Elements of Set Theory

Author: Herbert B. Enderton

Publisher: Academic Press

ISBN: 0080570429

Category: Mathematics

Page: 279

View: 8205

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.

Elements of set theory

Author: Peter W. Zehna,Robert Leo Johnson

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 197

View: 3426

Theory of Sets

Author: N. Bourbaki

Publisher: Springer Science & Business Media

ISBN: 3642593097

Category: Mathematics

Page: 414

View: 7511

This is a softcover reprint of the English translation of 1968 of N. Bourbaki's, Thorie des Ensembles (1970).

The Joy of Sets

Fundamentals of Contemporary Set Theory

Author: Keith Devlin

Publisher: Springer Science & Business Media

ISBN: 146120903X

Category: Mathematics

Page: 194

View: 6320

This text covers the parts of contemporary set theory relevant to other areas of pure mathematics. After a review of "naïve" set theory, it develops the Zermelo-Fraenkel axioms of the theory before discussing the ordinal and cardinal numbers. It then delves into contemporary set theory, covering such topics as the Borel hierarchy and Lebesgue measure. A final chapter presents an alternative conception of set theory useful in computer science.

Naive Mengenlehre

Author: Paul R. Halmos

Publisher: Vandenhoeck & Ruprecht

ISBN: 9783525405277

Category: Arithmetic

Page: 132

View: 1071

Set Theory Essentials

Author: Emil G. Milewski

Publisher: Research & Education Assoc.

ISBN: 9780738672069

Category: Mathematics

Page: 108

View: 7520

REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Set Theory includes elementary logic, sets, relations, functions, denumerable and non-denumerable sets, cardinal numbers, Cantor's theorem, axiom of choice, and order relations.

Handbook of Set Theory

Author: Matthew Foreman,Akihiro Kanamori

Publisher: Springer Science & Business Media

ISBN: 1402057644

Category: Mathematics

Page: 2230

View: 5621

Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.

Elements of Mathematics

Theory of Sets

Author: Nicolas Bourbaki

Publisher: N.A

ISBN: N.A

Category: Set theory

Page: 414

View: 9349

Set Theory for the Working Mathematician

Author: Krzysztof Ciesielski

Publisher: Cambridge University Press

ISBN: 9780521594653

Category: Mathematics

Page: 236

View: 4569

Presents those methods of modern set theory most applicable to other areas of pure mathematics.

A Book of Set Theory

Author: Charles C Pinter

Publisher: Courier Corporation

ISBN: 0486795497

Category: Mathematics

Page: 256

View: 8795

Accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Topics include classes and sets, functions, natural and cardinal numbers, arithmetic of ordinal numbers, and more. 1971 edition with new material by author.

Principia mathematica

Vorwort und Einleitungen

Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: 9783518281932

Category: Mathematische Logik

Page: 167

View: 4814

Der Wüstenplanet

Roman

Author: Frank Herbert

Publisher: Heyne Verlag

ISBN: 3641173086

Category: Fiction

Page: 800

View: 9689

Der erfolgreichste Science-Fiction-Roman aller Zeiten - jetzt neu übersetzt Tausende von Jahren in der Zukunft und eine fantastische Welt: Arrakis, der Wüstenplanet. Einzigartig, herrlich – und grausam. Und doch haben es die Menschen geschafft, sich dieser lebensfeindlichen Umwelt anzupassen ... Vor fünfzig Jahren erschien Frank Herberts Roman Der Wüstenplanet – ein Datum, das den Beginn einer großartigen Erfolgsgeschichte markiert: Der Wüstenplanet wurde zum weltweiten Bestseller und von David Lynch spektakulär verfilmt. Heute gilt das Buch als Meilenstein der Zukunftsliteratur – ein monumentales Epos, das jede Generation von Leserinnen und Lesern neu für sich entdeckt.

Labyrinth of Thought

A History of Set Theory and Its Role in Modern Mathematics

Author: Jose Ferreiros

Publisher: Birkhäuser

ISBN: 3034850492

Category: Mathematics

Page: 440

View: 430

"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)

Elementary Set Theory, Part I/II

Author: K.T. Leung,Doris Lai-chue Chen

Publisher: Hong Kong University Press

ISBN: 9789622090262

Category: Mathematics

Page: 148

View: 7657

This book provides students of mathematics with the minimum amount of knowledge in logic and set theory needed for a profitable continuation of their studies. There is a chapter on statement calculus, followed by eight chapters on set theory.

Theory of Sets

Author: E. Kamke

Publisher: Courier Corporation

ISBN: 048645083X

Category: Mathematics

Page: 144

View: 5565

This introduction to the theory of sets employs the discoveries of Cantor, Russell, Weierstrass, Zermelo, Bernstein, Dedekind, and others. It analyzes concepts and principles, offering numerous examples. Topics include the rudiments of set theory, arbitrary sets and their cardinal numbers, ordered sets and their order types, and well-ordered sets and their ordinal numbers. 1950 edition.

Die Grundlagenkrise der Mathematik - Ein Wissenschaftsskandal

Null und Unendlich - Beweis und Widerlegung

Author: Gert Dr. Treiber

Publisher: tredition

ISBN: 3849590119

Category: Art

Page: 212

View: 6987

In »Die Grundlagenkrise der Mathematik« werden Widersprüche in den Grundlagen dieser Wissenschaft nachgewiesen. Dazu gehört die Mathematik des Unendlichen, die Georg Cantor (1845-1918) erschaffen hat. Sie war bereits ursprünglich in wissenschaftsuntypischer Weise hochemotional umstritten. Hilbert sah sich im Paradies, aus dem man sich nicht mehr vertreiben ließe, Poincaré diagnostizierte eine Krankheit, von der die Mathematik genesen werde. Widersprüche wurden allerdings nicht nachgewiesen, der Autor zeigt diese aber auf. Bei der auf Cantor folgenden axiomatischen Begründung seiner Theorie wurde die Null falsch definiert. Die Richtigstellung erzwingt auch eine grundlegende Korrektur der Mathematik des Unendlichen. Unumstritten waren dagegen bisher die Unvollständigkeitssätze Kurt Gödels (1906-1978), der die Existenz mathematischer Sätze fordert, für die weder Beweis noch Widerlegung möglich ist, obwohl sie wahr sind. Auch sie werden widerlegt. Eine widerspruchsfreie Theorie der Grundlagen der Mathematik wird vorgelegt. Die wissenschaftliche Publikation dieser Ergebnisse wurde durch die etablierten Mathematiker inquisitorisch verweigert, dies begründet den Untertitel »Ein Wissenschaftsskandal«. Die Thematik ist in einer Form aufbereitet, die sie einem breiten Leserkreis auch ohne vertiefte Kenntnisse der Mathematik zugänglich macht. In einer in der Wissenschaftsgeschichte einmaligen, nur durch das Internet möglichen Aktion fordert der Autor seine Leser auf, sich für die alte oder die neue Theorie zu entscheiden, um einen wissenschaftlichen Diskurs unumgänglich zu machen. Entscheiden Sie mit!