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Inmathematics, avector bundleis atopologicalconstruction that makes precise the idea of afamilyofvector spacesparameterized by anotherspaceX{\displaystyle X}(for exampleX{\displaystyle X}could be atopological space, amanifold, or analgebraic variety): to every pointx{\displaystyle x}of the spaceX{\displaystyle X}we ass... | https://en.wikipedia.org/wiki/Vector_bundle |
Intopologyandhigh energy physics, theWu–Yang dictionaryrefers to the mathematical identification that allows back-and-forth translation between the concepts ofgauge theoryand those ofdifferential geometry. The dictionary appeared in 1975 in an article byTai Tsun WuandC. N. Yangcomparingelectromagnetismandfiber bundle... | https://en.wikipedia.org/wiki/Wu%E2%80%93Yang_dictionary |
Ingraph theory, afriendly-index setis afinite setofintegersassociated with a givenundirected graphand generated by a type ofgraph labelingcalled afriendly labeling.
A friendly labeling of ann-vertex undirected graphG= (V,E)is defined to be an assignment of the values 0 and 1 to the vertices ofGwith the property that ... | https://en.wikipedia.org/wiki/Friendly-index_set |
Inmathematics, and more specifically inhomological algebra, thesplitting lemmastates that in anyabelian category, the following statements areequivalentfor ashort exact sequence
If any of these statements holds, the sequence is called asplit exact sequence, and the sequence is said tosplit.
In the above short exact s... | https://en.wikipedia.org/wiki/Splitting_lemma |
Inmathematics, theinverse functionof afunctionf(also called theinverseoff) is afunctionthat undoes the operation off. The inverse offexistsif and only iffisbijective, and if it exists, is denoted byf−1.{\displaystyle f^{-1}.}
For a functionf:X→Y{\displaystyle f\colon X\to Y}, its inversef−1:Y→X{\displaystyle f^{-1}\co... | https://en.wikipedia.org/wiki/Inverse_function#Left_and_right_inverses |
Inmathematics, particularly incombinatorics, given afamily of sets, here called a collectionC, atransversal(also called across-section[1][2][3]) is a set containing exactly one element from each member of the collection. When the sets of the collection are mutually disjoint, each element of the transversal corresponds ... | https://en.wikipedia.org/wiki/Transversal_(combinatorics) |
Inmathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. There is a large theory ofspecial functionswhich developed out ofstatisticsandmathematical physics. A modern, abstract point of view c... | https://en.wikipedia.org/wiki/List_of_mathematical_functions |
Setscan be classified according to the properties they have. | https://en.wikipedia.org/wiki/List_of_types_of_sets |
In applied mathematics,test functions, known asartificial landscapes, are useful to evaluate characteristics of optimization algorithms, such asconvergence rate, precision, robustness and general performance.
Here some test functions are presented with the aim of giving an idea about the different situations that opti... | https://en.wikipedia.org/wiki/Test_functions_for_optimization |
This following list features abbreviated names of mathematical functions, function-like operators and other mathematical terminology. | https://en.wikipedia.org/wiki/List_of_mathematical_abbreviations |
This is alist of special function eponymsinmathematics, to cover the theory ofspecial functions, thedifferential equationsthey satisfy, nameddifferential operatorsof the theory (but not intended to include every mathematicaleponym). Namedsymmetric functions, and other special polynomials, are included. | https://en.wikipedia.org/wiki/List_of_special_functions_and_eponyms |
Inanalytical chemistry, acalibration curve, also known as astandard curve, is a general method for determining the concentration of a substance in an unknown sample by comparing the unknown to a set of standard samples of known concentration.[1]A calibration curve is one approach to the problem of instrument calibratio... | https://en.wikipedia.org/wiki/Calibration_curve |
Curve-fitting compactionisdata compactionaccomplished by replacing data to be stored or transmitted with ananalytical expression.
Examples of curve-fitting compaction consisting ofdiscretizationand theninterpolationare:
This article incorporatespublic domain materialfromFederal Standard 1037C.General Services Adminis... | https://en.wikipedia.org/wiki/Curve-fitting_compaction |
Inapplied mathematics,discretizationis the process of transferringcontinuousfunctions, models, variables, and equations intodiscretecounterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers.Dichotomizationis the specia... | https://en.wikipedia.org/wiki/Discretization |
In general, afunction approximationproblem asks us to select afunctionamong awell-defined class[citation needed][clarification needed]that closely matches ("approximates") atarget function[citation needed]in a task-specific way.[1][better source needed]The need for function approximations arises in many branches ofappl... | https://en.wikipedia.org/wiki/Function_approximation |
Genetic programming(GP) is anevolutionary algorithm, an artificial intelligence technique mimicking natural evolution, which operates on a population of programs. It applies thegenetic operatorsselectionaccording to a predefinedfitness measure,mutationandcrossover.
The crossover operation involves swapping specified p... | https://en.wikipedia.org/wiki/Genetic_programming |
Inmathematicsand computing, theLevenberg–Marquardt algorithm(LMAor justLM), also known as thedamped least-squares(DLS) method, is used to solvenon-linear least squaresproblems. These minimization problems arise especially inleast squarescurve fitting. The LMA interpolates between theGauss–Newton algorithm(GNA) and th... | https://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm |
In mathematics,linear interpolationis a method ofcurve fittingusinglinear polynomialsto construct new data points within the range of a discrete set of known data points.
If the two known points are given by the coordinates(x0,y0){\displaystyle (x_{0},y_{0})}and(x1,y1){\displaystyle (x_{1},y_{1})},thelinear interpolan... | https://en.wikipedia.org/wiki/Linear_interpolation |
Amathematical modelis anabstractdescription of a concretesystemusingmathematicalconcepts andlanguage. The process of developing a mathematicalmodelis termedmathematical modeling. Mathematical models are used inapplied mathematicsand in thenatural sciences(such asphysics,biology,earth science,chemistry) andengineeringdi... | https://en.wikipedia.org/wiki/Mathematical_model |
Multi Expression Programming(MEP) is an evolutionary algorithm for generating mathematical functions describing a given set of data. MEP is aGenetic Programmingvariant encoding multiple solutions in the same chromosome. MEP representation is not specific (multiple representations have been tested). In the simplest vari... | https://en.wikipedia.org/wiki/Multi_expression_programming |
Infinance, aninterest rateswap(IRS) is aninterest rate derivative (IRD). It involves exchange of interest rates between two parties. In particular it is a"linear" IRDand one of the mostliquid, benchmark products. It has associations withforward rate agreements (FRAs), and withzero coupon swaps (ZCSs).
In its December ... | https://en.wikipedia.org/wiki/Multi-curve_framework |
Infinance,bootstrappingis a method for constructing a (zero-coupon) fixed-incomeyield curvefrom the prices of a set of coupon-bearing products, e.g.bondsandswaps.[1]
Abootstrapped curve, correspondingly, is one where the prices of the instruments used as aninputto the curve, will be an exactoutput, when these same ins... | https://en.wikipedia.org/wiki/Bootstrapping_(finance) |
In statistics,nonlinear regressionis a form ofregression analysisin which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations (iterations).
In nonlinear regre... | https://en.wikipedia.org/wiki/Nonlinear_regression |
Inmathematics, aplane curveis acurvein aplanethat may be aEuclidean plane, anaffine planeor aprojective plane. The most frequently studied cases are smooth plane curves (includingpiecewisesmooth plane curves), andalgebraic plane curves.
Plane curves also include theJordan curves(curves that enclose a region of the plan... | https://en.wikipedia.org/wiki/Plane_curve |
Probability distribution fittingor simplydistribution fittingis the fitting of aprobability distributionto a series of data concerning the repeated measurement of a variable phenomenon.
The aim of distribution fitting is topredicttheprobabilityor toforecastthefrequencyof occurrence of the magnitude of the phenomenon in... | https://en.wikipedia.org/wiki/Probability_distribution_fitting |
In mathematics, theprogressive-iterative approximation methodis aniterative methodofdata fittingwith geometric meanings.[1]Given a set of data points to be fitted, the method obtains a series of fitting curves (or surfaces) by iteratively updating the control points, and thelimitcurve (surface) caninterpolateorapproxim... | https://en.wikipedia.org/wiki/Progressive-iterative_approximation_method |
Instatisticsandimage processing, tosmoothadata setis to create an approximatingfunctionthat attempts to capture importantpatternsin the data, while leaving outnoiseor other fine-scale structures/rapid phenomena. In smoothing, the data points of a signal are modified so individual points higher than the adjacent points ... | https://en.wikipedia.org/wiki/Smoothing |
Inmathematics, asplineis afunctiondefinedpiecewisebypolynomials.
Ininterpolatingproblems,spline interpolationis often preferred topolynomial interpolationbecause it yields similar results, even when using lowdegreepolynomials, while avoidingRunge's phenomenonfor higher degrees.
In thecomputer sciencesubfields ofcomput... | https://en.wikipedia.org/wiki/Spline_(mathematics) |
In themathematicalfield ofnumerical analysis,spline interpolationis a form ofinterpolationwhere the interpolant is a special type ofpiecewisepolynomialcalled aspline. That is, instead of fitting a single, high-degree polynomial to all of the values at once, spline interpolation fits low-degree polynomials to small subs... | https://en.wikipedia.org/wiki/Spline_interpolation |
Inapplied statistics,total least squaresis a type oferrors-in-variables regression, aleast squaresdata modeling technique in which observational errors on both dependent and independent variables are taken into account. It is a generalization ofDeming regressionand also oforthogonal regression, and can be applied to bo... | https://en.wikipedia.org/wiki/Total_least_squares |
Inmathematics, animplicit curveis aplane curvedefined by animplicit equationrelating two coordinate variables, commonlyxandy. For example, theunit circleis defined by the implicit equationx2+y2=1{\displaystyle x^{2}+y^{2}=1}. In general, every implicit curve is defined by an equation of the form
for some functionFof t... | https://en.wikipedia.org/wiki/Implicit_curve |
Inmathematics, alevel setof areal-valued functionfofnreal variablesis asetwhere the function takes on a givenconstantvaluec, that is:
When the number of independent variables is two, a level set is called alevel curve, also known ascontour lineorisoline; so a levelcurveis the set of all real-valued solutions of an equ... | https://en.wikipedia.org/wiki/Level_set |
Acontour line(alsoisoline,isopleth,isoquantorisarithm) of afunction of two variablesis acurvealong which the function has a constant value, so that the curve joins points of equal value.[1][2]It is aplane sectionof thethree-dimensional graphof the functionf(x,y){\displaystyle f(x,y)}parallel to the(x,y){\displaystyle (... | https://en.wikipedia.org/wiki/Contour_line |
Anisosurfaceis a three-dimensional analog of anisoline. It is asurfacethat represents points of a constant value (e.g.pressure,temperature,velocity,density) within avolumeof space; in other words, it is alevel setof a continuousfunctionwhosedomainis3-space.
The termisolineis also sometimes used for domains of more th... | https://en.wikipedia.org/wiki/Isosurface |
In economics, themarginal rate of substitution(MRS) is the rate at which a consumer can give up some amount of one good in exchange for another good while maintaining the same level ofutility. At equilibrium consumption levels (assuming no externalities), marginal rates of substitution are identical. The marginal rate... | https://en.wikipedia.org/wiki/Marginal_rate_of_substitution |
Inmultivariable calculus, theimplicit function theorem[a]is a tool that allowsrelationsto be converted tofunctions of several real variables. It does so by representing the relation as thegraph of a function. There may not be a single function whose graph can represent the entire relation, but there may be such a funct... | https://en.wikipedia.org/wiki/Implicit_function_theorem |
Incalculus,logarithmic differentiationordifferentiation by taking logarithmsis a method used todifferentiatefunctionsby employing thelogarithmic derivativeof a functionf,[1](lnf)′=f′f⟹f′=f⋅(lnf)′.{\displaystyle (\ln f)'={\frac {f'}{f}}\quad \implies \quad f'=f\cdot (\ln f)'.}
The technique is often performed in case... | https://en.wikipedia.org/wiki/Logarithmic_differentiation |
Incomputer graphics, apolygonizeris a software component for converting a geometric model represented as animplicit surfaceto apolygon mesh.[1]
Thiscomputer graphics–related article is astub. You can help Wikipedia byexpanding it. | https://en.wikipedia.org/wiki/Polygonizer |
Indifferential calculus,related ratesproblems involve finding a rate at which a quantity changes byrelatingthat quantity to other quantities whose rates of change are known. The rate of change is usually with respect totime. Because science and engineering often relate quantities to each other, the methods of related... | https://en.wikipedia.org/wiki/Related_rates |
Ingeometry, thefolium of Descartes(fromLatinfolium'leaf'; named forRené Descartes) is analgebraic curvedefined by theimplicit equationx3+y3−3axy=0.{\displaystyle x^{3}+y^{3}-3axy=0.}
The curve was first proposed and studied byRené Descartesin 1638.[1]Its claim to fame lies in an incident in the development ofcalculus.... | https://en.wikipedia.org/wiki/Folium_of_Descartes |
"Argument Clinic" is a sketch fromMonty Python's Flying Circus, written byJohn CleeseandGraham Chapman. The sketch was originally broadcast as part of the television series and has subsequently been performed live by the group. It relies heavily on wordplay and dialogue, and has been used as an example of how language ... | https://en.wikipedia.org/wiki/Argument_Clinic |
Acontronymorcontranymis a word with twooppositemeanings. For example, the wordoriginalcan mean "authentic, traditional", or "novel, never done before". This feature is also calledenantiosemy,[1][2]enantionymy(enantio-means "opposite"),antilogyorautoantonymy. An enantiosemic term is by definitionpolysemic.
A contronym ... | https://en.wikipedia.org/wiki/Auto-antonym |
Interm logic(a branch ofphilosophical logic), thesquare of oppositionis adiagramrepresentingtherelationsbetween the four basiccategorical propositions.
The origin of the square can be traced back toAristotle's tractateOn Interpretationand its distinction between two oppositions:contradictionandcontrariety. However, Ari... | https://en.wikipedia.org/wiki/Contrary_(logic) |
Dialetheism(/daɪəˈlɛθiɪzəm/; fromGreekδι-di-'twice' andἀλήθειαalḗtheia'truth') is the view that there arestatementsthat are both true and false. More precisely, it is the belief that there can be a true statement whosenegationis also true. Such statements are called "truecontradictions",dialetheia, ornondualisms.
Dial... | https://en.wikipedia.org/wiki/Dialetheism |
Adouble standardis the application of different sets ofprinciplesfor situations that are, in principle, the same.[1]It is often used to describe treatment whereby one group is given more latitude than another.[2]A double standard arises when two or more people, groups, organizations, circumstances, or events are treate... | https://en.wikipedia.org/wiki/Double_standard |
Doublethinkis a process ofindoctrinationin which subjects are expected to simultaneously accept two conflicting beliefs as truth, often at odds with their own memory or sense of reality.[1]Doublethink is related to, but differs from,hypocrisy.
George Orwellcoined the termdoublethinkas part of the fictional language of... | https://en.wikipedia.org/wiki/Doublethink |
Paul Graham(/ɡræm/; born November 13, 1964)[3]is an English-Americancomputer scientist,writerandessayist,entrepreneurandinvestor. His work includes the programming languageArc, the startupViaweb(later renamedYahoo! Store), co-founding thestartup acceleratorand seed capital firmY Combinator, a number of essays and books... | https://en.wikipedia.org/wiki/Paul_Graham_(programmer)#Graham's_hierarchy_of_disagreement |
Irony, in its broadest sense, is thejuxtapositionof what appears to be the case on the surface and what is actually the case or to be expected. It typically figures as arhetorical deviceandliterary technique. In some philosophical contexts, however, it takes on a larger significance as an entire way of life.
Irony has... | https://en.wikipedia.org/wiki/Irony |
Inlogic, thelaw of noncontradiction(LNC; also known as thelaw of contradiction,principle of non-contradiction(PNC), or theprinciple of contradiction) states that propositions cannot both be true and false at the same time, e. g. the two propositions "the house is white" and "the house is not white" aremutually exclusiv... | https://en.wikipedia.org/wiki/Law_of_noncontradiction |
On Contradiction(simplified Chinese:矛盾论;traditional Chinese:矛盾論;pinyin:Máodùn Lùn;lit.'To Discuss Contradiction') is a 1937 essay by theChinese CommunistrevolutionaryMao Zedong. Along withOn Practice,it forms the philosophical underpinnings of the political ideology that would later becomeMaoism. It was written in Augu... | https://en.wikipedia.org/wiki/On_Contradiction |
Anoxymoron(plurals:oxymoronsandoxymora) is afigure of speechthatjuxtaposesconcepts with opposite meanings within a word or in a phrase that is aself-contradiction. As arhetorical device, an oxymoron illustrates a point to communicate and reveal aparadox.[1][2]A general meaning of "contradiction in terms" is recorded by... | https://en.wikipedia.org/wiki/Oxymoron |
Paraconsistent logicis a type ofnon-classical logicthat allows for the coexistence of contradictory statements without leading to a logical explosion where anything can be proven true. Specifically, paraconsistent logic is the subfield oflogicthat is concerned with studying and developing "inconsistency-tolerant" syste... | https://en.wikipedia.org/wiki/Paraconsistent_logic |
Aparadoxis alogicallyself-contradictory statement or a statement that runs contrary to one's expectation.[1][2]It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion.[3][4]A paradox usually involves... | https://en.wikipedia.org/wiki/Paradox |
TRIZ(/ˈtriːz/;Russian:теория решения изобретательских задач,romanized:teoriya resheniya izobretatelskikh zadach,lit.'theory of inventive problem solving') is a methodology that combines an organized, systematic method of problem-solving with analysis and forecasting techniques derived from the study of patterns of inve... | https://en.wikipedia.org/wiki/TRIZ |
"All models are wrong" is a commonaphorismandanapodotoninstatistics. It is often expanded as "All models are wrong, but some are useful". The aphorism acknowledges thatstatistical modelsalways fall short of the complexities of reality but can still be useful nonetheless. The aphorism is generally attributed toGeorge E.... | https://en.wikipedia.org/wiki/All_models_are_wrong |
Anelephant in Cairois a term used incomputer programmingto describe a piece of data that matches the search criteria purposefully inserted at the end of a search space, in order to make sure the search algorithm terminates; it is a humorous example of asentinel value. The term derives from a humorous essay circulated o... | https://en.wikipedia.org/wiki/Elephant_in_Cairo |
Statutory interpretationis the process by which courts interpret and applylegislation. Some amount of interpretation is often necessary when a case involves astatute. Sometimes the words of a statute have a plain and a straightforward meaning, but in many cases, there is someambiguityin the words of the statute that mu... | https://en.wikipedia.org/wiki/Expressio_unius_est_exclusio_alterius |
Falsifiability(orrefutability) is adeductivestandard of evaluation of scientific theories and hypotheses, introduced by thephilosopher of scienceKarl Popperin his bookThe Logic of Scientific Discovery(1934).[B]Atheoryorhypothesisisfalsifiableif it can be logically contradicted by anempirical test.
Popper emphasized th... | https://en.wikipedia.org/wiki/Falsifiability |
Moving the goalposts(orshifting the goalposts) is ametaphor, derived fromgoal-based sports such asfootballandhockey, that means to change the rule or criterion ("goal") of a process or competition while it is still in progress, in such a way that the new goal offers one side an advantage or disadvantage.[1]
This phras... | https://en.wikipedia.org/wiki/Moving_the_goalposts |
No true Scotsmanorappeal to purityis aninformal fallacyin which one modifies a prior claim in response to acounterexampleby asserting the counterexample is excluded by definition.[1][2][3]Rather than admitting error or providing evidence to disprove the counterexample, the original claim is changed by using a non-subst... | https://en.wikipedia.org/wiki/No_true_Scotsman |
"Out of left field" (also "out in left field", and simply "left field" or "leftfield") is American slang meaning "unexpected", "odd" or "strange".
InSafire's Political Dictionary, columnistWilliam Safirewrites that the phrase "out of left field" means "out of the ordinary, out of touch, far out."[1]The variation "out ... | https://en.wikipedia.org/wiki/Out_of_left_field |
Inlinguisticsandphilosophy, apresuppositionis animplicit assumptionabout the world or background belief relating to an utterance whose truth is taken for granted indiscourse. Examples of presuppositions include:
A presupposition is information that is linguistically presented as being mutually known or assumed by the ... | https://en.wikipedia.org/wiki/Presupposition |
Don Quixote,[a][b]the full title beingThe Ingenious Gentleman Don Quixote of La Mancha,[c]is a SpanishnovelbyMiguel de Cervantes. The novel, originally published in two parts, in 1605 and 1615 is considered a founding work ofWestern literature. It's often said to be the first modernnovel.[2][3]The novel has been labell... | https://en.wikipedia.org/wiki/The_proof_of_the_pudding |
Inlogic,reductio ad absurdum(Latinfor "reduction to absurdity"), also known asargumentum ad absurdum(Latinfor "argument to absurdity") orapagogical argument, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction.[1][2][3][4]
This argum... | https://en.wikipedia.org/wiki/Reductio_ad_absurdum |
Askunked termis a word or phrase that becomes difficult to use because it isevolvingfrom one meaning to another, perhaps inconsistent or evenopposite, usage,[1]or that becomes difficult to use due to other controversy surrounding the term.[2]Puristsmay insist on the old usage, whiledescriptivistsmay be more open to new... | https://en.wikipedia.org/wiki/Skunked_term |
Ingeometry, anincidencerelationis aheterogeneous relationthat captures the idea being expressed when phrases such as "a pointlies ona line" or "a line iscontained ina plane" are used. The most basic incidence relation is that between a point,P, and a line,l, sometimes denotedPIl. IfPandlare incident,PIl, the pair(P,l)i... | https://en.wikipedia.org/wiki/Incidence_(geometry) |
Inmathematics,incidence geometryis the study ofincidence structures. A geometric structure such as theEuclidean planeis a complicated object that involves concepts such as length, angles, continuity, betweenness, andincidence. Anincidence structureis what is obtained when all other concepts are removed and all that rem... | https://en.wikipedia.org/wiki/Incidence_geometry |
Inmathematics, specificallyprojective geometry, aconfigurationin the plane consists of a finite set ofpoints, and a finitearrangement of lines, such that each point isincidentto the same number of lines and each line is incident to the same number of points.[1]
Although certain specific configurations had been studied... | https://en.wikipedia.org/wiki/Projective_configuration |
Inmathematics, anabstract polytopeis an algebraicpartially ordered setwhich captures the dyadic property of a traditionalpolytopewithout specifying purely geometric properties such as points and lines.
A geometricpolytopeis said to be arealizationof an abstract polytope in some realN-dimensional space, typicallyEuclid... | https://en.wikipedia.org/wiki/Abstract_polytope |
Thecausal setsprogram is an approach toquantum gravity. Its founding principles are thatspacetimeis fundamentally discrete (a collection of discrete spacetime points, called the elements of the causal set) and that spacetime events are related by apartial order. This partial order has the physical meaning of thecausali... | https://en.wikipedia.org/wiki/Causal_sets |
Inmathematics, acyclic orderis a way to arrange a set of objects in acircle.[nb]Unlike most structures inorder theory, a cyclic order is not modeled as abinary relation, such as "a<b". One does not say that east is "more clockwise" than west. Instead, a cyclic order is defined as aternary relation[a,b,c], meaning "afte... | https://en.wikipedia.org/wiki/Cyclic_order |
Inorder theory, a field ofmathematics, anincidence algebrais anassociative algebra, defined for everylocally finite partially ordered setandcommutative ringwith unity.Subalgebrascalledreduced incidence algebrasgive a natural construction of various types ofgenerating functionsused incombinatoricsandnumber theory.
Aloc... | https://en.wikipedia.org/wiki/Incidence_algebra |
In the mathematical field ofcategory theory, anallegoryis acategorythat has some of the structure of the categoryRelofsetsandbinary relationsbetween them. Allegories can be used as an abstraction of categories of relations, and in this sense the theory of allegories is a generalization ofrelation algebrato relations be... | https://en.wikipedia.org/wiki/Allegory_(category_theory) |
All definitions tacitly require thehomogeneous relationR{\displaystyle R}betransitive: for alla,b,c,{\displaystyle a,b,c,}ifaRb{\displaystyle aRb}andbRc{\displaystyle bRc}thenaRc.{\displaystyle aRc.}A term's definition may require additional properties that are not listed in this table.
Inmathematics, abinary relation... | https://en.wikipedia.org/wiki/Binary_relation |
Inmathematics, specificallyset theory, theCartesian productof twosetsAandB, denotedA×B, is the set of allordered pairs(a,b)whereais an element ofAandbis an element ofB.[1]In terms ofset-builder notation, that isA×B={(a,b)∣a∈Aandb∈B}.{\displaystyle A\times B=\{(a,b)\mid a\in A\ {\mbox{ and }}\ b\in B\}.}[2][3]
A table ... | https://en.wikipedia.org/wiki/Cartesian_product |
Inmathematics, specificallyset theory, theCartesian productof twosetsAandB, denotedA×B, is the set of allordered pairs(a,b)whereais an element ofAandbis an element ofB.[1]In terms ofset-builder notation, that isA×B={(a,b)∣a∈Aandb∈B}.{\displaystyle A\times B=\{(a,b)\mid a\in A\ {\mbox{ and }}\ b\in B\}.}[2][3]
A table ... | https://en.wikipedia.org/wiki/Cartesian_square |
Inmathematics, the notion ofcylindric algebra, developed byAlfred Tarski, arises naturally in thealgebraizationoffirst-order logic with equality. This is comparable to the roleBoolean algebrasplay forpropositional logic. Cylindric algebras are Boolean algebras equipped with additional cylindrification operations that m... | https://en.wikipedia.org/wiki/Cylindric_algebra |
Theextensionof apredicate– atruth-valuedfunction– is thesetoftuplesof values that, used as arguments, satisfy the predicate. Such a set of tuples is arelation.
For example, the statement "d2follows the weekdayd1" can be seen as a truth function associating to each tuple (d2,d1) the valuetrueorfalse. The extension of t... | https://en.wikipedia.org/wiki/Extension_(predicate_logic) |
Charles Sanders Peirce(/pɜːrs/[a][8]PURSS; September 10, 1839 – April 19, 1914) was an American scientist, mathematician,logician, and philosopher who is sometimes known as "the father ofpragmatism".[9][10]According to philosopherPaul Weiss, Peirce was "the most original and versatile of America's philosophers and Amer... | https://en.wikipedia.org/wiki/Logic_of_relatives |
Alogical matrix,binary matrix,relation matrix,Boolean matrix, or(0, 1)-matrixis amatrixwith entries from theBoolean domainB= {0, 1}.Such a matrix can be used to represent abinary relationbetween a pair offinite sets. It is an important tool incombinatorial mathematicsandtheoretical computer science.
IfRis abinary rela... | https://en.wikipedia.org/wiki/Logical_matrix |
Inmathematical logic,predicate functor logic(PFL) is one of several ways to expressfirst-order logic(also known aspredicate logic) by purely algebraic means, i.e., withoutquantified variables. PFL employs a small number of algebraic devices calledpredicate functors(orpredicate modifiers)[1]that operate on terms to yiel... | https://en.wikipedia.org/wiki/Predicate_functor_logic |
Inmathematics,quantalesare certainpartially orderedalgebraic structuresthat generalizelocales(point free topologies) as well as various multiplicativelatticesofidealsfromring theoryandfunctional analysis(C*-algebras,von Neumann algebras).[1]Quantales are sometimes referred to ascompleteresiduated semigroups.
Aquantale... | https://en.wikipedia.org/wiki/Quantale |
Inmathematics, arelationdenotes some kind ofrelationshipbetween twoobjectsin aset, which may or may not hold.[1]As an example, "is less than" is a relation on the set ofnatural numbers; it holds, for instance, between the values1and3(denoted as1 < 3), and likewise between3and4(denoted as3 < 4), but not between the valu... | https://en.wikipedia.org/wiki/Relation_(mathematics) |
Inlogicandmathematics,relation constructionandrelational constructibilityhave to do with the ways that onerelationis determined by anindexed familyor asequenceof other relations, called therelation dataset. The relation in the focus of consideration is called thefaciendum. The relation dataset typically consists of a... | https://en.wikipedia.org/wiki/Relation_construction |
Therelational calculusconsists of two calculi, thetuple relational calculusand thedomain relational calculus, that is part of therelational modelfor databases and provide a declarative way to specify database queries. The raison d'être of relational calculus is the formalization ofquery optimization, which is finding m... | https://en.wikipedia.org/wiki/Relational_calculus |
Indatabase theory,relational algebrais a theory that usesalgebraic structuresfor modeling data and defining queries on it with well foundedsemantics. The theory was introduced byEdgar F. Codd.[1]
The main application of relational algebra is to provide a theoretical foundation forrelational databases, particularlyquer... | https://en.wikipedia.org/wiki/Relational_algebra |
Inmathematics, aresiduated Boolean algebrais aresiduated latticewhose lattice structure is that of aBoolean algebra. Examples include Boolean algebras with the monoid taken to be conjunction, the set of all formal languages over a given alphabet Σ under concatenation, the set of all binary relations on a given setXunde... | https://en.wikipedia.org/wiki/Residuated_Boolean_algebra |
Spatial–temporal reasoningis an area ofartificial intelligencethat draws from the fields ofcomputer science,cognitive science, andcognitive psychology. The theoretic goal—on the cognitive side—involves representing and reasoning spatial-temporal knowledge in mind. The applied goal—on the computing side—involves develop... | https://en.wikipedia.org/wiki/Spatial-temporal_reasoning |
Inmathematics, afinitary relationover a sequence of setsX1, ...,Xnis asubsetof theCartesian productX1× ... ×Xn; that is, it is a set ofn-tuples(x1, ...,xn), each being a sequence of elementsxiin the correspondingXi.[1][2][3]Typically, the relation describes a possible connection between the elements of ann-tuple. For e... | https://en.wikipedia.org/wiki/Theory_of_relations |
Inmathematics, aternary relationortriadic relationis afinitary relationin which the number of places in the relation is three.Ternaryrelations may also be referred to as3-adic,3-ary,3-dimensional, or3-place.
Just as abinary relationis formally defined as a set ofpairs, i.e. a subset of theCartesian productA×Bof some s... | https://en.wikipedia.org/wiki/Triadic_relation |
Inaxiomatic set theory, thegimel functionis the following function mappingcardinal numbersto cardinal numbers:
where cf denotes thecofinalityfunction; the gimel function is used for studying thecontinuum functionand thecardinal exponentiationfunction. The symbolℷ{\displaystyle \gimel }is a serif form of the Hebrew let... | https://en.wikipedia.org/wiki/Gimel_function |
Inset theory, aregular cardinalis acardinal numberthat is equal to its owncofinality. More explicitly, this means thatκ{\displaystyle \kappa }is a regular cardinal if and only if everyunboundedsubsetC⊆κ{\displaystyle C\subseteq \kappa }has cardinalityκ{\displaystyle \kappa }. Infinitewell-orderedcardinals that are no... | https://en.wikipedia.org/wiki/Regular_cardinal |
Infinityis something which is boundless, endless, or larger than anynatural number. It is denoted by∞{\displaystyle \infty }, calledthe infinity symbol.
From the time of theancient Greeks, thephilosophical nature of infinityhas been the subject of many discussions among philosophers. In the 17th century, with the intr... | https://en.wikipedia.org/wiki/Infinity |
Inmathematics,transfinite numbersorinfinite numbersare numbers that are "infinite" in the sense that they are larger than allfinitenumbers. These include thetransfinite cardinals, which arecardinal numbersused to quantify the size of infinite sets, and thetransfinite ordinals, which areordinal numbersused to provide an... | https://en.wikipedia.org/wiki/Transfinite_number |
Acalculationis a deliberatemathematicalprocess that transforms a plurality of inputs into a singular or plurality of outputs, known also as a result or results. The term is used in a variety of senses, from the very definitearithmeticalcalculation of using analgorithm, to the vagueheuristicsof calculating a strategy in... | https://en.wikipedia.org/wiki/Calculation |
Incontract bridge,card reading(orcounting the hand) is the process of inferring which remaining cards are held by each opponent. The reading is based on information gained in the bidding and the play to previous tricks.[1]The technique is used by the declarer and defenders primarily to determine the probablesuitdistrib... | https://en.wikipedia.org/wiki/Card_reading_(bridge) |
Inmathematics, acardinal number, orcardinalfor short, is what is commonly called the number of elements of aset. In the case of afinite set, its cardinal number, orcardinalityis therefore anatural number. For dealing with the case ofinfinite sets, theinfinite cardinal numbershave been introduced, which are often denote... | https://en.wikipedia.org/wiki/Cardinal_number |
Instatistics,count datais astatistical data typedescribingcountable quantities,datawhich can take only thecounting numbers, non-negativeintegervalues {0, 1, 2, 3, ...}, and where these integers arise fromcountingrather thanranking. The statistical treatment of count data is distinct from that ofbinary data, in which t... | https://en.wikipedia.org/wiki/Count_data |
Inmusic,countingis a system of regularly occurringsoundsthat serve to assist with theperformanceorauditionof music by allowing the easy identification of thebeat. Commonly, this involves verballycountingthe beats in eachmeasureas they occur, whether there be 2 beats, 3 beats, 4 beats, or even 5 beats. In addition to he... | https://en.wikipedia.org/wiki/Counting_(music) |
Incomputational complexity theoryandcomputability theory, acounting problemis a type ofcomputational problem. IfRis asearch problemthen
is the correspondingcounting functionand
denotes the corresponding decision problem.
Note thatcRis a search problem while #Ris a decision problem, howevercRcan beCCook-reducedto #R(... | https://en.wikipedia.org/wiki/Counting_problem_(complexity) |
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