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Handbook of Set Theory

Handbook of Set Theory Author Matthew Foreman
ISBN-10 9781402057649
Release 2009-12-10
Pages 2230
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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.



Handbook of set theory 2 2010

Handbook of set theory  2  2010 Author Matthew Foreman
ISBN-10 OCLC:699768131
Release 2010
Pages 14
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Handbook of set theory 2 2010 has been writing in one form or another for most of life. You can find so many inspiration from Handbook of set theory 2 2010 also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Handbook of set theory 2 2010 book for free.



Handbook of Set Theory

Handbook of Set Theory Author Matthew Foreman
ISBN-10 9048118069
Release 2010-11-15
Pages 2196
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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.



Handbook of Set Theoretic Topology

Handbook of Set Theoretic Topology Author K. Kunen
ISBN-10 9781483295152
Release 2014-06-28
Pages 1282
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This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest. In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhász on cardinal functions; Roitman and Abraham-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.



Handbook of Research on Fuzzy and Rough Set Theory in Organizational Decision Making

Handbook of Research on Fuzzy and Rough Set Theory in Organizational Decision Making Author Sangaiah, Arun Kumar
ISBN-10 9781522510093
Release 2016-10-17
Pages 474
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Soft computing techniques are innovative tools that use nature-inspired algorithms to run predictive analysis of industries from business to software measurement. These tools have gained momentum in recent years for their practicality and flexibility. The Handbook of Research on Fuzzy and Rough Set Theory in Organizational Decision Making collects both empirical and applied research in the field of fuzzy set theory, and bridges the gap between the application of soft computational approaches and the organizational decision making process. This publication is a pivotal reference for business professionals, IT specialists, software engineers, and advanced students of business and information technology.



Handbook of Mathematical Logic

Handbook of Mathematical Logic Author J. Barwise
ISBN-10 0080933645
Release 1982-03-01
Pages 1164
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The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.



Handbook of Analysis and Its Foundations

Handbook of Analysis and Its Foundations Author Eric Schechter
ISBN-10 0080532993
Release 1996-10-24
Pages 883
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Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/



Handbook of Measure Theory

Handbook of Measure Theory Author E. Pap
ISBN-10 0080533094
Release 2002-10-31
Pages 1632
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The main goal of this Handbook is to survey measure theory with its many different branches and its relations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications which support the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the various areas they contain many special topics and challenging problems valuable for experts and rich sources of inspiration. Mathematicians from other areas as well as physicists, computer scientists, engineers and econometrists will find useful results and powerful methods for their research. The reader may find in the Handbook many close relations to other mathematical areas: real analysis, probability theory, statistics, ergodic theory, functional analysis, potential theory, topology, set theory, geometry, differential equations, optimization, variational analysis, decision making and others. The Handbook is a rich source of relevant references to articles, books and lecture notes and it contains for the reader's convenience an extensive subject and author index.



Handbook of Proof Theory

Handbook of Proof Theory Author S.R. Buss
ISBN-10 0080533183
Release 1998-07-09
Pages 810
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This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.



The Higher Infinite

The Higher Infinite Author Akihiro Kanamori
ISBN-10 9783540888673
Release 2008-11-23
Pages 538
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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.



Higher Education Handbook of Theory and Research

Higher Education  Handbook of Theory and Research Author John C. Smart
ISBN-10 9400707029
Release 2011-03-24
Pages 506
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Published annually since 1985, the Handbook series provides a compendium of thorough and integrative literature reviews on a diverse array of topics of interest to the higher education scholarly and policy communities. Each chapter provides a comprehensive review of research findings on a selected topic, critiques the research literature in terms of its conceptual and methodological rigor, and sets forth an agenda for future research intended to advance knowledge on the chosen topic. The Handbook focuses on twelve general areas that encompass the salient dimensions of scholarly and policy inquiries undertaken in the international higher education community. The series is fortunate to have attracted annual contributions from distinguished scholars throughout the world.



Intelligent Decision Support

Intelligent Decision Support Author Shi-Yu Huang
ISBN-10 9789401579759
Release 2013-03-09
Pages 473
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Intelligent decision support is based on human knowledge related to a specific part of a real or abstract world. When the knowledge is gained by experience, it is induced from empirical data. The data structure, called an information system, is a record of objects described by a set of attributes. Knowledge is understood here as an ability to classify objects. Objects being in the same class are indiscernible by means of attributes and form elementary building blocks (granules, atoms). In particular, the granularity of knowledge causes that some notions cannot be expressed precisely within available knowledge and can be defined only vaguely. In the rough sets theory created by Z. Pawlak each imprecise concept is replaced by a pair of precise concepts called its lower and upper approximation. These approximations are fundamental tools and reasoning about knowledge. The rough sets philosophy turned out to be a very effective, new tool with many successful real-life applications to its credit. It is worthwhile stressing that no auxiliary assumptions are needed about data, like probability or membership function values, which is its great advantage. The present book reveals a wide spectrum of applications of the rough set concept, giving the reader the flavor of, and insight into, the methodology of the newly developed disciplines. Although the book emphasizes applications, comparison with other related methods and further developments receive due attention.



Introduction to Modern Set Theory

Introduction to Modern Set Theory Author Judith Roitman
ISBN-10 0471635197
Release 1990-01-16
Pages 156
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This is modern set theory from the ground up--from partial orderings and well-ordered sets to models, infinite cobinatorics and large cardinals. The approach is unique, providing rigorous treatment of basic set-theoretic methods, while integrating advanced material such as independence results, throughout. The presentation incorporates much interesting historical material and no background in mathematical logic is assumed. Treatment is self-contained, featuring theorem proofs supported by diagrams, examples and exercises. Includes applications of set theory to other branches of mathematics.



Handbook of Identity Theory and Research

Handbook of Identity Theory and Research Author Seth J. Schwartz
ISBN-10 1441979883
Release 2011-06-22
Pages 998
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Identity is one of the most extensively studied constructs in the social sciences. Yet, despite the wealth of findings across many disciplines, identity researchers remain divided over such enduring fundamental questions as: What exactly is identity, and how do identity processes function? Do people have a single identity or multiple identities? Is identity individually or collectively oriented? Personally or socially constructed? Stable or constantly in flux? The Handbook of Identity Theory and Research offers the rare opportunity to address the questions and reconcile these seeming contradictions, bringing unity and clarity to a diverse and fragmented literature. This exhaustive reference work emphasizes the depth and complexity of identity processes and domains and presents perspectives from many different theoretical schools and empirical approaches. Contributing authors provide perspectives from psychology (e.g., narrative, social identity theory, neo-Eriksonian) and from other disciplines (e.g., sociology, political science, ethnic studies); and the editors highlight the links between chapters that provide complementary insights on related subjects. In addition to covering identity processes and categories that are well-known to the field, the Handbook tackles many emerging issues, including: - Identity development among adopted persons. - Identity processes in interpersonal relationships. - Effects of globalization on cultural identity. - Transgender experience and identity. - Consumer identity and shopping behavior. - Social identity processes in xenophobia and genocide. The Handbook of Identity Theory and Research lends itself to a wealth of uses by scholars, clinicians, and graduate students across many disciplines, including social, developmental, and child/school psychology; human development and family studies; sociology; cultural anthropology; gender, ethnic, and communication studies; education; and counseling.



Handbook of Mathematical Induction

Handbook of Mathematical Induction Author David S. Gunderson
ISBN-10 113819901X
Release 2016-10
Pages 921
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Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics. In the first part of the book, the author discusses different inductive techniques, including well-ordered sets, basic mathematical induction, strong induction, double induction, infinite descent, downward induction, and several variants. He then introduces ordinals and cardinals, transfinite induction, the axiom of choice, Zorn s lemma, empirical induction, and fallacies and induction. He also explains how to write inductive proofs. The next part contains more than 750 exercises that highlight the levels of difficulty of an inductive proof, the variety of inductive techniques available, and the scope of results provable by mathematical induction. Each self-contained chapter in this section includes the necessary definitions, theory, and notation and covers a range of theorems and problems, from fundamental to very specialized. The final part presents either solutions or hints to the exercises. Slightly longer than what is found in most texts, these solutions provide complete details for every step of the problem-solving process. "



Handbook of Mathematical Formulas

Handbook of Mathematical Formulas Author Hans-Jochen Bartsch
ISBN-10 9781483267425
Release 2014-05-10
Pages 528
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Handbook of Mathematical Formulas presents a compilation of formulas to provide the necessary educational aid. This book covers the whole field from the basic rules of arithmetic, via analytic geometry and infinitesimal calculus through to Fourier's series and the basics of probability calculus. Organized into 12 chapters, this book begins with an overview of the fundamental notions of set theory. This text then explains linear expression wherein the variables are only multiplied by constants and added to constants or expressions of the same kind. Other chapters consider a variety of topics, including matrices, statistics, linear optimization, Boolean algebra, and Laplace's transforms. This book discusses as well the various systems of coordinates in analytical geometry. The final chapter deals with algebra of logic and its development into a two-value Boolean algebra as switching algebra. This book is intended to be suitable for students of technical schools, colleges, and universities.



Handbook of the Geometry of Banach Spaces

Handbook of the Geometry of Banach Spaces Author
ISBN-10 0080533507
Release 2003-05-06
Pages 870
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Handbook of the Geometry of Banach Spaces