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Inmathematics, and especially incategory theory, acommutative diagramis adiagramsuch that all directed paths in the diagram with the same start and endpoints lead to the same result.[1]It is said that commutative diagrams play the role in category theory thatequationsplay inalgebra.[2]
A commutative diagram often cons... | https://en.wikipedia.org/wiki/Commutative_diagram |
Inneurophysiology,commutationis the process by which the brain'sneural circuitsexhibit non-commutativity.
Physiologist Douglas B. Tweed and coworkers have considered whether certain neural circuits in thebrainexhibit noncommutativity and state:
Innoncommutative algebra, order makes a difference to multiplication, so ... | https://en.wikipedia.org/wiki/Commutative_(neurophysiology) |
Inmathematics, thecommutatorgives an indication of the extent to which a certainbinary operationfails to becommutative. There are different definitions used ingroup theoryandring theory.
Thecommutatorof two elements,gandh, of agroupG, is the element
This element is equal to the group's identity if and only ifgandhcom... | https://en.wikipedia.org/wiki/Commutator |
Particle statisticsis a particular description of multipleparticlesinstatistical mechanics. A key prerequisite concept is that of astatistical ensemble(an idealization comprising thestate spaceof possible states of a system, each labeled with a probability) that emphasizes properties of a large system as a whole at the... | https://en.wikipedia.org/wiki/Particle_statistics |
Physicsis thescientificstudy ofmatter, itsfundamental constituents, itsmotionand behavior throughspaceandtime, and the related entities ofenergyandforce.[1]It is one of the most fundamental scientific disciplines.[2][3][4]A scientist who specializes in the field of physics is called aphysicist.
Physics is one of the o... | https://en.wikipedia.org/wiki/Physics |
Inmathematics, thequasi-commutative propertyis an extension or generalization of the generalcommutative property. This property is used in specific applications with various definitions.
Twomatricesp{\displaystyle p}andq{\displaystyle q}are said to have thecommutative propertywheneverpq=qp{\displaystyle pq=qp}
The qu... | https://en.wikipedia.org/wiki/Quasi-commutative_property |
Incomputer science, atraceis anequivalence classofstrings, wherein certain letters in the string are allowed tocommute, but others are not. Traces generalize the concept of strings by relaxing the requirement for all the letters to have a definite order, instead allowing for indefinite orderings in which certain reshuf... | https://en.wikipedia.org/wiki/Trace_monoid |
First-order logic, also calledpredicate logic,predicate calculus, orquantificational logic, is a collection offormal systemsused inmathematics,philosophy,linguistics, andcomputer science. First-order logic usesquantified variablesover non-logical objects, and allows the use of sentences that contain variables. Rather t... | https://en.wikipedia.org/wiki/First-order_logic |
Inlogic, a set ofsymbolsis commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field ofmathematics. Additionally, the subsequent columns contains an informal explanation, a short example, theUnicodelo... | https://en.wikipedia.org/wiki/List_of_logic_symbols |
Inmathematical logic,abstract algebraic logicis the study of the algebraization ofdeductive systemsarising as an abstraction of the well-knownLindenbaum–Tarski algebra, and how the resulting algebras are related to logical systems.[1]
The archetypal association of this kind, one fundamental to the historical origins o... | https://en.wikipedia.org/wiki/Abstract_algebraic_logic |
Inmathematicsandmathematical logic,Boolean algebrais a branch ofalgebra. It differs fromelementary algebrain two ways. First, the values of thevariablesare thetruth valuestrueandfalse, usually denoted by 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra useslogical ... | https://en.wikipedia.org/wiki/Boolean_algebra_(logic) |
Inmathematicsandabstract algebra, aBoolean domainis asetconsisting of exactly two elements whose interpretations includefalseandtrue. Inlogic, mathematics andtheoretical computer science, a Boolean domain is usually written as {0, 1},[1][2][3][4][5]orB.{\displaystyle \mathbb {B} .}[6][7]
Thealgebraic structurethat nat... | https://en.wikipedia.org/wiki/Boolean_domain |
Inmathematics, aBoolean functionis afunctionwhoseargumentsand result assume values from a two-element set (usually {true, false}, {0,1} or {−1,1}).[1][2]Alternative names areswitching function, used especially in oldercomputer scienceliterature,[3][4]andtruth function(orlogical function), used inlogic. Boolean function... | https://en.wikipedia.org/wiki/Boolean_function |
Inmathematicsandmathematical logic,Boolean algebrais a branch ofalgebra. It differs fromelementary algebrain two ways. First, the values of thevariablesare thetruth valuestrueandfalse, usually denoted by 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra useslogical ... | https://en.wikipedia.org/wiki/Boolean_logic |
Causalityis an influence by which oneevent,process, state, orobject(acause) contributes to the production of another event, process, state, or object (aneffect) where the cause is at least partly responsible for the effect, and the effect is at least partly dependent on the cause.[1]Thecauseof something may also be des... | https://en.wikipedia.org/wiki/Causality |
Deductive reasoningis the process of drawing validinferences. An inference isvalidif its conclusion followslogicallyfrom itspremises, meaning that it is impossible for the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and "Socratesis a man" to the ... | https://en.wikipedia.org/wiki/Deductive_reasoning |
Inlogic,Peirce's lawis named after thephilosopherandlogicianCharles Sanders Peirce. It was taken as anaxiomin his first axiomatisation ofpropositional logic. It can be thought of as thelaw of excluded middlewritten in a form that involves only one sort of connective, namely implication.
Inpropositional calculus,Peir... | https://en.wikipedia.org/wiki/Peirce%27s_law |
Probabilistic logic(alsoprobability logicandprobabilistic reasoning) involves the use of probability and logic to deal with uncertain situations. Probabilistic logic extends traditional logictruth tableswith probabilistic expressions. A difficulty of probabilistic logics is their tendency to multiply thecomputational c... | https://en.wikipedia.org/wiki/Probabilistic_logic |
Inlogic, afunctionally completeset oflogical connectivesorBoolean operatorsis one that can be used to express all possibletruth tablesby combining members of thesetinto aBoolean expression.[1][2]A well-known complete set of connectives is{AND,NOT}. Each of thesingletonsets{NAND}and{NOR}is functionally complete. However... | https://en.wikipedia.org/wiki/Sole_sufficient_operator |
Informal semantics,Strawson entailmentis a variant of the concept ofentailmentwhich is insensitive topresuppositionfailures. Formally, a sentencePStrawson-entails a sentenceQiffQis always true whenPis true andQs presuppositions are satisfied. For example, "Maria loves every cat" Strawson-entails "Maria loves her cat" b... | https://en.wikipedia.org/wiki/Strawson_entailment |
Inlogic, astrict conditional(symbol:◻{\displaystyle \Box }, or ⥽) is a conditional governed by amodal operator, that is, alogical connectiveofmodal logic. It islogically equivalentto thematerial conditionalofclassical logic, combined with thenecessityoperator frommodal logic. For any twopropositionspandq, theformulap→q... | https://en.wikipedia.org/wiki/Strict_conditional |
Inmathematical logic, atautology(fromAncient Greek:ταυτολογία) is aformulathat is true regardless of the interpretation of its componentterms, with only thelogical constantshaving a fixed meaning. For example, a formula that states, "the ball is green or the ball is not green," is always true, regardless of what a bal... | https://en.wikipedia.org/wiki/Tautology_(logic) |
Inpropositional logic,tautological consequenceis a strict form oflogical consequence[1]in which thetautologousnessof apropositionis preserved from one line of a proof to the next. Not all logical consequences are tautological consequences. ApropositionQ{\displaystyle Q}is said to be a tautological consequence of one or... | https://en.wikipedia.org/wiki/Tautological_consequence |
Inlogical argumentandmathematical proof, thetherefore sign,∴, is generally used before alogical consequence, such as the conclusion of asyllogism. The symbol consists of three dots placed in an upright triangle and is readtherefore. While it is not generally used in formal writing, it is used inmathematicsandshorthand.... | https://en.wikipedia.org/wiki/Therefore_sign |
Inmathematical logicandcomputer sciencethe symbol ⊢ (⊢{\displaystyle \vdash }) has taken the nameturnstilebecause of its resemblance to a typicalturnstileif viewed from above. It is also referred to asteeand is often read as "yields", "proves", "satisfies" or "entails".
The turnstile represents abinary relation. It ha... | https://en.wikipedia.org/wiki/Turnstile_(symbol) |
Inlogic, thesymbol⊨, ⊧ or⊨{\displaystyle \models }is called thedouble turnstile. It is often read as "entails", "models", "is asemanticconsequenceof" or "is stronger than".[1]It is closely related to theturnstilesymbol⊢{\displaystyle \vdash }, which has a single bar across the middle, and which denotessyntacticconseque... | https://en.wikipedia.org/wiki/Double_turnstile |
Anexistential clauseis aclausethat refers to the existence or presence of something, such as "There is a God" and "There are boys in the yard". The use of such clauses can be considered analogous toexistential quantificationin predicate logic, which is often expressed with the phrase "There exist(s)...".
Different lan... | https://en.wikipedia.org/wiki/Existential_clause |
Inmathematics, anexistence theoremis atheoremwhich asserts the existence of a certain object.[1]It might be a statement which begins with the phrase "there exist(s)", or it might be a universal statement whose lastquantifierisexistential(e.g., "for allx,y, ... there exist(s) ..."). In the formal terms ofsymbolic logic,... | https://en.wikipedia.org/wiki/Existence_theorem |
Inmathematical logic, aLindström quantifieris ageneralized polyadic quantifier. Lindström quantifiers generalize first-order quantifiers, such as theexistential quantifier, theuniversal quantifier, and thecounting quantifiers. They were introduced byPer Lindströmin 1966. They were later studied for their applications i... | https://en.wikipedia.org/wiki/Lindstr%C3%B6m_quantifier |
The termquantifier variancerefers to claims that there is no uniquely best ontological language with which to describe the world.[1]The term "quantifier variance" rests upon the philosophical term 'quantifier', more preciselyexistential quantifier. A 'quantifier' is an expression like "there exists at least one 'such-a... | https://en.wikipedia.org/wiki/Quantifier_variance |
Inmathematicsandlogic, the term "uniqueness" refers to the property of being the one and only object satisfying a certain condition.[1]This sort ofquantificationis known asuniqueness quantificationorunique existential quantification, and is often denoted with the symbols "∃!"[2]or "∃=1". It is defined to meanthere exis... | https://en.wikipedia.org/wiki/Uniqueness_quantification |
Inmathematics, the termessentially uniqueis used to describe a weaker form of uniqueness, where an object satisfying a property is "unique" only in the sense that all objects satisfying the property are equivalent to each other. The notion of essential uniqueness presupposes some form of "sameness", which is often form... | https://en.wikipedia.org/wiki/Essentially_unique |
Indigital circuitsandmachine learning, aone-hotis a group ofbitsamong which the legal combinations of values are only those with a single high (1) bit and all the others low (0).[1]A similar implementation in which all bits are '1' except one '0' is sometimes calledone-cold.[2]Instatistics,dummy variablesrepresent a si... | https://en.wikipedia.org/wiki/One-hot |
Inmathematics, asingleton(also known as aunit set[1]orone-point set) is asetwithexactly oneelement. For example, the set{0}{\displaystyle \{0\}}is a singleton whose single element is0{\displaystyle 0}.
Within the framework ofZermelo–Fraenkel set theory, theaxiom of regularityguarantees that no set is an element of its... | https://en.wikipedia.org/wiki/Singleton_(mathematics) |
In mathematics, auniqueness theorem, also called aunicity theorem, is atheoremasserting the uniqueness of an object satisfying certain conditions, or the equivalence of all objects satisfying the said conditions.[1]Examples of uniqueness theorems include:
The worduniqueis sometimes replaced byessentially unique, whene... | https://en.wikipedia.org/wiki/Uniqueness_theorem |
Quantificationmay refer to: | https://en.wikipedia.org/wiki/Quantification_(disambiguation) |
bijective
injective-only
injective
surjective-only
general
Inmathematics,injections,surjections, andbijectionsare classes offunctionsdistinguished by the manner in whicharguments(inputexpressionsfrom thedomain) andimages(output expressions from thecodomain) are related ormapped toeach other.
A functionmapselement... | https://en.wikipedia.org/wiki/Bijection,_injection_and_surjection |
Inmetric geometry, aninjective metric space, or equivalently ahyperconvex metric space, is ametric spacewith certain properties generalizing those of thereal lineand ofL∞distancesin higher-dimensionalvector spaces. These properties can be defined in two seemingly different ways: hyperconvexity involves the intersection... | https://en.wikipedia.org/wiki/Injective_metric_space |
Inmathematics, amonotonic function(ormonotone function) is afunctionbetweenordered setsthat preserves or reverses the givenorder.[1][2][3]This concept first arose incalculus, and was later generalized to the more abstract setting oforder theory.
Incalculus, a functionf{\displaystyle f}defined on asubsetof thereal numb... | https://en.wikipedia.org/wiki/Monotonic_function |
Inmathematics, in the branch ofcomplex analysis, aholomorphic functionon anopen subsetof thecomplex planeis calledunivalentif it isinjective.[1][2]
The functionf:z↦2z+z2{\displaystyle f\colon z\mapsto 2z+z^{2}}is univalent in the open unit disc, asf(z)=f(w){\displaystyle f(z)=f(w)}implies thatf(z)−f(w)=(z−w)(z+w+2)=0{... | https://en.wikipedia.org/wiki/Univalent_function |
Inabstract algebra, acoveris one instance of somemathematical structuremappingontoanother instance, such as agroup(trivially) covering asubgroup. This should not be confused with the concept of acover in topology.
When some objectXis said to cover another objectY, the cover is given by somesurjectiveandstructure-prese... | https://en.wikipedia.org/wiki/Cover_(algebra) |
Intopology, acoveringorcovering projectionis amapbetweentopological spacesthat, intuitively,locallyacts like aprojectionof multiple copies of a space onto itself. In particular, coverings are special types oflocal homeomorphisms. Ifp:X~→X{\displaystyle p:{\tilde {X}}\to X}is a covering,(X~,p){\displaystyle ({\tilde {X}... | https://en.wikipedia.org/wiki/Covering_map |
Anenumerationis a complete, orderedlistingof all the items in a collection. The term is commonly used inmathematicsandcomputer scienceto refer to a listing of all of theelementsof aset. The precise requirements for an enumeration (for example, whether the set must befinite, or whether the list is allowed to contain rep... | https://en.wikipedia.org/wiki/Enumeration |
Inmathematics, and particularlytopology, afiber bundle(Commonwealth English:fibre bundle) is aspacethat islocallyaproduct space, butgloballymay have a differenttopological structure. Specifically, the similarity between a spaceE{\displaystyle E}and a product spaceB×F{\displaystyle B\times F}is defined using acontinuous... | https://en.wikipedia.org/wiki/Fiber_bundle |
Inmathematics, anindex setis a set whose members label (or index) members of another set.[1][2]For instance, if the elements of asetAmay beindexedorlabeledby means of the elements of a setJ, thenJis an index set. The indexing consists of asurjective functionfromJontoA, and the indexed collection is typically called ani... | https://en.wikipedia.org/wiki/Index_set |
Incategory theory, a branch ofmathematics, asectionis aright inverseof somemorphism.Dually, aretractionis aleft inverseof somemorphism.
In other words, iff:X→Y{\displaystyle f:X\to Y}andg:Y→X{\displaystyle g:Y\to X}are morphisms whose compositionf∘g:Y→Y{\displaystyle f\circ g:Y\to Y}is theidentity morphismonY{\displays... | https://en.wikipedia.org/wiki/Section_(category_theory) |
Themathematicalconcept of afunctiondates from the 17th century in connection with the development ofcalculus; for example, the slopedy/dx{\displaystyle dy/dx}of agraphat a point was regarded as a function of thex-coordinate of the point. Functions were not explicitly considered in antiquity, but some precursors of the ... | https://en.wikipedia.org/wiki/History_of_the_function_concept |
Inmathematics,functionscan be identified according to the properties they have. These properties describe the functions' behaviour under certain conditions. A parabola is a specific type of function.
These properties concern thedomain, thecodomainand theimageof functions.
These properties concern how the function is ... | https://en.wikipedia.org/wiki/List_of_types_of_functions |
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_functions |
Curve fitting[1][2]is the process of constructing acurve, ormathematical function, that has the best fit to a series ofdata points,[3]possibly subject to constraints.[4][5]Curve fitting can involve eitherinterpolation,[6][7]where an exact fit to the data is required, orsmoothing,[8][9]in which a "smooth" function is co... | https://en.wikipedia.org/wiki/Function_fitting |
Inmathematics, animplicit equationis arelationof the formR(x1,…,xn)=0,{\displaystyle R(x_{1},\dots ,x_{n})=0,}whereRis afunctionof several variables (often apolynomial). For example, the implicit equation of theunit circleisx2+y2−1=0.{\displaystyle x^{2}+y^{2}-1=0.}
Animplicit functionis afunctionthat is defined by an... | https://en.wikipedia.org/wiki/Implicit_function |
Intraditional logic, acontradictionoccurs when apropositionconflicts either with itself or establishedfact. It is often used as a tool to detectdisingenuousbeliefs andbias. Illustrating a general tendency in applied logic,Aristotle'slaw of noncontradictionstates that "It is impossible that the same thing can at the sam... | https://en.wikipedia.org/wiki/Contradiction |
"The exception that proves the rule" is a saying whose meaning is contested.Henry Watson Fowler'sModern English Usageidentifies five ways in which the phrase has been used,[1]and each use makes some sort of reference to the role that a particular case or event takes in relation to a more general rule.
Two original mea... | https://en.wikipedia.org/wiki/Exception_that_proves_the_rule |
Inmathematics, aminimal counterexampleis the smallest example which falsifies a claim, and aproof by minimal counterexampleis a method ofproofwhich combines the use of a minimal counterexample with the methods ofproof by inductionandproof by contradiction.[1][2]More specifically, in trying to prove a propositionP, one ... | https://en.wikipedia.org/wiki/Minimal_counterexample |
Inmathematics, anincidence structureis an abstract system consisting of two types of objects and a single relationship between these types of objects. Consider thepointsandlinesof theEuclidean planeas the two types of objects and ignore all the properties of this geometry except for therelationof which points areincide... | https://en.wikipedia.org/wiki/Incidence_structure |
Order theoryis a branch ofmathematicsthat investigates the intuitive notion of order usingbinary relations. It provides a formal framework for describing statements such as "this isless thanthat" or "this precedes that". This article introduces the field and provides basic definitions. A list of order-theoretic terms c... | https://en.wikipedia.org/wiki/Order_theory |
Inmathematicsandabstract algebra, arelation algebrais aresiduated Boolean algebraexpandedwith aninvolutioncalledconverse, aunary operation. The motivating example of a relation algebra is the algebra 2X2of allbinary relationson a setX, that is, subsets of thecartesian squareX2, withR•Sinterpreted as the usualcompositio... | https://en.wikipedia.org/wiki/Relation_algebra |
Inmathematics, particularly inset theory, thealeph numbersare asequenceof numbers used to represent thecardinality(or size) ofinfinite sets.[a]They were introduced by the mathematicianGeorg Cantor[1]and are named after the symbol he used to denote them, the Hebrew letteraleph(ℵ).[2][b]
The smallest cardinality of an i... | https://en.wikipedia.org/wiki/Aleph_number |
Countingis the process of determining thenumberofelementsof afinite setof objects; that is, determining thesizeof a set. The traditional way of counting consists of continually increasing a (mental or spoken) counter by aunitfor every element of the set, in some order, while marking (or displacing) those elements to av... | https://en.wikipedia.org/wiki/Counting |
Hilbert's paradox of the Grand Hotel(colloquial:Infinite Hotel ParadoxorHilbert's Hotel) is athought experimentwhich illustrates acounterintuitiveproperty ofinfinite sets. It is demonstrated that a fully occupied hotel with infinitely many rooms may still accommodate additional guests, even infinitely many of them, and... | https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel |
Inmathematics, particularly inset theory, thebeth numbersare a certain sequence ofinfinitecardinal numbers(also known astransfinite numbers), conventionally writtenℶ0,ℶ1,ℶ2,ℶ3,…{\displaystyle \beth _{0},\beth _{1},\beth _{2},\beth _{3},\dots }, whereℶ{\displaystyle \beth }is theHebrew letterbeth. The beth numbers are r... | https://en.wikipedia.org/wiki/Beth_number |
Inmathematics, thefirst uncountable ordinal, traditionally denoted byω1{\displaystyle \omega _{1}}or sometimes byΩ{\displaystyle \Omega }, is the smallestordinal numberthat, considered as aset, isuncountable. It is thesupremum(least upper bound) of all countable ordinals. When considered as a set, the elements ofω1{\di... | https://en.wikipedia.org/wiki/First_uncountable_ordinal |
Cantor's first set theory articlecontainsGeorg Cantor's first theorems of transfiniteset theory, which studiesinfinite setsand their properties. One of these theorems is his "revolutionary discovery" that thesetof allreal numbersisuncountably, rather thancountably, infinite.[1]This theorem is proved usingCantor's first... | https://en.wikipedia.org/wiki/Cantor%27s_first_uncountability_proof |
Inmathematics, specificallyset theory, thecontinuum hypothesis(abbreviatedCH) is a hypothesis about the possible sizes ofinfinite sets. It states:
There is no set whosecardinalityis strictly between that of theintegersand thereal numbers.
Or equivalently:
Any subset of the real numbers is either finite, or countably... | https://en.wikipedia.org/wiki/Continuum_hypothesis |
Inmathematical logic, the theory ofinfinite setswas first developed byGeorg Cantor. Although this work has become a thoroughly standard fixture of classicalset theory, it has been criticized in several areas by mathematicians and philosophers.
Cantor's theoremimplies that there are sets havingcardinalitygreater than t... | https://en.wikipedia.org/wiki/Controversy_over_Cantor%27s_theory |
Inmathematical logic, thediagonal lemma(also known asdiagonalization lemma,self-reference lemmaorfixed point theorem) establishes the existence ofself-referentialsentences in certain formal theories.
A particular instance of the diagonal lemma was used byKurt Gödelin 1931 to construct his proof of theincompleteness th... | https://en.wikipedia.org/wiki/Diagonal_lemma |
Aternary search algorithm[1]is a technique incomputer sciencefor finding theminimum or maximumof aunimodalfunction.
Assume we are looking for a maximum off(x){\displaystyle f(x)}and that we know the maximum lies somewhere betweenA{\displaystyle A}andB{\displaystyle B}. For the algorithm to be applicable, there must be... | https://en.wikipedia.org/wiki/Ternary_search |
Incomputational complexity theory, thelinear search problemis an optimal search problem introduced byRichard E. Bellman[1]and independently considered byAnatole Beck.[2][3][4]
"An immobile hider is located on the real line according to a knownprobability distribution. A searcher, whose maximal velocity is one, starts ... | https://en.wikipedia.org/wiki/Linear_search_problem |
Algorismis the technique of performing basicarithmeticby writing numbers inplace valueform and applying a set of memorized rules andfactsto the digits. One who practices algorism is known as analgorist. Thispositional notationsystem has largely superseded earlier calculation systems that used a different set of symbols... | https://en.wikipedia.org/wiki/Algorism |
Incomputingandelectronicsystems,binary-coded decimal(BCD) is a class ofbinaryencodings ofdecimalnumbers where eachdigitis represented by a fixed number ofbits, usually four or eight. Sometimes, special bit patterns are used for asignor other indications (e.g. error or overflow).
Inbyte-oriented systems (i.e. most mode... | https://en.wikipedia.org/wiki/Binary-coded_decimal |
Decimal classificationis a type oflibrary classification. Examples include: | https://en.wikipedia.org/wiki/Decimal_classification |
Adecimal computeris acomputerthat represents and operates onnumbersandaddressesindecimalformat – instead ofbinaryas is common in most modern computers. Some decimal computers had a variableword length, which enabled operations on relatively large numbers.
Decimal computers were common from the early machines through t... | https://en.wikipedia.org/wiki/Decimal_computer |
Decimal timeis the representation of the time of day using units which aredecimallyrelated. This term is often used specifically to refer to theFrench Republican calendartime system used inFrancefrom 1794 to 1800, during theFrench Revolution, which divided the day into 10 decimal hours, each decimal hour into 100 decim... | https://en.wikipedia.org/wiki/Decimal_time |
Adecimal representationof anon-negativereal numberris its expression as asequenceof symbols consisting ofdecimal digitstraditionally written with a single separator:r=bkbk−1⋯b0.a1a2⋯{\displaystyle r=b_{k}b_{k-1}\cdots b_{0}.a_{1}a_{2}\cdots }Here.is thedecimal separator,kis anonnegative integer, andb0,⋯,bk,a1,a2,⋯{\dis... | https://en.wikipedia.org/wiki/Decimal_representation |
Aparagraph(fromAncient Greekπαράγραφος (parágraphos)'to write beside') is a self-contained unit of discourse inwritingdealing with a particular point oridea. Though not required by the orthographic conventions of any language with awriting system, paragraphs are a conventional means of organizing extended segments ofpr... | https://en.wikipedia.org/wiki/Decimal_section_numbering |
Adecimal separatoris a symbol that separates theintegerpart from thefractional partof anumberwritten indecimalform. Different countries officially designate different symbols for use as the separator. The choice of symbol can also affect the choice of symbol for thethousands separatorused in digit grouping.
Any such s... | https://en.wikipedia.org/wiki/Decimal_separator |
Decimalisationordecimalization(seespelling differences) is the conversion of a system of currency or of weights and measures to units related bypowers of 10.
Most countries have decimalised their currencies, converting them from non-decimal sub-units to adecimalsystem, with one basic currency unit and sub-units that a... | https://en.wikipedia.org/wiki/Decimalisation |
Densely packed decimal(DPD) is an efficient method forbinaryencodingdecimaldigits.
The traditional system of binary encoding for decimal digits, known asbinary-coded decimal(BCD), uses four bits to encode each digit, resulting in significant wastage ofbinary databandwidth (since four bits can store 16 states and are b... | https://en.wikipedia.org/wiki/Densely_packed_decimal |
Theduodecimalsystem, also known asbase twelveordozenal, is apositionalnumeral systemusingtwelveas itsbase. In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0units; in thedecimalsystem, this number is instead written as "12" meaning 1 ten and 2 units, and the string "10" means ten. In duodecimal, "... | https://en.wikipedia.org/wiki/Duodecimal |
Ametric prefixis aunit prefixthat precedes a basic unit of measure to indicate amultiple or submultipleof the unit. All metric prefixes used today aredecadic. Each prefix has a unique symbol that is prepended to any unit symbol. The prefixkilo, for example, may be added togramto indicatemultiplicationby one thousand: o... | https://en.wikipedia.org/wiki/Metric_prefix |
Standard formis a way of expressingnumbersthat are too large or too small to be conveniently written indecimal form, since to do so would require writing out an inconveniently long string of digits. It may be referred to asscientific formorstandard index form, orScientific notationin the United States. Thisbase tennota... | https://en.wikipedia.org/wiki/Scientific_notation |
In computers, aserial decimalnumeric representation is one in which tenbitsare reserved for each digit, with a different bit turned on depending on which of the ten possible digits is intended.ENIACandCALDICused this representation.[1]
Thiscomputer-storage-related article is astub. You can help Wikipedia byexpanding i... | https://en.wikipedia.org/wiki/Serial_decimal |
Acomputer number formatis the internal representation of numeric values in digital device hardware and software, such as in programmablecomputersandcalculators.[1]Numerical values are stored as groupings ofbits, such asbytesand words. The encoding between numerical values and bit patterns is chosen for convenience of t... | https://en.wikipedia.org/wiki/Computer_number_format |
Octal gamesare asubclassofheap gamesthat involve removing tokens (game pieces or stones) from heaps of tokens.
They have been studied incombinatorial game theoryas a generalization ofNim,Kayles, and similar games.[1][2]
Octal games areimpartialmeaning that every move available to one player is also available to the ot... | https://en.wikipedia.org/wiki/Octal_games |
Combinatorial game theoryis a branch ofmathematicsandtheoretical computer sciencethat typically studiessequential gameswithperfect information. Study has been largely confined to two-playergamesthat have apositionthat the players take turns changing in defined ways ormovesto achieve a defined winning condition. Combina... | https://en.wikipedia.org/wiki/Combinatorial_game_theory |
Syllabic octalandsplit octalare two similar notations for 8-bit and 16-bitoctal numbers, respectively, used in some historical contexts.
Syllabic octalis an 8-bit octalnumber representationthat was used byEnglish Electricin conjunction with theirKDF9machine in the mid-1960s.
Although the word 'byte' had been coined b... | https://en.wikipedia.org/wiki/Split_octal |
Atransponder(short fortransmitter-responder[1]and sometimes abbreviated to XPDR,[2]XPNDR,[3]TPDR[4]or TP[5]) is an electronic device that produces a response when it receives a radio-frequency interrogation. Aircraft havetranspondersto assist in identifying them on air traffic controlradar.Collision avoidance systemsha... | https://en.wikipedia.org/wiki/Squawk_code |
Gillham codeis a zero-padded 12-bitbinary codeusing a parallel nine-[1]to eleven-wireinterface,[2]theGillham interface, that is used to transmit uncorrectedbarometricaltitudebetween an encodingaltimeteror analogair data computerand adigitaltransponder. It is a modified form of aGray codeand is sometimes referred to sim... | https://en.wikipedia.org/wiki/Gillham_code |
Syllabic octalandsplit octalare two similar notations for 8-bit and 16-bitoctal numbers, respectively, used in some historical contexts.
Syllabic octalis an 8-bit octalnumber representationthat was used byEnglish Electricin conjunction with theirKDF9machine in the mid-1960s.
Although the word 'byte' had been coined b... | https://en.wikipedia.org/wiki/Syllabic_octal |
Base32(also known asduotrigesimal) is an encoding method based on thebase-32numeral system. It uses an alphabet of 32digits, each of which represents a different combination of 5bits(25). Since base32 is not very widely adopted, the question of notation—which characters to use to represent the 32 digits—is not as settl... | https://en.wikipedia.org/wiki/Base32 |
Incomputer programming,Base64(also known astetrasexagesimal) is a group ofbinary-to-text encodingschemes that transformsbinary datainto a sequence ofprintablecharacters, limited to a set of 64 unique characters. More specifically, the source binary data is taken 6 bits at a time, then this group of 6 bits is mapped to... | https://en.wikipedia.org/wiki/Base64 |
Hexadecimal timeis the representation of thetimeofdayas ahexadecimalnumberin theinterval[0, 1).
The day is divided into 1016(1610) hexadecimal hours, each hour into 10016(25610) hexadecimal minutes, and each minute into 1016(1610) hexadecimal seconds.
This time format was proposed by the Swedish-American engineerJohn... | https://en.wikipedia.org/wiki/Hexadecimal_time |
Hexadecimalfloating point(now calledHFPbyIBM) is a format for encoding floating-point numbers first introduced on theIBMSystem/360computers, and supported on subsequent machines based on that architecture,[1][2][3]as well as machines which were intended to be application-compatible with System/360.[4][5]
In comparison... | https://en.wikipedia.org/wiki/IBM_hexadecimal_floating-point |
Ahex editor(orbinary file editororbyte editor) is acomputer programthat allows for manipulation of the fundamentalbinarydata that constitutes acomputer file. The name 'hex' comes from 'hexadecimal', a standard numerical format for representing binary data. A typical computer file occupies multiple areas on the storage ... | https://en.wikipedia.org/wiki/Hex_editor |
Incomputing, ahex dumpis atextualhexadecimalview (on screen or paper) of (often, but not necessarilybinary) computer data, frommemoryor from acomputer fileorstoragedevice. Looking at a hex dump of data is usually done in the context of eitherdebugging,reverse engineeringordigital forensics.[1]Interactive editors that p... | https://en.wikipedia.org/wiki/Hex_dump |
TheBailey–Borwein–Plouffe formula(BBP formula) is a formula forπ. It was discovered in 1995 bySimon Plouffeand is named after the authors of the article in which it was published,David H. Bailey,Peter Borwein, and Plouffe.[1]The formula is:
The BBP formula gives rise to aspigot algorithmfor computing thenthbase-16(hex... | https://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula |
Hexspeakis a novelty form of variantEnglishspelling using the hexadecimal digits. Created by programmers as memorablemagic numbers, hexspeak words can serve as a clear and unique identifier with which to mark memory or data.
Hexadecimal notationrepresents numbers using the 16 digits0123456789ABCDEF. Using only the let... | https://en.wikipedia.org/wiki/Hexspeak |
Standard formis a way of expressingnumbersthat are too large or too small to be conveniently written indecimal form, since to do so would require writing out an inconveniently long string of digits. It may be referred to asscientific formorstandard index form, orScientific notationin the United States. Thisbase tennota... | https://en.wikipedia.org/wiki/P_notation |
Mixed radixnumeral systemsarenon-standard positional numeral systemsin which the numericalbasevaries from position to position. Such numerical representation applies when a quantity is expressed using a sequence of units that are each a multiple of the next smaller one, but not by the same factor. Such units are common... | https://en.wikipedia.org/wiki/Mixed_radix |
Inmathematics, apolynomialis amathematical expressionconsisting ofindeterminates(also calledvariables) andcoefficients, that involves only the operations ofaddition,subtraction,multiplicationandexponentiationtononnegative integerpowers, and has a finite number of terms.[1][2][3][4][5]An example of a polynomial of a sin... | https://en.wikipedia.org/wiki/Polynomial |
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