A set decorator is in charge of the set dressing on a film set , which includes the furnishing s, wallpaper, lighting fixtures, and many of the other objects that will be seen in the film . Props and set dressing often overlap, but are provided by different departments. Props are defined as items which are handled directly by actors, and discussions take place between set decorator and prop masters in order to check that everything is being covered. The set decorator gives direction to buyers and to the leadman, who is in charge of the set dresser s. The set decorator maintains a set dressing budget separate from the set budget or the prop budget and answers directly to view the work they have done. Noted Set decorators See Category Set decorators , Academy Award for Best Art Direction References reflist External links http www.setdecorators.org Set Decorators Society of America film crew Category Film crew Category Arts occupations Category Scenic design job stub Filming stub fr Chef d corateur ... more details
Unreferenced date August 2010 Expert subject date August 2010 An ordered set is in order theory in mathematics is an ambiguous term referring to a Set mathematics set that is either a partially ordered set or a totally ordered set . A set with a binary relation R on its elements that is reflexive relation reflexive for all a in the set, a R a , antisymmetric relation antisymmetric if a R b and b R a , then a b and transitive relation transitive if a R b and b R c , then a R c is described as a partially ordered set or poset . If the binary relation is antisymmetric, transitive and also total for all a and b in the set, a R b or b R a , then the set is a totally ordered set . If every non empty subset has a least element, then the set is a Well order well ordered set . In information theory , an ordered set is a non data carrying set of bits as used in 8b 10b encoding . See also Array data structure computing ordered set not mentioned on blue link List computing ordered set not mentioned on blue link Category Order theory is R un mengjafr i mk nn Velordna mengd sr uk ... more details
A budget set or opportunity set includes all possible consumption bundles that someone can afford given the price s of goods and the person s income level. The budget set is bounded above by the budget line . Graphically speaking , all the consumption bundles that lie inside the budget constraint and on the budget constraint form the budget set or opportunity set. By most definitions, budget sets must be compact and convex. Microeconomics stub microeconomics Category Budgets Set Category Consumer theory ... more details
Set in Stone may refer to Set in Stone Brian McFadden album Set in Stone Brian McFadden album , 2008 Set in Stone Lord album Set in Stone Lord album , 2009 Set in Stone novel , a children s fantasy novel by Linda Newbery disambiguation Short pages monitor This long comment was added to the page to prevent it from being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Long comment. Please do not remove the monitor template without removing the comment as well. ... more details
Unreferenced auto yes date December 2009 Orphan date February 2009 In telecommunication s, a station set is the basic telephone set equipped with function keys. The telephone normally used in a business office. Category Telephony equipment DEFAULTSORT Station Set Telecomm stub ... more details
Technical date July 2010 In mathematics, a soft set is a ordered pair pair A , M where A is a set mathematics set and M is a function mathematics function such that M x is a subset of the interval mathematics interval 0,1 , where x is element mathematics element of the set A . For each x the set M x is called the set of membership of x in A , M . The set M is a subset of any well ordered set or lattice order lattice , generally M selected interval 0, 1 . Only if a set of elements M included one element for any x can the soft set be regarded as a fuzzy set . Soft sets are also called type 2 fuzzy sets and systems type 2 fuzzy sets . A Type 2 fuzzy set is a soft set such that M x is a fuzzy set . References Molodtsov D. A. A theory of soft sets . Moscow Editorial URSS, 2004. Matsievsky S. V. Sets, multisets, fuzzy and soft sets without universe . Vestnik IKSUR, 2007, N. 10, pp. 44&ndash 52. Ahmad, B., Kharal, A. http www.hindawi.com journals afs 2009 586507.html On Fuzzy Soft Sets . Advances in Fuzzy Systems Volume 2009 2009 , Article ID 586507, 6 pages doi 10.1155 2009 586507 . DEFAULTSORT Soft Set Category Set theory Math stub ru ... more details
Refimprove date September 2011 In set theory , an infinite set is a Set mathematics set that is not a finite set . Infinite sets may be countable set countable or uncountable set uncountable . Some examples are the set of all integer s, ..., 1, 0, 1, 2, ... , is a countably infinite set and the set of all real number s is an uncountable set uncountably infinite set . Properties The set of natural numbers whose existence is postulated by the axiom of infinity is infinite. It is the only set which is directly required by the axioms to be infinite. The existence of any other infinite set can be proved in Zermelo Fraenkel set theory ZFC only by showing that it follows from the existence of the natural numbers. A set is infinite if and only if for every natural number the set has a subset whose cardinality is that natural number. If the axiom of choice holds, then a set is infinite if and only if it includes a countable infinite subset. If a set of sets is infinite or contains an infinite element, then its union is infinite. The powerset of an infinite set is infinite. Any superset of an infinite set is infinite. If an infinite set is partitioned into finitely many subsets, then at least one of them must be infinite. Any set which can be mapped onto an infinite set is infinite. The Cartesian product of an infinite set and a nonempty set is infinite. The Cartesian product of an infinite ... holds, then it is infinite. If an infinite set is a well ordered set , then it must have a nonempty subset which has no greatest element. In ZF, a set is infinite if and only if the powerset of its powerset is a Dedekind infinite set , having a proper subset equinumerous to itself. If the axiom of choice is also true, infinite sets are precisely the Dedekind infinite sets. If an infinite set is a well orderable set , then it has many well orderings which are non isomorphic. History The first ... argues that the set of squares S 1,4,9,16,25,... is the same size as N 1,2,3,4,5,... because there is a one ... more details
Image Upset.svg thumb The powerset algebra of the set math 1,2,3,4 math with the upset math uparrow 1 math colored green. In mathematics , an upper set also called an upward Closure mathematics Closed sets closed set or just an upset of a partially ordered set X ,&le is a subset U with the property that, if x is in U and x y , then y is in U . The duality order theory dual notion is lower set alternatively, down set , decreasing set , initial segment the set is downward closed , which is a subset L with the property that, if x is in L and y x , then y is in L . Properties Every partially ordered set is an upper set of itself. The intersection set theory intersection and the union set theory union of upper sets is again an upper set. The complement set theory complement of any upper set is a lower set, and vice versa. Given a partially ordered set X ,&le , the family of lower sets of X ordered with the inclusion set theory inclusion relation is a complete lattice , the down set lattice O X . Given an arbitrary subset Y of an ordered set X , the smallest upper set containing Y is denoted using an up arrow as &uarr Y . Dually, the smallest lower set containing Y is denoted using a down arrow as &darr Y . A lower set is called principal if it is of the form &darr x where x is an element of X . Every lower set Y of a finite ordered set X is equal to the smallest lower set containing all maximal element s of Y Y &darr Max Y where Max Y denotes the set containing the maximal elements of Y . A directed set directed lower set is called an order ideal . The minimal element s of any upper set form an antichain . Conversely any antichain A determines an upper set x for some ... numbers An ordinal number is usually identified with the set of all smaller ordinal numbers. Thus each ordinal number forms a lower set in the class of all ordinal numbers, which are totally ordered by set inclusion. References Blanck, J. 2000 Domain representations of topological spaces . Theoretical ... more details
In mathematics, a set function is a function whose input is a set. The output is usually a number. Often the input is a set of real number s, a set of points in Euclidean space , or a set of points in some measure space . Examples Examples of set functions include The function that assigns to each set its cardinality , i.e. the number of members of the set, is a set function. The function math d A lim n to infty frac A cap 1, dots,n n , math assigning Schnirelmann density densities to sufficiently well behaved subsets A 1, 2, 3, ... , is a set function. The Lebesgue measure is a set function that assigns a non negative real number to each set of real numbers. Kolmogorov and Fomin 1975 A probability measure assigns a probability to each set in a sigma algebra algebra . Specifically, the probability of the empty set is zero and the probability of the sample space is 1, with other sets given probabilities between 0 and 1. A Possibility measure assigns a number between zero and one to each set in the powerset of some given set. See Possibility theory . A Random set is a set valued random variable . See Random compact set . References A.N. Kolmogorov and S.V. Fomin 1975 , Introductory Real Analysis , Dover. ISBN 0 486 61226 0 Further reading springer title Set function id S s084730 last Sobolev first V.I. Category Functions and mappings Category Basic concepts in set theory math stub de Mengenfunktion et Hulgafunktsioon ... more details
Precompact set may refer to Relatively compact subspace , a subset whose closure is compact Totally bounded set , a subset that can be covered by finitely many subsets of fixed size disambig ... more details
About separating sets for functions use in graph theory connectivity graph theory In mathematics a Set mathematics set of Function mathematics function s S from a set D to a set C is called a separating set for D or said to separate the points of D if for any two distinct elements x and y of D , there exists a function f in S so that f x f y . Examples The singleton set consisting of the identity function on R separates the points of R . If X is a normal topological space , then Urysohn s lemma states that the set C X of continuous function s on X with real number real or complex number complex values separates points on X . See also Stone Weierstrass theorem Category Set theory mathlogic stub ... more details
In voting system s, the Smith set , named after John H. Smith mathematician John H. Smith , is the smallest non empty set of candidates in a particular election such that each member beats every other candidate outside the set in a pairwise election. The Smith set provides one standard of optimal choice for an election outcome. Voting systems that always elect a candidate from the Smith set pass the Smith criterion and are said to be Smith efficient . A set of candidates where every member of the set pair wise beats every member outside of the set is also known as a dominating set . Properties The Smith set always exists and is well defined. There is only one smallest dominating set since dominating sets are nested, non empty, and the set of candidates is finite. The Smith set can have more ... . The Condorcet criterion Condorcet winner , if one exists, is the sole member of the Smith set. If Condorcet method Related terms weak Condorcet winner s exist, they are in the Smith set. Schwartz set comparison The Schwartz set is closely related to and is always a subset of the Smith set. The Smith set is larger if and only if a candidate in the Schwartz set has a pair wise tie with a candidate that is not in the Schwartz set. The Smith set can be constructed from the Schwartz set by repeatedly adding two types of candidates until no more such candidates exist outside the set candidates that have pair wise ties with candidates in the set, candidates that beat a candidate in the set .... Alternative formulation Any binary relation R on a set A can Preorder Constructions generate a natural partial order on the R cycle graph theory cycle equivalence class es of set A, so that xRy implies x y . When R is the Beats or Ties binary relation on the set of candidates defined by x Beats ... or tie order which is a total order . The Smith set is the maximal element of the beat or tie order. Algorithms The Smith set can be calculated with the Floyd Warshall algorithm in time big O notation ... more details
In mathematics , in the area of potential theory , a pluripolar set is the analog of a polar set potential theory polar set for plurisubharmonic function s. Definition Let math G subset mathbb C n math and let math f colon G to mathbb R cup infty math be a plurisubharmonic function which is not identically math infty math . The set math mathcal P z in G mid f z infty math is called a complete pluripolar set . A pluripolar set is any subset of a complete pluripolar set. If math f math is a holomorphic function then math log f math is a plurisubharmonic function. The zero set of math f math is then a pluripolar set. See also Skoda El Mir theorem References Steven G. Krantz. Function Theory of Several Complex Variables , AMS Chelsea Publishing, Providence, Rhode Island, 1992. PlanetMath attribution id 6021 title pluripolar set Category potential theory ... more details
ref improve date August 2011 In mathematical logic , an arithmetical set or arithmetic set is a set of natural ... countable set A e.g. the set of n tuple s of integers , the set of rational numbers , the set of formulas in some formal language , etc by using G del number s to represent elements of the set and declaring a subset of A to be arithmetical if the set of corresponding G del numbers is arithmetical. A function ... of a function graph of math f math is an arithmetical set. A real number is called arithmetical if the set ... real and imaginary parts are both arithmetical. Formal definition A set X of natural numbers is arithmetical ... is called arithmetical if its graph is an arithmetical binary relation. A set A is said to be arithmetical in a set B if A is definable by an arithmetical formula which has B as a set parameter. Examples The set of all prime number s is arithmetical. Every recursively enumerable set is arithmetical. Every computable function is arithmetically definable. The set encoding the Halting problem is arithmetical ... that the set of true formulas of first order arithmetic is not arithmetically definable. Properties The complement set theory complement of an arithmetical set is an arithmetical set. The Turing jump of an arithmetical set is an arithmetical set. The collection of arithmetical sets is countable, but there is no arithmetically definable sequence that enumerates all arithmetical sets. The set of real arithmetical numbers is denumerable , Dense order dense and order isomorphic to the set of rational numbers. Implicitly arithmetical sets Each arithmetical set has an arithmetical formula which tells whether particular numbers are in the set. An alternative notion of definability allows for a formula that does not tell whether particular numbers are in the set but tells whether the set itself satisfies some arithmetical property. A set Y of natural numbers is implicitly arithmetical or implicitly ... with no free number variables and a new set parameter Z and set membership relation math in math ... more details
In the mathematical fields of general topology and descriptive set theory , a meagre set also called a meager set or a set of first category is a set that, considered as a subset of a usually larger topological space , is in a precise sense small or negligible set negligible . The meagre subsets of a fixed space form a sigma ideal of subsets that is, any subset of a meagre set is meagre, and the union mathematics union of countable set countably many meagre sets is meagre. General topologists use ... set is not trivial in particular, the entire space is not meagre . Descriptive set theorists mostly ... the term Baire space set theory Baire space for one particular Polish space. The complement set theory complement of a meagre set is a comeagre set or residual set . Definition Given a topological space ... subsets of X . Duality mathematics Dually , a comeagre set is one whose complement set theory complement is meagre, or equivalently, the intersection set theory intersection of countably many sets with dense ... on which B is dense set dense for any nonempty open set U in X , there is a nonempty open set V contained in U such that V and B are disjoint sets disjoint . The complement of a nowhere dense set is a dense set, but not every dense set is of this form. More precisely, the complement of a nowhere dense set is a set with dense interior topology interior . Relation to Borel hierarchy Just as a nowhere ..., its closure , a meagre set need not be an F set F sub sub set countable union of closed sets , but is always contained in an F sub sub set made from nowhere dense sets by taking the closure of each set . Dually, just as the complement of a nowhere dense set need not be open, but has a dense interior topology interior contains a dense open set , a comeagre set need not be a G set G sub sub set countable intersection of open set open sets , but contains a dense G sub sub set formed from dense open sets. Terminology A meagre set is also called a set of first category a nonmeagre set ... more details
In computability theory , a Set mathematics set of natural number s is called recursive , computable or decidable if there is an algorithm which terminates after a finite amount of time and correctly decides whether or not a given number belongs to the set. A more general class of sets consists of the recursively enumerable set s, also called semidecidable sets. For these sets, it is only required that there is an algorithm that correctly decides when a number is in the set the algorithm may give no answer but not the wrong answer for numbers not in the set. A set which is not computable is called noncomputable or undecidable . Formal definition A subset math var S var of the natural number s is called ... S var . In other words, the set math var S var is recursive if and only if the indicator function ... of the natural numbers is computable. This includes these special cases The empty set is computable. The entire set of natural numbers is computable. Each natural number Set theoretic definition of natural numbers The contemporary standard as defined in standard set theory is computable that is, the set of natural numbers less than a given natural number is computable. The set of prime number s is computable. A recursive language is a recursive subset of a formal language . The set of G del numbers ... set then the complement set theory complement of A is a recursive set. If A and B are recursive ... sets. A set A is a recursive set if and only if A and the complement set theory complement of A are both recursively enumerable set s. The preimage of a recursive set under a total function total computable function is a recursive set. The image of a computable set under a total computable bijection is computable. A set is recursive if and only if it is at level math &Delta su p 0 b 1 of the arithmetical hierarchy . A set is recursive if and only if it is either the range of a nondecreasing total computable function or the empty set. The image of a computable set under a nondecreasing total ... more details
about the largest set in some set theories a proper class universe mathematics the meaning in probability theory sample space In set theory , a universal set is a Set mathematics set which contains all objects, including itself. ref Forster 1995 p. 1. ref In set theory as usually formulated, the conception of a set of all sets leads to a paradox . The reason for this lies with Zermelo s axiom of comprehension for any formula math varphi x math and set mvar A , there exists a set math x in A mid varphi ... s paradox would arise from math x in V mid x not in x math . More generally, for any set mvar A we ... set of the set of all sets would be a subset of the set of all sets, providing that both exist. This conflicts with Cantor s theorem that the power set of any set whether infinite or not always has strictly higher cardinality than the set itself. The idea of a universal set seems intuitively desirable in the Zermelo Fraenkel set theory , particularly because most versions of this theory ... carefully circumscribed mention of mvar V and similar large collections as Class set theory proper ... proper class es cannot be elements. Set theories with a universal set There are set theories known to be consistent if the usual set theory is consistent in which the universal set mvar V does exist ..., and the axiom of comprehension of naive set theory is restricted in a different way. The most widely studied set theory with a universal set is Willard Van Orman Quine s New Foundations . Alonzo Church and de Arnold Oberschelp Arnold Oberschelp also published work on such set theories. Church ... in it the singleton function is provably a set, ref Oberschelp 1973 p. 40. ref which leads immediately to paradox in New Foundations. ref Holmes 1998 p. 110. ref Zermelo Fraenkel set theory and related set theories, which are based on the idea of the cumulative hierarchy , do not allow for the existence of a universal set. See also Category of sets Non well founded set theory Russell s paradox ... more details
A test set is a set of data used in various areas of information science to assess the strength and utility of a predictive relationship. Test sets are used in artificial intelligence , machine learning , genetic programming , intelligent systems , and statistics . In all these fields, a test set has much the same role. Rationale Many procedures have been developed regression analysis was one of the earliest such approaches to be developed. The data used to construct or discover a predictive relationship are called the training set training data set. Most approaches that search through training data for empirical relationships tend to overfit the data, meaning that they can identify apparent relationships in the training data that do not hold in general. A test set is a set of data that is independence probability theory independent of the training data, but that follows the same probability distribution as the training data. If a model fit to the training set also fits the test set well, minimal overfitting has taken place. If the model fits the training set much better than it fits the test set, overfitting is likely the cause. Example Image traintest.svg center 700px thumb A training set left and a test set right from the same statistical population are shown as blue points. Two predictive models are fit to the training data. Both fitted models are plotted with both the training and test sets. In the training set, the mean squared error MSE of the fit shown in orange is 4 whereas the MSE for the fit shown in green is 9. In the test set, the MSE for the fit shown in orange is 15 and the MSE for the fit shown in green is 13. The orange curve severely overfits the training data, since its MSE increases by almost a factor of four when comparing the test set to the training set. The green curve overfits the training data much less, as its MSE increases by less than a factor ... Data analysis it Test set ... more details
In mathematics, a Bernstein set is a subset of the real line that meets every uncountable closed subset of the real line but that contains none of them. ref name oxtoby Cite book last Oxtoby first John C. title Measure and Category edition 2nd year 1980 page 24 ref A Bernstein set Partition of an interval partitions the real line into two pieces in a peculiar way every set of positive outer measure meets both the Bernstein set and its Complement set theory complement , as does every set with the property of Baire that is not a meagre set . Citation needed date December 2010 Notes Reflist References John C. Oxtoby, Measure and Category , 2nd edition 1980 Use dmy dates date December 2010 Category Mathematical structures pl Zbi r Bernsteina ... more details
In set theory , an amorphous set is an Cardinality Infinite sets infinite Set mathematics set which is not the disjoint union of two infinite subset s. Amorphous sets are Dedekind infinite set Dedekind finite . There are no such sets, if the axiom of choice is assumed. A model of Zermelo Fraenkel set theory ZF in which an amorphous set exists was given by Azriel Levy , using an earlier model of Andrzej Mostowski Mostowski . References A. Levy http matwbn.icm.edu.pl ksiazki fm fm46 fm4611.pdf The independence of various definition of finiteness , Fundamenta Mathematicae Fund. Math. , 46 1958 , 1&ndash 13. Category Axiom of choice Category Infinity settheory stub ... more details
Math stub In mathematics , an upwards centered set A is a subset of a partially ordered set P , such that any finite subset of A has an upper bound in P . Similarly, any finite subset of a downwards centered set has a lower bound. Note that any directed set is neccessarily centered, and any centered set is linked set linked . A subset B of a partial order is said to be centered if it is a countable Union set theory union of centered sets. References cite book last Fremlin first David H. title Consequences of Martin s axiom publisher Cambridge University Press location Cambridge year 1984 isbn 0 521 25091 9 others Cambridge tracts in mathematics, no. 84 Category Order theory ... more details
Set List may refer to Set List The Frames album Set List The Frames album , 2002 Set List Duane Steele album Set List Duane Steele album , 2004 Set List Greatest Songs 2006 2007 , an album by AKB48 See also Set list disambiguation Short pages monitor This long comment was added to the page to prevent it from being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Long comment. Please do not remove the monitor template without removing the comment as well. ... more details
Set piece may refer to In literature , a set piece is an at least somewhat self contained part of a work Set piece film , an elaborate sequence which sees either a chase, fight, or other action taking place in an original and memorable way In video games , a set piece is a specific, often one time gameplay mechanic that is choreographed by game designers to solve or address a particular in game situation. Set piece football , when a dead ball re enters open play, such as at a free kick or corner kick In warfare, a set piece battle may involve large formations moving according to a plan and responding to the opposing force also by plan In theatre , a set piece refers to an individual piece of furniture or other object placed on a stage. Set Piece Doctor Who , a novel based on the science fiction television series Doctor Who In architecture , set piece architecture refers to a simple, clearly ordered correspondence between interior volumes and exterior forms. Often bilaterally symmetrical or radially ordered. disambig interwiki ... more details
Unreferenced stub auto yes date December 2009 A production set is the set of all possible output bundles that a firm can produce given its vector of inputs. Used as part of profit maximization calculations. DEFAULTSORT Production Set Category Economics Category Microeconomics Microeconomics stub ... more details
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