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# Topic: Cover set theory

 Paracompact space - Wikipedia, the free encyclopedia A cover of a set X is a collection of subsets of X whose union is X. A refinement of a cover of a space X is a new cover of the same space such that every set in the new cover is a subset of some set in the old cover. Given a cover and a point, the star of the point in the cover is the union of all the sets in the cover that contain the point. en.wikipedia.org /wiki/Paracompact_space   (1258 words)

 Covering (graph theory) - Wikipedia, the free encyclopedia In the mathematical discipline of graph theory a covering for a graph is a set of vertices (or edges) so that the elements of the set are close (adjacent) to all edges (or vertices) of the graph. A vertex covering for a graph G is a set of vertices V so that every edge of G is incident to at least one vertex in V. An edge covering for a graph G is a set of edges E so that every vertex of G is adjacent to at least one edge in E. en.wikipedia.org /wiki/Covering_(graph_theory)   (269 words)

 Conspiracy theory - Wikipedia, the free encyclopedia The term "conspiracy theory" is usually used by mainstream scholars and in popular culture to identify a type of folklore similar to an urban legend, especially an explanatory narrative which is constructed with methodological flaws. According to many psychologists, a person who believes in one conspiracy theory is often a believer in other conspiracy theories and conversely for a person who does not believe in one conspiracy theory there is a lower probability that he, or she, will believe in another one. The term conspiracy theory is itself the object of a type of conspiracy theory, which argues that those using the term are manipulating their audience to disregard the topic under discussion, either in a deliberate attempt to conceal the truth, or as dupes of more deliberate conspirators. en.wikipedia.org /wiki/Conspiracy_theory   (4720 words)

 Set Theory :: 3DSoftware.com For a set to be finite (and countable), none of the elements of the set are duplicated. The complement of C is the set of all elements in the superset B that are not in C. A mapping (to map a set of points) is a transformation of elements of one set into the elements of another set. www.3dsoftware.com /Math/Programming/SetTheory   (2035 words)

 Georg Cantor's set theory proof of the existence of number larger than infinity still fascinates me to this day Together they set the basis for set theory, and their somewhat obvious proof schemes are now called Zermelo-Fraenkel Theory (ZF) and are the starting point for all set theory study. There are some aspect of set theory that I omit from this essay in the interest of space and clarity. Set theory differentiates between the number of elements in a set and the value of the number of elements in a set. members.tripod.com /~Robleh/cantor_set_theory.htm   (1751 words)

 Set Theory Sets are often also represented by letters, so this set might be E = {2, 4, 6, 8, 10,...}. All sets are therefore subsets of the universal set. The set A is a subset of the universal set and so it is within the rectangle. www.mathsrevision.net /alevel/pure/set_theory.php   (286 words)

 PlanetMath: cover The cover is correspondingly called a finite cover, countable cover, or uncountable cover. A topology for a set is a cover of that set. This is version 11 of cover, born on 2002-01-04, modified 2005-11-21. planetmath.org /encyclopedia/Cover.html   (99 words)

 80.07.04: Logic and Set Theory A set is a well defined collection of “objects.” The term “well defined” means that the set is described in such a way that we can determine whether or not any given object belongs to that set. Note: The definition for union says that in order for an element to be part of the solution set for AU B it must only be a member of either set A or of set B. The definition of the disjunction “or” also requires that only one statement p or q be true. In set theory there is also a similar term to that of negation in logic. www.yale.edu /ynhti/curriculum/units/1980/7/80.07.04.x.html   (3651 words)

 Set theory This is because n(A) means the number of members in set A. The universal set is the set of all sets. The set A is therefore a subset of the universal set. AuB means the union of sets A and B and contains all of the elements of both A and B. www.projectalevel.co.uk /maths/settheory.htm   (216 words)

 Introduction to Scientific Theory We have two rival theories of what it is to be a connected series of claims that are capable of explaining and facing the evidence, which are independent of other rival theories of what it is to explain or confirm scientific theories. Included in these complicated pieces of set theory will be, for example, ordered pairs of numbers that scientists regard as the energy of a photon in electron volts followed by its frequency per second. So that theory, the theory of meaning, is known only because of the connections between observed utterances of words and the observable circumstances that obtain when the utterances are made. www.mtholyoke.edu /courses/rschwart/mac/philosophy/theory.shtml   (9040 words)

 Amazon.ca: Elements of Information Theory: Books: Thomas M. Cover,Joy A. Thomas   (Site not responding. Last check: 2007-10-31) Following a brief introduction and overview, early chapters cover the basic algebraic relationships of entropy, relative entropy and mutual information, AEP, entropy rates of stochastics processes and data compression, duality of data compression and the growth rate of wealth. It covers the theory very well, but is light on the practical application (which is what drew me to the subject). Tom Cover, as one of the major contributors to the development of information theory over the years, wrote a clear and understandable book on a somewhat involved topic. www.amazon.ca /Elements-Information-Theory-Thomas-Cover/dp/0471062596   (1013 words)

 Viktor's Home Page: From Set Theory to Electromagnetism The rules of formal logic, in particular being able to formulate "compound statements" such as "A and B" where A and B are both statements (e.g., "the sky is blue and it is raining") and determine their truth value from the truth values of the individual statements. We call a set that can be subdivided into parts that can be mapped by one or more real numbers (i.e., you can cover the set with one or more coordinate charts) a manifold. So far, this is mathematics: specifically, all this stuff is constructed from the concept of a set, being a member of a set, and formal logic. www.vttoth.com /settheory.htm   (1126 words)

 Theory of Data Compression In his 1948 paper, ``A Mathematical Theory of Communication,'' Claude E. Shannon formulated the theory of data compression. Lossless data compression theory and rate-distortion theory are known collectively as source coding theory. The theory assumes that the statistical properties of the source is known. www.data-compression.com /theory.shtml   (2876 words)

 Amazon.com: Set Theory (Perspectives in Mathematical Logic): Books: Thomas J. Jech   (Site not responding. Last check: 2007-10-31) Set Theory (Studies in Logic and the Foundations of Mathematics) by Kenneth Kunen This introduction to modern set theory covers all aspects of its two main general areas: classical set theory including large cardinals, infinitary combinatorics, desriptive set theory, and independence proofs starting with Goedel's proof around 1938 followed by Cohen's proof in 1963, whereby Cohen's method of forcing probably had a greater influence on mathematics. Covers major areas of modern set theory: cardinal arithmetic, constructible sets, forcing and Boolean-valued models, large cardinals and descriptive set theory. www.amazon.com /Set-Theory-Perspectives-Mathematical-Logic/dp/3540630481   (1551 words)

 Truth, Prosentential Theory of [Internet Encyclopedia of Philosophy] The correspondence theory claims that snow’s being white is necessary but not sufficient for the truth of ‘snow is white.’ In addition to snow’s being white, the proposition that snow is white must stand in a relation of correspondence to the fact that snow is white. The prosentential theory, by contrast, claims that snow’s being white is both necessary and sufficient for the truth of ‘snow is white.’ As Alston (1996, p. The prosentential theory explains that any referring expression (e.g., a name, definite description, etc.) inherits its content from its anaphoric antecedent(s) and, when such an expression is conjoined to the truth predicate, a prosentence with the same content as the antecedent(s) results. www.iep.utm.edu /t/truthpro.htm   (6647 words)

 f06-sched   (Site not responding. Last check: 2007-10-31) We will discuss set theory (Cantor's notion of size for sets and gradations of infinity, maps between sets, equivalence relations, partitions of sets), basic logic (truth tables, negation, quatifiers), and a number of theory (divisibility, Euclidean algorithm, congruences). This theory is developed in the context of the prototypical PDEs arising in mathematical physics - The Laplace/Poisson equation, the Heat/Diffusion equation, and the Wave equation. Description: Probability theory is one of the most powerful areas of mathematics in its ability to model and to predict the behavior of physical systems as well as systems arising in technological applications. www.math.umass.edu /Course_info/courseF06.html   (3961 words)

 Amazon.ca: Set Theory, Logic and their Limitations: Books: Moshe Machover   (Site not responding. Last check: 2007-10-31) In this introduction to set theory and logic, the author discusses first order logic, and gives a rigorous axiomatic presentation of Zermelo-Fraenkel set theory. This is an outstanding advanced undergraduate treatment of the following topics at the core of modern mathematics: set theory, equivalence and ordering relations, cardinals, ordinals, propositional logic, quantifier logic, and just enough recursion theory to explain the paradoxical undecidability theorems. The treatment is thoroughly contemporary (eg, Hintikka sets) but not too difficult, because this text emerged out of the philosophy rather than the mathematics classroom. www.amazon.ca /Set-Theory-Logic-their-Limitations/dp/0521474930   (445 words)

 Amazon.com: Elements of Set Theory: Books: Herbert B. Enderton   (Site not responding. Last check: 2007-10-31) 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. It is an insightful development of set theory, both as a foundation for mathematics and a distinctive mathematical discipline in its own right. www.amazon.com /Elements-Set-Theory-Herbert-Enderton/dp/0122384407   (1492 words)

 Books on acoustics   (Site not responding. Last check: 2007-10-31) Synthesizing acoustical theory with its practical applications, it provides exhaustive narrative coverage of the subject (including advanced optional content and extensive mathematical appendixes) and extensive high-quality stand-alone illustrations for those who need to grasp concepts quickly without wading through long descriptions of complex acoustical phenomena. Carefully organized and cross-referenced to cover an enormous field, 166 articles address linear and nonlinear acoustics and cavitation, aeroacoustics and atmospheric sound propagation, underwater acoustics, ultrasonics, mechanical vibrations and shock, statistical methods, noise control, architectural acoustics, signal processing, physiological acoustics, psychological acoustics, speech communications, musical acoustics, bioacoustics, animal bioacoustics, measurements and instrumentation, and transducer design. It covers engineering aspects (aerodynamics and jet noise, interaction of fluid motion and sound, infrasound, ultrasonics, quantum acoustics, etc.) and scientific aspects (auditory function, acoustical properties of the outer and inner ear, psychological speech perception, music and musical acoustics, hearing and sound perception among vertebrate/invertebrate animals). www.tlpsound.com /acoustics-books.htm   (627 words)

 MTH-3E17: Set theory   (Site not responding. Last check: 2007-10-31) Introduction: This unit is concerned with foundational issues of mathematics and provides the appropriate mathematical framework in which to discuss ‘sizes of infinity.’ It will cover cardinality, ordinals, the Zermelo - Fraenkel axioms for set theory and the Axiom of Choice. Assessment is by exercises set throughout the unit (20%) and a written exam (80%). For example without this axiom (or rather, method of construction of a new set from given ones) we cannot show that every vector space has a basis. www.mth.uea.ac.uk /maths/syllabuses/0405/3E1704.html   (397 words)

 The Encyclopedia of Water The goal is to prepare an encyclopedia that covers designated topics in a clear concise and authoritative manner. Theory will be included only where it is required for an understanding of the topic. The data set can be submitted in tabular or graphic form. wileywater.com /Encyclopedia.htm   (602 words)

 Cover Pages: W3C Recommendations: Resource Description Framework (RDF) and Web Ontology Language (OWL). Model theory assumes that the language refers to a 'world', and describes the minimal conditions that a world must satisfy in order to assign an appropriate meaning for every expression in the language. The chief utility of a formal semantic theory is not to provide any deep analysis of the nature of the things being described by the language or to suggest any particular processing model, but rather to provide a technical way to determine when inference processes are valid, i.e. An ontology formally defines a common set of terms that are used to describe and represent a domain. xml.coverpages.org /ni2004-02-10-a.html   (4068 words)

 Extended Set Theory Storage Model It seems kind of obvious to me that a unified theory that can cover everything would be the preferred approach, just as we seek in physics and other sciences. Those few who have built things based on the theory have this in common: we all got something good, and we are to this day not sure that what we did was what Dave was talking about. However it is rather easier to write in set theory, with the right set of operations. c2.com /cgi/wiki?ExtendedSetTheoryStorageModel   (2258 words)

 What is set theory? - Ask.com Web Search Set theory is the mathematical theory of sets, which represent collections of abstract objects. set theory is often assumed to be the application of mathematical set theory to music, there is little coincidence between the terminology and even less between the methods of the two. continuum hypothesis statement of set theory that the set of real numbers (the continuum) is in a sense as small as it can be. www.ask.com /web?q=What+is+set+theory?&qsrc=62   (267 words)

 1.7.1 Set Cover   (Site not responding. Last check: 2007-10-31) Excerpt from The Algorithm Design Manual: Set cover arises when you try to efficiently acquire or represent items that have been packaged in a fixed set of lots. An interesting application of set cover is Boolean logic minimization. Given a set of feasible ``and'' terms, each of which covers a subset of the vectors we need, we seek to ``or'' together the smallest number of terms that realize the function. www.cs.sunysb.edu /~algorith/files/set-cover.shtml   (253 words)

 597 Modern Set Theory   (Site not responding. Last check: 2007-10-31) The course is an introduction to modern set theory. It will cover basic set theory, set operations, antinomies, axioms, set theory as foundations of mathematics, cardinal and ordinal arithmetic, the Axiom of Choice, and an introduction to the metamathematics of set theory. The textbook will be Discovering Modern Set Theory I by W.Just and M.Weese. math.boisestate.edu /~hudson/courses/597modernsettheory.html   (55 words)

 Set Theory book download page   (Site not responding. Last check: 2007-10-31) Kenneth Kunen, Set Theory: An introduction to independence proofs: This is the most elegant and rigorous introduction to independence proofs. Kechris, Classical Descriptive Set Theory: A very well written introduction to descriptive set theory, containing most of the results in the field which you are going to use frequently. Tomek Bartoszynski and Haim Judah, Set Theory: On the structure of the real line: This is perhaps the best book about set theoretic analysis of the real line, special sets of real numbers, and forcing notions adding new reals. www.cs.biu.ac.il /~tsaban/SetTheory/sets.html   (165 words)

 The Math Forum - Math Library - Graph Theory   (Site not responding. Last check: 2007-10-31) A graph is a set V of vertices and a set E of edges - pairs of elements of V. This simple definition makes Graph Theory the appropriate language for discussing (binary) relations on sets. It consists of a set of four cubes with one of four colors on each of their six faces. One set of Penrose tilings consists of a pair of diamond-shaped figures--one fat and one skinny. mathforum.org /library/topics/graph_theory   (2440 words)

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