theory , as well as the philosophy of social science itself. br br Forms of relation and interaction Forms of relation and interaction in sociology and anthropology may be described as follows first ... interaction Yes Yes Yes Yes Yes Yes Yes Yes Yes Socialrelation Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes See also Social action Reflexivity social theory Affectional action Interpersonal relationship ...Sociology about social relations in sociology personal social relations Interpersonal relationship In social science , a socialrelation or social interaction refers to a relationship between two i.e. dyad sociology a dyad , three i.e. triad sociology a triad or more individuals e.g. a social group . Social relations, derived from individual agency sociology agency , form the basis of the social structure . To this extent social relations are always the basic object of analysis for social scientists . Fundamental enquiries into the nature of social relations are to be found in the work of the classical sociologists, for instance, in Max Weber s theory of social action . Further categories must be established in the abstract in order to form observations and conduct social research, such as Gemeinschaft ... the conduct of investigating social interaction relate to the core debates in sociology and the other social sciences positivism quantitative research against antipositivism qualitative research , social ... philosophy action s movements with a meaning and purpose. Then there are social behavior s, or social ... another agent. Next are social contact s, a pair of social actions, which form the beginning of social interactions. Social interactions in turn form the basis of social relations. br br These divisions ... interaction Regular Interactions described by law, custom or tradition A scheme of social interactions Behavior Yes Action philosophy Action Yes Yes Social behavior Yes Yes Yes Social action Yes Yes Yes Yes Social contact Yes Yes Yes Yes Yes Social interaction Yes Yes Yes Yes Yes Yes Repeated ... more details
wiktionary Relationrelation relations Relation or Relations may refer to tocright General use Kinship , relationship by genealogical origin Socialrelation s, in social science, social interaction between two or more individuals International relations , strategies chosen by a state to safeguard its national interests and achieve its foreign policy objectives Logic and philosophy Relation philosophy , links between properties of an object Relation logic , term in set theory and logic, for a property that assigns truth values to k tuples of individuals Relation of Ideas , in the Humean sense, is the type of knowledge that can be characterized as arising out of pure conceptual thought and logical operations in contrast to a Matter of Fact Relational theory , framework to understand reality or a physical ... relative to other objects Computers and technology Relation database , in the relational model ... Relationships Ontology components relation , a component of an ontology Binary relation , a synonym for dyadic relation and 2 place relation Mathematics Relational algebra , an offshoot of first order logic and of algebra of sets , deals with a set of finitary relations see also relation database which is closed under certain operators Relation mathematics , a generalization of arithmetic relations, such as and , that occur in statements, such as 5 6 and 2 2 4 Ternary relation ,finitary relation in which the number of places in the relation is three. Ternary relations may also be referred ... as being observer dependent, that is, the state is the relation between the observer and the system Relation journal Relation journal , the first newspaper Sexual relations, euphemistic term for human ... Relativity disambiguation disambig bs Relacija vor cs Relace de Relation Begriffskl rung es Relaci n eo Rilato fr Relation io Relato it Relazione nl Verhouding ja pl Relacja ro Rela ie ru simple Relation uk vi Quan h ... more details
Quasitransitivity is a weakened version of transitive relation transitivity that is used in social choice theory or microeconomics . Informally, a relation is quasitransitive if it is symmetric for some values and transitive elsewhere. Formal definition A binary relation T over a Set mathematics set X is quasitransitive if for all a , b , and c in X the following holds math a operatorname T b wedge neg b operatorname T a wedge b operatorname T c wedge neg c operatorname T b Rightarrow a operatorname T c wedge neg c operatorname T a . math If the relation is also antisymmetric, T is transitive. Alternately, for a relation T, define the symmetric relation asymmetric part P math a operatorname P b Leftrightarrow a operatorname T b wedge neg b operatorname T a . math Then T is quasitransitive iff P is transitive. Examples Preference s are assumed to be quasitransitive rather than transitive in some economic contexts. The classic example is a person indifferent between 10 and 11 grams of sugar and indifferent between 11 and 12 grams of sugar, but who prefers 12 grams of sugar to 10. See also Intransitivity Reflexive relation Category Mathematical relations math stub ... more details
Unreferenced date December 2009 In logic and mathematics , relation construction and relational constructibility have to do with the ways that one relation mathematics relation is determined by an indexed family or a sequence of other relations, called the relation dataset . The relation in the focus of consideration is called the faciendum . The relation dataset typically consists of a specified relation over sets of relations, called the constructor , the factor , or the method of construction , plus a specified set of other relations, called the faciens , the ingredients , or the makings . Relation composition and relation reduction are special cases of relation constructions. See also Projection mathematics Projection Relation mathematics RelationRelation composition Relation reduction DEFAULTSORT Relation Construction Category Mathematical relations ... more details
Einstein relation can refer to Einstein relation kinetic theory , a kinetic relation found independently by Albert Einstein 1905 and Marian Smoluchowski 1906 Mass energy equivalence , sometimes called Einstein s mass energy relation disambig ... more details
Mergefrom Dependency relation date February 2010 In mathematics, a tolerance relation is a binary relationrelation that is reflexive relation reflexive and symmetric relation symmetric . It does not need to be transitive relation transitive . External links Gerasin, S. N., Shlyakhov, V. V., and Yakovlev, S. V. 2008. Set coverings and tolerance relations. Cybernetics and Sys. Anal. 44, 3 May 2008 , 333&ndash 340. DOI http dx.doi.org 10.1007 s10559 008 9007 y Hryniewiecki, K. 1991, Relations of Tolerance http mizar.org fm 1991 2 pdf2 1 toler 1.pdf FORMALIZED MATHEMATICS, Vol. 2, No. 1, January February 1991. Category Mathematical relations ... more details
In mathematics , the inverse relation of a binary relation is the relation that occurs when you switch the order of the elements in the relation. For example, the inverse of the relation child of is the relation parent of . In formal terms, if math L subseteq X times Y math is a relation from X to Y then math L 1 math is the relation defined so that math y ,L 1 ,x math if and only if math x ,L ,y math ... every relation does. The inverse relation is also called the converse relation or transpose relation ... breve L math . Note that, despite the notation, the converse relation is not an inverse in the sense of composition of relations math L circ L 1 neq mathrm id math in general. Properties A relation equal to its inverse is a symmetric relation in the language of dagger category dagger categories , it is self adjoint . If a relation is reflexive relation reflexive , irreflexive relation irreflexive , symmetric relation symmetric , antisymmetric relation antisymmetric , asymmetric relation asymmetric , transitive relation transitive , total relation total , ml Binary relation Relations over ... preorders total preorder weak order , or an equivalence relation , its inverse is too. However, if a relation is ml Binary relation Relations over a set extendable , this need not be the case for the inverse. The operation of taking a relation to its inverse gives the category of relations Rel the structure of a dagger category . The the set of all binary relation s B X on a set X is a semigroup with involution with the involution being the mapping of a relation to its inverse relation. Examples For usual maybe strict or partial order relation s, the converse is the naively expected opposite order, e.g. math le 1 ge , 1 math , etc. Inverse relation of a function A function is invertible if and only if its inverse relation is a function, in which case the inverse relation is the inverse function. The inverse relation of a function mathematics function math f X to Y math is the relation math ... more details
In mathematics , a binary relation R over a Set mathematics set X is symmetric if it holds for all a and b in X that if a is related to b then b is related to a . In mathematical notation , this is math forall a, b in X, a R b Rightarrow b R a. math Note symmetry is not the exact opposite of antisymmetric relation antisymmetry aRb and bRa implies b a . There are relations which are both symmetric and antisymmetric equality mathematics equality and its subrelations, including, vacuous truth vacuously , the empty relation , there are relations which are neither symmetric nor antisymmetric the relation divides on the set the relation preys on in biological sciences , there are relations which are symmetric and not antisymmetric congruence relation congruence modular arithmetic modulo n , and there are relations which are not symmetric but are antisymmetric is less than or equal to . A symmetric relation that is also transitive relation transitive and reflexive relation reflexive is an equivalence relation . Graph theoretic interpretation In an undirected graph , the relation over the set of vertex graph theory vertices of the graph under which v and w are related if and only if they are adjacent forms a symmetric relation. Conversely, if R is a symmetric relation over a set X , one can interpret it as describing an undirected graph with the elements of X as the vertices and the pairs in R as the edges. Thus, symmetric relations and undirected graphs are combinatorially equivalent objects. Examples is married to is a symmetric relation, while is less than is not. is equal ... and ... is odd too Image Bothodd.png See also Symmetry in mathematics Asymmetric relation Antisymmetric relation Category Mathematical relations Category Symmetry ca Relaci sim trica cs Symetrick relace de Symmetrische Relation et S mmeetriline seos es Relaci n sim trica it Relazione simmetrica ... rel cia sl Simetri nost sv Symmetrisk relation uk zh ... more details
The term Legendre relation may refer to The Legendre sieve , for determining whether an integer is prime. The Legendre duplication formula for the gamma function. The elliptic integral Functional relations functional relation for the elliptic integral . Category Number theory mathdab ... more details
Context date October 2009 unreferenced date March 2011 A relation is involutive if it is both bijection bijective and symmetric relation symmetric . See also idempotency Category Mathematical relations logic stub ... more details
Unreferenced date December 2009 Asymmetry Asymmetric often means, simply not symmetric. In this sense an asymmetric relation is a binary relation which is not a symmetric relation . That is, math lnot forall a, b in X, a R b Rightarrow b R a math . or equivalently, math exists a, b in X, a R b land lnot b R a math . In some texts the word is given the following stronger definition For all a and b in X , if a is related to b , then b is not related to a . In mathematical notation, this is math forall a, b in X, a R b Rightarrow lnot b R a math . In this sense, a relation is asymmetric if and only if it is both antisymmetric relation antisymmetric and reflexive relation irreflexive . For a transitive relation , asymmetry is equivalent to irreflexivity. For nonempty relations, asymmetry in the second definition given here implies asymmetry in the first sense, but the reverse does not hold. Empty relations are, vacuous truth vacuously , both asymmetric in the second sense only and symmetric. See also Symmetry in mathematics Symmetry Antisymmetric relation DEFAULTSORT Asymmetric Relation Category Mathematical relations cs Antisymetrick relace eo Kontra simetria rilato ja pl Relacja przeciwsymetryczna sk Asymetrick rel cia uk zh ... more details
In relational model A relation is a data structure which consists of a heading and an unordered set computer ... invented the relational model, he generalized the concept of binary relation binary relation mathematical relation to n arity ary relation . Relation is a fundamental concept in relational model. A relation has zero or more tuples. A relation value is an instance of a relation. A relvar relation variable relvar is a variable which has a relation value. In some context, relation means relation variable. In another context, relation means relation value. In SQL , a database language for relational database s, a relation variable is called a table database table . File Relational model concepts.png thumbnail right 540px Relational model concepts including relation A relation value, which is assigned to a certain relation variable, is time varying. By using a Data Definition Language DDL , it is able to define relation variables. A heading is the unordered set of certain column database attributes ... constitutes a relation value. In other words, a relation value consists of a heading and a body. A Tuple ... structured value. The comparative degree of a relation is the number of attributes which constitute a heading. The degree of a relation value is zero or more integer. An n ary relation is a relation value in which its degree is n . The cardinality of a relation is the number of tuples which constitutes a relation value. The cardinality of a relation value is zero or more integer. There are no duplicate tuples in a relation value. A candidate key is a certain minimal set of one or more attributes that can uniquely identify individual tuples in a relation value. Examples The following is an example ... science String Address String The following is an example of a relation value which consists of the above ... shows a relation value in visual table database table form for the sake of convenience. class ... relation value includes four tuples which share the same type. As mentioned above, the attributes ... more details
Mergeto Tolerance relation date February 2010 Unreferenced date March 2008 In mathematics and computer science , a dependency relation is a binary relation that is finite, symmetric relation symmetric , and reflexive relation reflexive i.e. a finite tolerance relation . That is, it is a finite set of ordered pairs math D math , such that If math a,b in D math then math b,a in D math symmetric If math a math is an element of the set on which the relation is defined, then math a,a in D math reflexive In general, dependency relations are not transitive relation transitive thus, they generalize the notion of an equivalence relation by discarding transitivity. Let math Sigma math denote the alphabet computer science alphabet of all the letters of math D math . Then the independency induced by math D math is the binary relation math I math math I Sigma times Sigma D math That is, the independency is the set of all ordered pairs that are not in math D math . Clearly, the independency is symmetric and irreflexive. The pairs math Sigma, D math and math Sigma, I math , or the triple math Sigma, D, I math with math I math induced by math D math are sometimes called the concurrent alphabet or the reliance alphabet . The pairs of letters in an independency relation induce an equivalence relation on the free monoid of all possible strings of finite length. The elements of the equivalence class es induced by the independency are called trace monoid traces , and are studied in trace theory . Examples Consider the alphabet math Sigma a,b,c math . A possible dependency relation is math begin matrix D & & a,b times a,b quad cup quad a,c times a,c & & a,b 2 cup a,c 2 & & a,b , b,a , a,c , c,a , a,a , b,b , c,c end matrix math The corresponding independency is math I D b,c ,, , c,b math Therefore, the letters math b,c math commute, or are independent of one another. Category Mathematical relations es Relaci n de dependencia it Alfabeto concorrente uk ... more details
unreferenced date June 2007 In mathematics , a binary relation R on a set mathematics set X is Euclidean sometimes called right Euclidean if it satisfies the following for every a , b , c in X , if a is related to b and c , then b is related to c . To write this in predicate logic math forall a, b, c in X , a ,R , b land a ,R , c to b ,R , c . math Dually, a relation R on X is left Euclidean if for every a , b , c in X , if a is related to b and c , then b is related to c math forall a, b, c in X , b ,R , a land c ,R , a to b ,R , c . math The property of being Euclidean is different from transitive relation transitivity . However, if a relation is symmetric relation symmetric , then it is Euclidean if and only if it is transitive. If a relation is Euclidean and reflexive, it is also symmetric and transitive, hence it is an equivalence relation . Consequently, equivalence relations are exactly the reflexive Euclidean relations. Category Mathematical relations Category Euclid Relation ... more details
In mathematics , a reflexive relation is a binary relation on a set for which every element is related to itself, i.e., a relation R on S where xRx holds true for every x in S. ref Levy 1979 74 ref For example, R could be is equal to . Related terms An irreflexive , or anti reflexive, relation is the opposite of a reflexive relation. It is a binary relation on a set where no element is related to itself. An example is the greater than relation x> y . Note that not every relation which is not reflexive is irreflexive it is possible to define relations where some elements are related to themselves but not others. For example, the binary relation the product of x and y is even is reflexive on the set of even numbers, irreflexive on the set of odd numbers, and neither on the set of natural number s. The reflexive closure of a binary relation R on a set S is the smallest relation R&prime such that R&prime is a superset of R and R&prime is reflexive on S. This is equivalent to the union of R and the Equality mathematics identity relation on S. For example, the reflexive closure of x y is x&le y. The reflexive reduction of a binary relation R on a set S is the smallest relation R&prime such that R&prime shares the same reflexive closure as R. It can be seen in a way as the opposite of the reflexive closure. It is equivalent to the complement of the identity relation on S with regard to R. That is, it is equivalent to R except for where xRx is true. For example, the reflexive reduction of x&le y is x y. Examples Image GreaterThanOrEqualTo.png left 250px Image GreaterThan.png right ... Sequences OEIS A053763 A053763 ref Number of relations Notes reflist See also Binary relation Symmetric relation Transitive relation References Levy, A. 1979 Basic Set Theory , Perspectives in Mathematical ... Relation et Refleksiivsus es Relaci n reflexiva eo Refleksiva rilato fr Relation r flexive ko ... zwrotna ru sk Reflex vna rel cia sl Refleksivnost sv Reflexiv relation ... more details
Dablink Relation mathematics redirects here. For a more general notion of relation, see Finitary relation . For a more combinatorial viewpoint, see Theory of relations . In mathematics , a binary relation ... of the Cartesian product A sup 2 sup nowrap A A . More generally, a binary relation between two sets A and B is a subset of nowrap A B . The terms dyadic relation and 2 place relation are synonyms for binary relations. An example is the divides relation between the set of prime number ... multiple of p and not with any integer that is not a multiple of p . In this relation ... of function mathematics function is defined as a special kind of binary relation. Binary relations are also heavily used in computer science . A binary relation is the special case nowrap 1 n 2 of an finitary relation n ary relation R A sub 1 sub A sub ... th domain A sub j sub of the relation. In some systems of axiomatic set theory , relations are extended ... relation R is usually defined as an ordered triple X , Y , G where X and Y are arbitrary sets or classes ... domain or the set of departure and codomain or the set of destination , respectively, of the relation ... other. Is a relation more than its graph? According to the definition above, two relations with the same ... not consider the sets X and Y to be part of the relation, and therefore define a binary relation as being ... , 2,7 is a relation from any set that contains 1,2 to any set that contains 2,3,7 . A special case ... , inverse relation , and so on. The choice between the two definitions usually matters only in very ... and Ian owns nothing. Then the binary relation is owned by is given as R ball, car, doll, gun , John ... is owned by John. Two different relations could have the same graph. For example the relation ball ... R . Special types of binary relations functional relation redirects to this section Some important ... relation is called a partial function . one to one also written 1 to 1 injective and functional ... more details
In mathematics , a coreflexive relation is a binary relation that is a subset of the identity relation . ref Fonseca de Oliveira, J. N., & Pereira Cunha Rodrigues, C. D. J. 2004 . Transposing Relations From Maybe Functions to Hash Tables. In Mathematics of Program Construction p. 337 . ref Thus if a is related to b aRb then a is equal to b a b , but if c is equal to d c d it does not necessarily hold that c is related to d cRd . In mathematical notation , this is math forall a, b in X, a R b Rightarrow a b. math The identity relation is coreflexive by definition. Any relation that is coreflexive is thus a subset of the identity relation. For example, consider the relation R as equal to and odd . Over the set of positive integers, the relationship R holds over the pairs 1, 1 , 3, 3 , ... but does not hold over 2, 2 , 4, 4 , ... . Notes references Category Mathematical relations ... more details
Refimprove date January 2010 Textbook date January 2010 In mathematics , a binary relation R on a Set mathematics set X is antisymmetric if, for all a and b in X if R a,b and R b,a , then a b , or, equivalently, if R a,b with a b , then R b,a must not hold. In mathematical notation , this is math forall a, b in X, R a,b and R b,a Rightarrow a b math or, equivalently, this is the same formula as above, but due to the addition of the negation, it is more clear where the term anti symmetric comes from math forall a, b in X, R a,b and a ne b Rightarrow lnot R b,a . math An example of an antisymmetric relation is the subset relation math A subseteq B and B subseteq A Rightarrow A B math Or in words, if every Element mathematics element in A also is in B and all elements in B are in A, then A and B must be equal, i.e. containing all the same elements. partial order Partial and total order s are antisymmetric by definition. Therefore the usual order relation on the real number s, the subset order on the subsets of any given set and the divisibility order of the natural number s are antisymmetric. For example, if for two real numbers x and y both inequality mathematics inequalities x y and y x hold then x and y must be equal. A relation can be both symmetric relation symmetric and antisymmetric e.g., equality mathematics the equality relation , and there are relations which are neither symmetric nor antisymmetric e.g., the preys on relation on biological species . Antisymmetry is different from Asymmetric relation asymmetry . According ... of asymmetric makes asymmetry equivalent to antisymmetry plus reflexive relation irreflexivity . Examples The relation x is even, y is odd between a pair x , y of integer s is antisymmetric Image ... title Antisymmetric Relation DEFAULTSORT Antisymmetric Relation Category Mathematical relations cs Antisymetrick relace de Antisymmetrische Relation et Antis mmeetriline seos es Relaci n antisim trica ... more details
In mathematics , a binary relation R over a Set mathematics set X is transitive if whenever an element a is related to an element b , and b is in turn related to an element c , then a is also related to c . Transitivity is a key property of both partial order relations and equivalence relation s. Examples This section is linked from Indifference curve For example, is greater than, is at least as great ... A C. On the other hand, is the mother of is not a transitive relation, because if Alice is the mother ... need to consider motherhood over an arbitrary number of generations the relation is a matrilinear ancestor of . This is a transitive relation. More precisely, it is the transitive closure of the relation ... relation is always transitive e.g. knowing that is a subset of is transitive and is a superset ... before or has the same first name as is not generally a transitive relation. The complement of a transitive relation is not always transitive. For instance, while equal to is transitive, not equal to is only ... a reflexive relation reflexive transitive relation Partially ordered set partial order an antisymmetric relation antisymmetric preorder Total preorder a total relation total preorder Equivalence relation a symmetric relation symmetric preorder Strict weak ordering a strict partial order in which incomparability is an equivalence relation Total ordering a total relation total , antisymmetric relation antisymmetric transitive relation Counting transitive relations Unlike other relation properties ... that are simultaneously reflexive, symmetric, and transitive in other words, equivalence relation ... also Transitive closure Transitive reduction Intransitivity Reflexive relation Symmetric relation Quasitransitive relation Notes references References More footnotes date November 2010 Discrete and Combinatorial ... DEFAULTSORT Transitive Relation Category Mathematical relations Category Elementary algebra ar ... fi Transitiivisuus matematiikka sv Transitiv relation tr Ge i lilik matematik uk ... more details
Unreferenced date December 2009 In mathematics , a ternary relation or triadic relation is a finitary relation in which the number of places in the relation is three. Ternary relations may also be referred to as 3 adic , 3 ary , 3 dimensional , or 3 place . Just as a binary relation is formally defined as a set of pairs , i.e. a subset of the Cartesian product Nowrap A B of some sets A and B , so a ternary relation is a set of triples, forming a subset of the Cartesian product Nowrap A B C of three sets A , B and C . An example of a ternary relation in elementary geometry is the line geometry Collinear points collinearity of points . Example graph of a binary function Further Graph of a function binary function A function Nowrap A B C in two variables, taking values in two sets A and B , respectively, is formally a function that associates to every pair a , b in Nowrap A B an element a , b in C . Therefore its graph consists of pairs of the form Nowrap a , b , a , b . Such pairs in which the first element is itself a pair are often identified with triples. This makes the graph of a ternary relation between A , B and C , consisting of all triples Nowrap a , b , a , b , for all a in A and b in B . Example cyclic orders Main Cyclic order Given any set A whose elements are arranged on a circle, one can define a ternary relation R on A , i.e. a subset of A sup 3 sup Nowrap A A A , by stipulating that Nowrap R a , b , c holds if and only if the elements a , b and c are pairwise different and when going from a to c in a clockwise direction one passes through b . For example if A Nowrap 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 represents the hours on a clock face , then Nowrap R 8, 12, 4 holds and Nowrap R 12, 8, 4 does not hold. DEFAULTSORT Ternary Relation Category Mathematical relations es Relaci n ternaria pt Rela o tern ria ru ... more details
Refimprove date April 2009 Context date April 2009 Gotthard Gunther introduced the term proemial relation in his 1970 paper Cognition and Volition . Meaning to preface , it specifically refers to the intercoherence prerequisite relation of subject grammar subject and object grammar object . Subject and object arise together. In fact, subject is a mere abbreviation of Subject superject which is an actual entity in Alfred North Whitehead s technical phraseology. The abstractions related are Subjectivity and Profundity . In Gotthard Gunther s mathematics, Subjectivity is called polycontexturality . References Reflist DEFAULTSORT Proemial Relation Category Syntactic entities ... more details
Merge Dense order date June 2010 Unreferenced date April 2010 In mathematics , a binary relation R is said to be dense if, for all R related x and y , there is a z such that x and z and also z and y are R related. Formally math forall x forall y xRy Rightarrow exists z xRz land zRy . math For example, a strict partial order is a dense order iff is a dense relation. Every reflexive relation is dense. See also Dense order Kripke semantics Category Mathematical relations math stub ... more details
A false relation also known as cross relation , non harmonic relation is the name of a type of Consonance and dissonance dissonance that sometimes occurs in Classical music classical Polyphony polyphonic music, most commonly in vocal music of the Renaissance music Renaissance . The term describes i a diatonic and chromatic chromatic contradiction ref name one GroveOnline False relation Dyson, George 16 February 2007 ref between two note music notes sounding simultaneously, or in close proximity , in two different melody voices or parts or ii in music written before 1600, the occurrence of a tritone between two notes of adjacent chord music chords . ref Arnold Whittall 2002 . False Relation , The Oxford Companion to Music . Ed. Alison Latham. Oxford University Press. King s College London. http www.oxfordreference.com views ENTRY.html?subview Main&entry t114.e2404 Oxford Reference Online . Accessed 18 March 2007. ref Image False relation byrd.svg center thumb 550px Ex. 1, from Ave Verum Corpus, by William Byrd In the above example, a chromatic false relation occurs in two adjacent voices sounding at the same time shown in red . The tenor voice sings G music while the bass vocal range bass sings G music natural momentarily beneath it, producing the clash of an augmented unison . Image Baroque false relation.svg center thumb 550px Ex. 2, typical example of a false relation in the Late Baroque Style In this instance, the false relation is less pronounced the contradicting E music ... relation occurs because the top voice is descending in a minor key, and therefore takes the notes ... makes use of the ascending melodic minor scale the raised sixth degree . False relation is permitted ... of false relation in Byrd s Ave Verum Corpus . Counterpoint & polyphony Category Chromaticism Category Counterpoint False relation Category Harmony False relation de Querstand Musik fr Fausse relation it Falsa relazione nl Querstand ja ... more details
In mathematics , a dependence relation is a binary relation which generalizes the relation of linear dependence . Let math X math be a set mathematics set . A binary relation math triangleleft math between an element math a math of math X math and a subset math S math of math X math is called a dependence relation , written math a triangleleft S math , if it satisfies the following properties if math a in S math , then math a triangleleft S math if math a triangleleft S math , then there is a finite set finite subset math S 0 math of math S math , such that math a triangleleft S 0 math if math T math is a subset of math X math such that math b in S math implies math b triangleleft T math , then math a triangleleft S math implies math a triangleleft T math if math a triangleleft S math but math a not triangleleft S lbrace b rbrace math for some math b in S math , then math b triangleleft S lbrace b rbrace cup lbrace a rbrace math . Given a dependence relation math triangleleft math on math X math , a subset math S math of math X math is said to be independent if math a not triangleleft S lbrace a rbrace math for all math a in S. math If math S subseteq T math , then math S math is said to span math T math if math t triangleleft S math for every math t in T. math math S math is said to be a basis of math X math if math S math is independent and math S math spans math X. math Remark. If math X math is a non empty set with a dependence relation math triangleleft math , then math X math always has a basis with respect to math triangleleft. math Furthermore, any two bases of math ... field math F. math The relation math triangleleft math , defined by math upsilon triangleleft S math ... relation. This is logical equivalence equivalent to the definition of linear independence linear dependence ... triangleleft math is a dependence relation. This is equivalent to the definition of algebraic dependence . See also matroid planetmath id 5792 title Dependence relation Category Mathematical ... more details
Dablink This article sets out the set theoretic notion of relation. For a more elementary point of view, see Binary relation . For a combinatorial viewpoint, see Theory of relations . Other uses Relation disambiguation In set theory and logic , a relation is a property that assigns truth values to tuple ... k tuple according to whether the property does or does not hold. An example of a ternary relation i.e. ... the number of places in the relation, 3 for the above example, is a non negative integer zero, one, two, ... , called the relation s arity , adicity , or dimension . A relation with k places is variously called a k ary , a k adic , or a k dimensional relation. Relations with a finite number of places ... prize . Two place relations are called binary relation s or dyadic relations . The latter term has historic priority. Binary relation s are very common, given the ubiquity of relations such as Equality ... N . A k ary relation, k 2, is a straightforward generalization of a binary relation. Informal introduction Relation is formally defined in the next section. In this section we introduce the concept of a relation with a familiar everyday example. Consider the relation involving three roles that people ... 4 cellspacing 0 style background lightcyan text align center width 60 Relation S X thinks that Y ... thinks that Bob likes Denise . The Table represents a relation S over the set P of people under ... S Alice, Bob, Denise to say the same thing as the first row of the Table. The relation S is a ternary relation, since there are three items involved in each row. The relation itself is a mathematical object defined in terms of concepts from set theory i.e., the relation is a subset ... the Table in one neat package. Mathematically, then, a relation is simply a set . The Table for relation ... concept of a relation. For one thing, databases are designed to deal with empirical data, and experience ... a relation. Augustus De Morgan ref De Morgan, A. 1858 On the syllogism, part 3 in Heath, P., ed ... more details
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