Essential Concepts Of Set Theory
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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.
Set Theory
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Author : Norman T. Hamilton
language : en
Publisher: Forgotten Books
Release Date : 2018-09-22
Set Theory written by Norman T. Hamilton and has been published by Forgotten Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-22 with Mathematics categories.
Excerpt from Set Theory: The Structure of Arithmetic What prior knowledge is required to read this book? In the strictest sense one need only know how to read carefully and to write; little previous mathematical experience is needed. However, we shall, on occasion, rely upon the reader's acquaintance with some of the simplest facts of elementary arithmetic, algebra and geometry. These facts Will not be used' directly in the development of the subjects under con sideration. Their sole uses Will be to illustrate certain concepts, to motivate others and, in general, to act as a source of inspiration for What we do here. This book should not be read as a novel or a newspaper a sharp pencil and a pad of paper are essential tools for a comprehension of what fol lows. Careful attention to details Will be rewarded. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Some Basic Concepts Of Set Theory
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Author : Vincent N. Campbell
language : en
Publisher:
Release Date : 1962
Some Basic Concepts Of Set Theory written by Vincent N. Campbell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Set theory categories.
Fuzzy Set Theory
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Author : R. Lowen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Fuzzy Set Theory written by R. Lowen 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.
The purpose of this book is to provide the reader who is interested in applications of fuzzy set theory, in the first place with a text to which he or she can refer for the basic theoretical ideas, concepts and techniques in this field and in the second place with a vast and up to date account of the literature. Although there are now many books about fuzzy set theory, and mainly about its applications, e. g. in control theory, there is not really a book available which introduces the elementary theory of fuzzy sets, in what I would like to call "a good degree of generality". To write a book which would treat the entire range of results concerning the basic theoretical concepts in great detail and which would also deal with all possible variants and alternatives of the theory, such as e. g. rough sets and L-fuzzy sets for arbitrary lattices L, with the possibility-probability theories and interpretations, with the foundation of fuzzy set theory via multi-valued logic or via categorical methods and so on, would have been an altogether different project. This book is far more modest in its mathematical content and in its scope.
Set Theory Logic And Their Limitations
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Author : Moshe Machover
language : en
Publisher: Cambridge University Press
Release Date : 1996-05-23
Set Theory Logic And Their Limitations written by Moshe Machover 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 1996-05-23 with Mathematics categories.
This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.
Foundations Of Point Set Theory
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Author : Robert Lee Moore
language : en
Publisher:
Release Date : 2012-07-01
Foundations Of Point Set Theory written by Robert Lee Moore and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-01 with categories.
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.
Mathematical Methods In Linguistics
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Author : Barbara B.H. Partee
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Methods In Linguistics written by Barbara B.H. Partee 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 Language Arts & Disciplines categories.
Elementary set theory accustoms the students to mathematical abstraction, includes the standard constructions of relations, functions, and orderings, and leads to a discussion of the various orders of infinity. The material on logic covers not only the standard statement logic and first-order predicate logic but includes an introduction to formal systems, axiomatization, and model theory. The section on algebra is presented with an emphasis on lattices as well as Boolean and Heyting algebras. Background for recent research in natural language semantics includes sections on lambda-abstraction and generalized quantifiers. Chapters on automata theory and formal languages contain a discussion of languages between context-free and context-sensitive and form the background for much current work in syntactic theory and computational linguistics. The many exercises not only reinforce basic skills but offer an entry to linguistic applications of mathematical concepts. For upper-level undergraduate students and graduate students in theoretical linguistics, computer-science students with interests in computational linguistics, logic programming and artificial intelligence, mathematicians and logicians with interests in linguistics and the semantics of natural language.
Set Theory And Logic
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Author : Robert R. Stoll
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23
Set Theory And Logic written by Robert R. Stoll and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Mathematics categories.
Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.
Naive Set Theory
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Author : Paul R. Halmos
language : en
Publisher: Courier Dover Publications
Release Date : 2017-04-19
Naive Set Theory written by Paul R. Halmos and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-19 with Mathematics categories.
Classic by prominent mathematician offers a concise introduction to set theory using language and notation of informal mathematics. Topics include the basic concepts of set theory, cardinal numbers, transfinite methods, more. 1960 edition.