Elements of Set Theory

Author: Herbert B. Enderton

Publisher: Academic Press

ISBN: 0080570429

Category: Mathematics

Page: 279

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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.

Theory of Sets

Author: N. Bourbaki

Publisher: Springer Science & Business Media

ISBN: 3642593097

Category: Mathematics

Page: 414

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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: 9780387940946

Category: Mathematics

Page: 194

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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.

Set Theory for the Working Mathematician

Author: Krzysztof Ciesielski,None

Publisher: Cambridge University Press

ISBN: 9780521594653

Category: Mathematics

Page: 236

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

Handbook of Set Theory

Author: Matthew Foreman,Akihiro Kanamori

Publisher: Springer Science & Business Media

ISBN: 1402057644

Category: Mathematics

Page: 2230

View: 6050

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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.

A Book of Set Theory

Author: Charles C Pinter

Publisher: Courier Corporation

ISBN: 0486795497

Category: Mathematics

Page: 256

View: 1321

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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.

The Philosophy of Set Theory

An Historical Introduction to Cantor's Paradise

Author: Mary Tiles

Publisher: Courier Corporation

ISBN: 0486138550

Category: Mathematics

Page: 256

View: 3650

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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

Introduction to the Theory of Sets

Author: Joseph Breuer

Publisher: Courier Corporation

ISBN: 0486154874

Category: Mathematics

Page: 128

View: 3364

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This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.