Set Theory Essentials
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Set Theory Essentials
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Author : Emil Milewski
language : en
Publisher: Research & Education Assoc.
Release Date : 2013-01-01
Set Theory Essentials written by Emil Milewski and has been published by Research & Education Assoc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-01 with Mathematics categories.
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.
Set Theory Essentials
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Author : Emil Milewski
language : en
Publisher: Research & Education Assoc.
Release Date : 2013-01-01
Set Theory Essentials written by Emil Milewski and has been published by Research & Education Assoc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-01 with Mathematics categories.
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.
Essential Concepts Of Set Theory
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Author : Robert S. Y. Wong
language : en
Publisher: 香港教育圖書公司
Release Date : 2016-07-01
Essential Concepts Of Set Theory written by Robert S. Y. Wong and has been published by 香港教育圖書公司 this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-01 with Mathematics categories.
For thousands of years, it is generally believed that mathematics begins with the natural numbers and counting. But there is something more fundamental than counting. It is the grouping of things. If a child is shown a picture of a farm with sheep and cows here and there and asked to count the number of sheep, the child would first put the sheep in a group mentally and then count the number of sheep in the group. Without grouping, counting cannot happen. Therefore, mathematics begins with the grouping of objects, which is the object of study of set theory. In this book, we explore the fundamental concepts of sets and related topics: propositional logic, methods of proof, relations and functions. Unlike the technical approach adopted in most books, we use many everyday examples to show that these concepts can be found everywhere in our daily life. The book also has plenty of exercises and solutions to all exercises are provided.
Fundamentals Of Contemporary Set Theory
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Author : K. J. Devlin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Fundamentals Of Contemporary Set Theory written by K. J. Devlin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is intended to provide an account of those parts of contemporary set theory which are of direct relevance to other areas of pure mathematics. The intended reader is either an advanced level undergraduate, or a beginning graduate student in mathematics, or else an accomplished mathematician who desires or needs a familiarity with modern set theory. The book is written in a fairly easy going style, with a minimum of formalism (a format characteristic of contemporary set theory) • In Chapter I the basic principles of set theory are developed in a "naive" tl manner. Here the notions of "set I II union " , "intersection", "power set" I "relation" I "function" etc. are defined and discussed. One assumption in writing this chapter has been that whereas the reader may have met all of these concepts before, and be familiar with their usage, he may not have considered the various notions as forming part of the continuous development of a pure subject (namely set theory) • Consequently, our development is at the same time rigorous and fast. Chapter II develops the theory of sets proper. Starting with the naive set theory of Chapter I, we begin by asking the question "What is a set?" Attempts to give a rLgorous answer lead naturally to the axioms of set theory introduced by Zermelo and Fraenkel, which is the system taken as basic in this book.
The Joy Of Sets
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Author : Keith Devlin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Joy Of Sets written by Keith Devlin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Discovering Modern Set Theory The Basics
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Author : Winfried Just
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Discovering Modern Set Theory The Basics written by Winfried Just and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This book is an introduction to set theory for beginning graduate students who want to get a sound grounding in those aspects of set theory used extensively throughout other areas of mathematics. Topics covered include formal languages and models, the power and limitation of the Axiomatic Method, the Axiom of Choice, including the fascinating Banach-Tarski Paradox, applications of Zorn's Lemma, ordinal arithmetic, including transfinite induction, and cardinal arithmetic. The style of writing, more a dialogue with the reader than that of the Master indoctrinating the pupil, makes this also very suitable for self-study.
Set Theory
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Author : Andras Hajnal
language : en
Publisher: Cambridge University Press
Release Date : 1999-11-11
Set Theory written by Andras Hajnal and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-11 with Mathematics categories.
This is a classic introduction to set theory, from the basics through to the modern tools of combinatorial set theory.
The Joy Of Sets
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Author : Keith J. Devlin
language : en
Publisher: Springer
Release Date : 1993-01-01
The Joy Of Sets written by Keith J. Devlin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Mengenlehre categories.
"This book provides an account of those parts of contemporary set theory that are relevant to other areas of pure mathematics. Intended for advanced undergraduates and beginning graduate students, the text is written in an easy-going style, with a minimum of formalism. The book begins with a review of "naive" set theory; it then develops the Zermelo-Fraenkel axioms of the theory, showing how they arise naturally from a rigorous answer to the question, "what is a set?" After discussing the ordinal and cardinal numbers, the book then delves into contemporary set theory, covering such topics as: the Borel hierarchy, stationary sets and regressive functions, and Lebesgue measure. Two chapters present an extension of the Zermelo-Fraenkel theory, discussing the axiom of constructibility and the question of provability in set theory. A final chapter presents an account of an alternative conception of set theory that has proved useful in computer science, the non-well-founded set theory of Peter Aczel"--Back cover.
An Introduction To Proofs With Set Theory
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Author : Daniel Ashlock
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2020-06-24
An Introduction To Proofs With Set Theory written by Daniel Ashlock and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-24 with Mathematics categories.
This text is intended as an introduction to mathematical proofs for students. It is distilled from the lecture notes for a course focused on set theory subject matter as a means of teaching proofs. Chapter 1 contains an introduction and provides a brief summary of some background material students may be unfamiliar with. Chapters 2 and 3 introduce the basics of logic for students not yet familiar with these topics. Included is material on Boolean logic, propositions and predicates, logical operations, truth tables, tautologies and contradictions, rules of inference and logical arguments. Chapter 4 introduces mathematical proofs, including proof conventions, direct proofs, proof-by-contradiction, and proof-by-contraposition. Chapter 5 introduces the basics of naive set theory, including Venn diagrams and operations on sets. Chapter 6 introduces mathematical induction and recurrence relations. Chapter 7 introduces set-theoretic functions and covers injective, surjective, and bijective functions, as well as permutations. Chapter 8 covers the fundamental properties of the integers including primes, unique factorization, and Euclid's algorithm. Chapter 9 is an introduction to combinatorics; topics included are combinatorial proofs, binomial and multinomial coefficients, the Inclusion-Exclusion principle, and counting the number of surjective functions between finite sets. Chapter 10 introduces relations and covers equivalence relations and partial orders. Chapter 11 covers number bases, number systems, and operations. Chapter 12 covers cardinality, including basic results on countable and uncountable infinities, and introduces cardinal numbers. Chapter 13 expands on partial orders and introduces ordinal numbers. Chapter 14 examines the paradoxes of naive set theory and introduces and discusses axiomatic set theory. This chapter also includes Cantor's Paradox, Russel's Paradox, a discussion of axiomatic theories, an exposition on Zermelo‒Fraenkel Set Theory with the Axiom of Choice, and a brief explanation of Gödel's Incompleteness Theorems.
The Essentials Of Set Theory
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Author : Emil G. Milewski
language : en
Publisher: Research & Education Assoc.
Release Date : 1989
The Essentials Of Set Theory written by Emil G. Milewski and has been published by Research & Education Assoc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
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.