013-03-09 It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook of Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other. |
Georg Cantor - Wikipedia
In a 1971 article entitled "Towards a Biography of Georg Cantor", the British historian of mathematics Ivor Grattan-Guinness mentions (Annals of Science 27, pp. 345–391, 1971) that …
Georg Cantor | Biography, Contributions, Books, & Facts
Georg Cantor, German mathematician who founded set theory and introduced the mathematically meaningful concept of transfinite numbers, indefinitely large but distinct from one another. His …
Georg Cantor (1845 - 1918) - Biography - MacTutor History of ...
Georg Cantor was a Russian-born mathematician who can be considered as the founder of set theory and introduced the concept of infinite numbers with his discovery of cardinal numbers. …
GEORG CANTOR – THE MAN WHO FOUNDED SET THEORY
Georg Cantor was an outstanding mathematician and violinist born in Saint Petersburg who founded Set Theory.
Georg Cantor Facts & Biography | Famous Mathematicians
Georg Cantor was a German mathematician who made significant advances in set theory. He was often unpopular with his fellows who objected to the revolutionary nature of his work, but he …
Georg Cantor - History of Math and Technology
Georg Cantor’s groundbreaking work on set theory, infinite sets, and transfinite numbers changed the course of mathematical history. Despite the opposition he faced during his lifetime, …
Georg Cantor Biography - Life of German Mathematician - Totally History
Georg Cantor was a popular German mathematician. He is best known as the inventor of set theory that later became a fundamental theory in mathematics. He was able to establish the …
Georg Cantor - Encyclopedia.com
Jun 8, 2018 · Cantor’s father, Georg Waldemar Cantor, was a successful and cosmopolitan merchant. His extant letters to his son attest to a cheerfulness of spirit and deep appreciation …
Georg Ferdinand Ludwig Philip Cantor - 5010.mathed.usu.edu
Cantor studied at the University of Berlin under mathematicians Karl Weierstrass, Ernst Kummer, and Leopold Kronecker. He became a professor at the University of Halle, where he spent the …
Georg Cantor - German Culture
Georg Cantor invented set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of …
Georg Cantor - Wikipedia
In a 1971 article entitled "Towards a Biography of Georg Cantor", the British historian of mathematics Ivor Grattan-Guinness mentions (Annals of Science 27, pp. 345–391, 1971) that he …
Georg Cantor | Biography, Contributions, Books, & Facts - Britannica
Georg Cantor, German mathematician who founded set theory and introduced the mathematically meaningful concept of transfinite numbers, indefinitely large but distinct from one another. His …
Georg Cantor (1845 - 1918) - Biography - MacTutor History of ...
Georg Cantor was a Russian-born mathematician who can be considered as the founder of set theory and introduced the concept of infinite numbers with his discovery of cardinal numbers. He …
GEORG CANTOR – THE MAN WHO FOUNDED SET THEORY
Georg Cantor was an outstanding mathematician and violinist born in Saint Petersburg who founded Set Theory.
Georg Cantor Facts & Biography | Famous Mathematicians
Georg Cantor was a German mathematician who made significant advances in set theory. He was often unpopular with his fellows who objected to the revolutionary nature of his work, but he …
Georg Cantor - History of Math and Technology
Georg Cantor’s groundbreaking work on set theory, infinite sets, and transfinite numbers changed the course of mathematical history. Despite the opposition he faced during his lifetime, Cantor’s …
Georg Cantor Biography - Life of German Mathematician - Totally History
Georg Cantor was a popular German mathematician. He is best known as the inventor of set theory that later became a fundamental theory in mathematics. He was able to establish the importance …
Georg Cantor - Encyclopedia.com
Jun 8, 2018 · Cantor’s father, Georg Waldemar Cantor, was a successful and cosmopolitan merchant. His extant letters to his son attest to a cheerfulness of spirit and deep appreciation of …
Georg Ferdinand Ludwig Philip Cantor - 5010.mathed.usu.edu
Cantor studied at the University of Berlin under mathematicians Karl Weierstrass, Ernst Kummer, and Leopold Kronecker. He became a professor at the University of Halle, where he spent the …
Georg Cantor - German Culture
Georg Cantor invented set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, …
