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alternate case: binary relation
Intransitive game
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If strategy A beats strategy B, B beats C, and C beats A, then the binary relation "to beat" is intransitive, since transitivity would require that AContinuous function (9,404 words) [view diff] no match in snippet view article find links to article
In mathematics, a continuous function is a function such that a small variation of the argument induces a small variation of the value of the functionPartial equivalence relation (1,138 words) [view diff] exact match in snippet view article find links to article
literature also called restricted equivalence relation) is a homogeneous binary relation that is symmetric and transitive. If the relation is also reflexiveSubstructure (mathematics) (734 words) [view diff] exact match in snippet view article
of A. In the language consisting of the binary functions + and ×, binary relation <, and constants 0 and 1, the structure (Q, +, ×, <, 0, 1) is a substructureList of first-order theories (5,269 words) [view diff] exact match in snippet view article find links to article
theory in some language, we define a new theory 2T by adding a new binary relation to the language, and adding axioms stating that it is an equivalenceResiduated Boolean algebra (1,155 words) [view diff] exact match in snippet view article find links to article
relation algebras as a finitely axiomatized generalization of the binary relation example, but there exist interesting examples of residuated BooleanNon-logical symbol (783 words) [view diff] exact match in snippet view article find links to article
consist of a binary function symbol +, a constant symbol 0, and a binary relation symbol <. Structures over a signature, also known as models, provideAxiom of dependent choice (947 words) [view diff] exact match in snippet view article find links to article
{\displaystyle (\,\Longleftarrow \,)} Let R {\displaystyle R} be an entire binary relation on X {\displaystyle X} . The strategy is to define a tree T {\displaystyleCritical pair (order theory) (235 words) [view diff] exact match in snippet view article
in S, if y < z then x < z. If (x, y) is a critical pair, then the binary relation obtained from P by adding the single relationship x ≤ y is also a partialBerkeley cardinal (271 words) [view diff] exact match in snippet view article find links to article
choice. A weakening of being a Berkeley cardinal is that for every binary relation R on Vκ, there is a nontrivial elementary embedding of (Vκ, R) intoTrakhtenbrot's theorem (1,894 words) [view diff] exact match in snippet view article find links to article
is undecidable. Let σ be a relational vocabulary with one at least binary relation symbol. The set of σ-sentences valid in all finite structures is notΠ-calculus (4,833 words) [view diff] exact match in snippet view article find links to article
Milner, Parrow and Walker in their original paper on the π-calculus. A binary relation R {\displaystyle R} over processes is an early bisimulation if forStructure (mathematical logic) (5,097 words) [view diff] exact match in snippet view article
_{f}} -structure. A signature for ordered fields needs an additional binary relation such as < {\displaystyle \,<\,} or ≤ , {\displaystyle \,\leq ,\,} andStochastic transitivity (1,839 words) [view diff] exact match in snippet view article find links to article
where transitivity is expected, however, empirical observations of the binary relation is probabilistic. For example, players' skills in a sport might beSchröder–Bernstein property (1,000 words) [view diff] exact match in snippet view article find links to article
binary relation "be a part of", A binary relation "be similar to" (similarity). Instead of the relation "be a part of" one may use a binary relation "beDouble turnstile (425 words) [view diff] exact match in snippet view article find links to article
syntactic consequence (in contrast to semantic). The double turnstile is a binary relation. It has several different meanings in different contexts: To show semanticInterpretation (logic) (4,421 words) [view diff] exact match in snippet view article
constant symbols 0 and 1, two binary function symbols + and ·, and no binary relation symbols. (Here the equality relation is taken as a logical constantTruth value (641 words) [view diff] exact match in snippet view article find links to article
the form of truth tables. Logical biconditional becomes the equality binary relation, and negation becomes a bijection which permutes true and false. ConjunctionFinite model theory (3,074 words) [view diff] exact match in snippet view article find links to article
sentence. The principle is illustrated here for a structure with one binary relation R {\displaystyle R} and without constants: say that there are at leastMonadic predicate calculus (699 words) [view diff] exact match in snippet view article find links to article
is logically valid (true for all nonempty domains). Adding a single binary relation symbol to monadic logic, however, results in an undecidable logic.Leibniz operator (1,167 words) [view diff] exact match in snippet view article find links to article
{\displaystyle {\mathcal {S}}} , if ≡ T {\displaystyle \equiv _{T}} denotes the binary relation on the set of formulas of S {\displaystyle {\mathcal {S}}} , definedHerbrand structure (495 words) [view diff] exact match in snippet view article find links to article
whose argument terms are elements of the Herbrand universe. For a binary relation symbol R, we get with the terms from above: {R(c, c), R(fc, c), R(cElementary function arithmetic (872 words) [view diff] exact match in snippet view article find links to article
{\textrm {exp}}(x,y)} usually written as x y {\displaystyle x^{y}} , a binary relation symbol < {\displaystyle <} (This is not really necessary as it canSubobject (907 words) [view diff] exact match in snippet view article find links to article
:S\to T} such that u = v ∘ ϕ {\displaystyle u=v\circ \phi } . The binary relation ≡ {\displaystyle \equiv } defined by u ≡ v ⟺ u ≤ v and v ≤ u {\displaystyleOrder (mathematics) (501 words) [view diff] exact match in snippet view article
Order in mathematics may refer to: Total order and partial order, a binary relation generalizing the usual ordering of numbers and of words in a dictionaryPostcolonialism (10,797 words) [view diff] exact match in snippet view article find links to article
is that the cultural representations generated with the us-and-them binary relation are social constructs, which are mutually constitutive and cannot existOther (philosophy) (5,191 words) [view diff] exact match in snippet view article
and fashion, which conflated different cultures and peoples into the binary relation of the Orient and the Occident. Orientalism created the artificialReification (computer science) (2,198 words) [view diff] exact match in snippet view article
Framework (RDF) and Web Ontology Language (OWL), a statement is a binary relation. It is used to link two individuals or an individual and a value. ApplicationsExtension by definitions (1,502 words) [view diff] exact match in snippet view article find links to article
everyday mathematics, however, many other symbols are used such as the binary relation symbol ⊆ {\displaystyle \subseteq } , the constant ∅ {\displaystyleElementary equivalence (956 words) [view diff] exact match in snippet view article find links to article
elementarily equivalent. For example, consider the language with one binary relation symbol '<'. The model R of real numbers with its usual order and theIdentity (philosophy) (1,128 words) [view diff] exact match in snippet view article
relation between objects, and Kai Wehmeier has argued that appealing to a binary relation that every object bears to itself, and to no others, is both logicallyModal logic (8,455 words) [view diff] exact match in snippet view article find links to article
{\displaystyle W} is a set of possible worlds R {\displaystyle R} is a binary relation on W {\displaystyle W} V {\displaystyle V} is a valuation functionEquivalent definitions of mathematical structures (3,272 words) [view diff] exact match in snippet view article find links to article
another signature (+, ·, ≤) consisting of two binary functions and one binary relation. The notion of isomorphism does not apply to structures of differentFlag (geometry) (450 words) [view diff] exact match in snippet view article
triple D = (V, B, I) where V and B are any two disjoint sets and I is a binary relation between V and B, that is, I ⊆ V × B. The elements of V will be calledSubsequence (828 words) [view diff] exact match in snippet view article find links to article
Mathematical binary relationMinimum relevant variables in linear system (1,053 words) [view diff] exact match in snippet view article find links to article
and even hard to approximate. A Min-RVLS problem is defined by: A binary relation R, which is one of {=, ≥, >, ≠}; An m-by-n matrix A (where m is theType (model theory) (2,253 words) [view diff] exact match in snippet view article
way of producing saturated models. Consider the language L with one binary relation symbol, which we denote as ∈ {\displaystyle \in } . Let M {\displaystyleEncompassment ordering (277 words) [view diff] exact match in snippet view article find links to article
constant symbols a, b i.e. irreflexive, transitive, and well-founded binary relation R such that sRt implies u[sσ]p R u[tσ]p for all terms s, t, u, eachOntology chart (681 words) [view diff] exact match in snippet view article find links to article
transitivity. Ontological dependency is a special poset because it is a binary relation, every thing is ontologically dependent on itself for its existencePPAD (complexity) (1,029 words) [view diff] exact match in snippet view article
guaranteed to be total. The TFNP formal definition is given as follows: A binary relation P(x,y) is in TFNP if and only if there is a deterministic polynomialAsymptotic analysis (2,763 words) [view diff] exact match in snippet view article find links to article
O notation. Formally, given functions f (x) and g(x), we define a binary relation f ( x ) ∼ g ( x ) ( as x → ∞ ) {\displaystyle f(x)\sim g(x)\quad ({\text{asKripke structure (model checking) (718 words) [view diff] exact match in snippet view article
for the states as well (L as defined above.) In this approach, the binary relation obtained by abstracting away the action labels is called a state graphViral phenomenon (4,676 words) [view diff] exact match in snippet view article find links to article
reality from fiction or social media Transitive relation – Type of binary relation Tony D. Sampson – British critical theorist (born 1964) (thesis andDatalogZ (500 words) [view diff] exact match in snippet view article find links to article
limit-closed. Given a constant w, a binary relation edge that represents the edges of a graph, and a binary relation sp with the last position of sp minimalTilde (6,975 words) [view diff] exact match in snippet view article find links to article
tilde \widetilde can be used. The \sim command produce a tilde-like binary relation symbol that is often used in mathematical expressions, and the double-tildeF-coalgebra (929 words) [view diff] exact match in snippet view article find links to article
The P-coalgebras are in bijective correspondence with sets with a binary relation. Now fix another set, A. Then coalgebras for the endofunctor P(A×(-))Kripke–Platek set theory with urelements (664 words) [view diff] exact match in snippet view article find links to article
sorted first order language L ∗ {\displaystyle L^{*}} with a single binary relation symbol ∈ {\displaystyle \in } . Letters of the sort p , q , r , .Phonetic Symbol Guide (1,258 words) [view diff] case mismatch in snippet view article find links to article
editions. It might be adequately rendered with U+2AFB ⫻ TRIPLE SOLIDUS BINARY RELATION. This is an allograph of a triple pipe, for which Unicode recommendsChurch–Rosser theorem (1,203 words) [view diff] exact match in snippet view article find links to article
method originates from William W. Tait and Per Martin-Löf. Say that a binary relation → {\displaystyle \rightarrow } satisfies the diamond property if: ∀Formal grammar (3,431 words) [view diff] exact match in snippet view article find links to article
grammar G = ( N , Σ , P , S ) {\displaystyle G=(N,\Sigma ,P,S)} , the binary relation ⇒ G {\displaystyle {\underset {G}{\Rightarrow }}} (pronounced as "GHeyting arithmetic (6,233 words) [view diff] exact match in snippet view article find links to article
is equivalent to (provably) being inhabited by some least member. A binary relation " < {\displaystyle <} " that validates the strong induction schemaO-minimal theory (1,294 words) [view diff] exact match in snippet view article find links to article
language of model theory. Specifically if L is a language including a binary relation <, and (M,<,...) is an L-structure where < is interpreted to satisfyCauchy sequence (3,218 words) [view diff] exact match in snippet view article find links to article
of the completion of a metric space, one can furthermore define the binary relation on Cauchy sequences in G {\displaystyle G} that ( x k ) {\displaystyleArchimedean property (2,386 words) [view diff] exact match in snippet view article find links to article
Alternative decimal expansion of 1 Archimedean ordered vector space – A binary relation on a vector space Construction of the real numbers "Math 2050C Lecture"Cave of La Pasiega (7,283 words) [view diff] exact match in snippet view article find links to article
together with more deer, the other five horses which apparently stand in binary relation to the cattle painted before the bend, which have been mentioned inEnriched category (1,966 words) [view diff] exact match in snippet view article find links to article
identity. The hom-objects 2(a, b) then simply deny or affirm a particular binary relation on the given pair of objects (a, b); for the sake of having more familiarDigital library (6,262 words) [view diff] exact match in snippet view article find links to article
objects through the inclusion property between sets, in contrast to the binary relation between nodes exploited by the tree. NESTOR has been used to formallyLinear subspace (4,653 words) [view diff] exact match in snippet view article find links to article
0), (2, 1, 0, 0), and (0, 0, 5, 1). The set-theoretical inclusion binary relation specifies a partial order on the set of all subspaces (of any dimension)Abstract cell complex (1,271 words) [view diff] exact match in snippet view article find links to article
is an abstract set, B is an asymmetric, irreflexive and transitive binary relation called the bounding relation among the elements of E and dim is a functionBinding (linguistics) (3,798 words) [view diff] exact match in snippet view article
Expression that gives its meaning to a pro-form in grammar C-command – binary relation between nodes in a parse tree, in which a node c-commands its sisterHomomorphism (4,196 words) [view diff] exact match in snippet view article find links to article
each n-ary relation symbol R in L. In the special case with just one binary relation, we obtain the notion of a graph homomorphism. Homomorphisms are alsoAhnentafel (3,851 words) [view diff] exact match in snippet view article find links to article
Demonstration decimal binary relation 1 1 proband 2 10 father 3 11 mother 4 100 paternal grandfather 5 101 paternal grandmother 6 110 maternal grandfatherAxiom of regularity (2,937 words) [view diff] exact match in snippet view article find links to article
every element of S has a non-empty intersection with S. We define a binary relation R on S by a R b :⇔ b ∈ S ∩ a {\displaystyle aRb:\Leftrightarrow b\inDescriptive complexity theory (2,545 words) [view diff] exact match in snippet view article find links to article
augmented with an operator that computes the transitive closure of a binary relation. The resulting transitive closure logic is known to characterise non-deterministicProper name (philosophy) (1,965 words) [view diff] exact match in snippet view article
proper names stand outside of the social construct of language as a binary relation between referent and sign. Rather, he argues the proper name as allModal μ-calculus (1,816 words) [view diff] exact match in snippet view article find links to article
states; R {\displaystyle R} maps to each label a {\displaystyle a} a binary relation on S {\displaystyle S} ; V : P → 2 S {\displaystyle V:P\to 2^{S}}P versus NP problem (7,720 words) [view diff] exact match in snippet view article find links to article
over a finite alphabet, Σ. L ∈ NP if, and only if, there exists a binary relation R ⊂ Σ ∗ × Σ ∗ {\displaystyle R\subset \Sigma ^{*}\times \Sigma ^{*}}Pairing function (2,292 words) [view diff] exact match in snippet view article find links to article
in ZFC. Define on κ × κ {\displaystyle \kappa \times \kappa } the binary relation ( α , β ) ≼ ( γ , δ ) if either { ( α , β ) = ( γ , δ ) , max ( αDehornoy order (1,551 words) [view diff] exact match in snippet view article find links to article
B_{n}^{*+}} is also ω ω n − 2 {\displaystyle \omega ^{\omega ^{n-2}}} . As a binary relation, the Dehornoy order is decidable. The best decision algorithm is basedMatrix grammar (1,225 words) [view diff] exact match in snippet view article find links to article
the following property. For a matrix grammar G {\displaystyle G} , a binary relation ⇒ G {\displaystyle \Rightarrow _{G}} is defined; also represented asOntoClean (1,824 words) [view diff] exact match in snippet view article find links to article
property of "being a person." In the semantic web, a property is a binary relation. The distinction between property and class is subtle, and probablyParaconsistent logic (5,527 words) [view diff] exact match in snippet view article find links to article
replace the usual functional valuation with a relational one. The binary relation V {\displaystyle V\,} relates a formula to a truth value: V ( A , 1Kenneth D. Mackenzie (1,109 words) [view diff] exact match in snippet view article find links to article
of an interaction from xi to xj. The value of rij can range from a binary relation such as a boss-subordinate to how many thousands of board feet of douglasBoolean algebra (9,405 words) [view diff] exact match in snippet view article find links to article
operation that returns a value in a Boolean algebra, the former is a binary relation which either holds or does not hold. In this sense, entailment is anTrace monoid (1,880 words) [view diff] exact match in snippet view article find links to article
{\displaystyle I} on Σ {\displaystyle \Sigma } then induces a (symmetric) binary relation ∼ {\displaystyle \sim } on Σ ∗ {\displaystyle \Sigma ^{*}} , whereRasdaman (1,585 words) [view diff] exact match in snippet view article find links to article
Anticipating a full integration with SQL, rasdaman collections represent a binary relation with the first attribute being an object identifier and the secondRelevance logic (3,940 words) [view diff] exact match in snippet view article find links to article
second way is to keep the semilattice conditions on frames and add a binary relation, J {\displaystyle J} , of disjointness to the frame. For these modelsPlural quantification (2,281 words) [view diff] exact match in snippet view article find links to article
D {\displaystyle D} ). The new component R {\displaystyle R} is a binary relation relating values in the domain to plural variable symbols. SatisfactionReduction (computability theory) (1,982 words) [view diff] exact match in snippet view article
proving that many sets are noncomputable. A reducibility relation is a binary relation on sets of natural numbers that is Reflexive: Every set is reducibleModel theory (9,086 words) [view diff] exact match in snippet view article find links to article
is a unary (= 1-ary) function symbol, and < {\displaystyle <} is a binary relation symbol. Then, when these symbols are interpreted to correspond withList of algorithms (7,843 words) [view diff] exact match in snippet view article find links to article
Transitive closure problem: find the transitive closure of a given binary relation Traveling salesman problem Christofides algorithm Nearest neighbourFormal concept analysis (5,372 words) [view diff] exact match in snippet view article find links to article
is a set of objects, M is a set of attributes, and I ⊆ G × M is a binary relation called incidence that expresses which objects have which attributesGraph homomorphism (4,800 words) [view diff] exact match in snippet view article find links to article
of relations on it). Directed graphs are structures with a single binary relation (adjacency) on the domain (the vertex set). Under this view, homomorphismsFirst-order logic (13,173 words) [view diff] exact match in snippet view article find links to article
one unary function symbol −, one binary function symbol +, and one binary relation symbol ≤. Then: The expressions +(x, y) and +(x, +(y, −(z))) are termsComplexity of constraint satisfaction (4,485 words) [view diff] exact match in snippet view article find links to article
allowing only domains of size 2 and only constraints whose relation is a binary relation. While the second fact implies that the scopes of the constraints areForcing (mathematics) (9,287 words) [view diff] exact match in snippet view article
is built up like ordinary first-order logic, with membership as the binary relation and all the P {\displaystyle \mathbb {P} } -names as constants. DefinePocket set theory (1,946 words) [view diff] exact match in snippet view article find links to article
reals. PST uses standard first-order language with identity and the binary relation symbol ∈ {\displaystyle \scriptstyle {\in }} . Ordinary variables areConsideration set (1,930 words) [view diff] exact match in snippet view article find links to article
undominated options according to an asymmetric, incomplete, or cyclic binary relation. Alternatives outside of this shortlist are moved to the inept or inertNet (mathematics) (7,344 words) [view diff] exact match in snippet view article
topological notions and results. Preorder – Reflexive and transitive binary relation Sequential space – Topological space characterized by sequences UltrafilterC-command (5,231 words) [view diff] exact match in snippet view article find links to article
that the current alternatives to c-command point to precedence, the binary relation between nodes in a tree structure, to be of great importance. KeekSurreal number (11,406 words) [view diff] exact match in snippet view article find links to article
and x(α) = y(α) for all α < dom(x). For surreal numbers define the binary relation < to be lexicographic order (with the convention that "undefined values"Logicism (11,826 words) [view diff] exact match in snippet view article find links to article
classes into 'bundles' : These above collections can be put into a "binary relation" (comparing for) similarity by "equinumerosity", symbolized here byEpsilon-induction (4,192 words) [view diff] exact match in snippet view article find links to article
induction.) The sets are ∈ {\displaystyle \in } -well-founded. For a binary relation R D {\displaystyle R_{D}} on a set D {\displaystyle D} , well-foundednessNear sets (9,533 words) [view diff] exact match in snippet view article find links to article
Φ B {\displaystyle A\ {\underline {\delta }}_{\Phi }\ B} ). The binary relation δ Φ {\displaystyle \delta _{\Phi }} is a descriptive EF-proximity,Glossary of set theory (11,511 words) [view diff] exact match in snippet view article find links to article
limit for comparison. LST The language of set theory (with a single binary relation ∈) m 1. A measure 2. A natural number 𝔪 The smallest cardinal atMobile membranes (7,128 words) [view diff] exact match in snippet view article find links to article
\Rightarrow _{amb}^{*}} denotes a reflexive and transitive closure of the binary relation ⇒ a m b {\displaystyle \Rightarrow _{amb}} . A translation from the