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Type of binary relation
In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates
Transitive_relation
Relationship between two sets, defined by a set of ordered pairs
is a relation that is reflexive, antisymmetric, and transitive, an equivalence relation is a relation that is reflexive, symmetric, and transitive, a function
Relation_(mathematics)
Smallest transitive relation containing a given binary relation
mathematics, the transitive closure R+ of a homogeneous binary relation R on a set X is the smallest relation on X that contains R and is transitive. For finite
Transitive_closure
Mathematical concept for comparing objects
mathematics, an equivalence relation is a binary relation that is reflexive, symmetric, and transitive. The equipollence relation between line segments in
Equivalence_relation
Binary relation over a set and itself
antisymmetric, let alone asymmetric. Transitive for all x, y, z ∈ X, if xRy and yRz then xRz. A transitive relation is irreflexive if and only if it is
Homogeneous_relation
Class of mathematical set whose elements are all subsets
theory, a branch of mathematics, a set A {\displaystyle A} is called transitive if either of the following equivalent conditions holds: whenever x ∈ A
Transitive_set
Relationship between elements of two sets
{\displaystyle xRz} . A transitive relation is irreflexive if and only if it is asymmetric. For example, "is ancestor of" is a transitive relation, while "is parent
Binary_relation
Binary relation that relates every element to itself
reflexive. An asymmetric relation is necessarily irreflexive. A transitive and irreflexive relation is necessarily asymmetric. left quasi-reflexive if whenever
Reflexive_relation
Mathematical ranking of a set
partially ordered sets in which incomparability is a transitive relation), as total preorders (transitive binary relations in which at least one of the two
Weak_ordering
Relationship between software
transitive dependency is an indirect dependency relationship between software components. This kind of dependency is held by virtue of a transitive relation
Transitive_dependency
Property of mathematical relations
Antitransitivity is a stronger property which describes a relation where, for any three values, the transitivity condition never holds. Some authors use the term
Intransitivity
Operation on the subsets of a set
{\displaystyle (x,z)} , we define the transitive closure of R {\displaystyle R} on A {\displaystyle A} as the smallest relation on A {\displaystyle A} that contains
Closure_(mathematics)
Type of binary relation
Symmetry, along with reflexivity and transitivity, are the three defining properties of an equivalence relation. "is equal to" (equality) (whereas "is
Symmetric_relation
Binary relation which never occurs in both directions
is also necessary) R {\displaystyle R} is irreflexive and transitive. A transitive relation is asymmetric if and only if it is irreflexive: if a R b {\displaystyle
Asymmetric_relation
Transformations induced by a mathematical group
this relation; two elements x and y are equivalent if and only if their orbits are the same, that is, G⋅x = G⋅y. The group action is transitive if and
Group_action
Mathematical concept for comparing objects
is symmetric and transitive. If the relation is also reflexive, then the relation is an equivalence relation. Formally, a relation R {\displaystyle R}
Partial_equivalence_relation
Topics referred to by the same term
Look up transitivity or transitive in Wiktionary, the free dictionary. Transitivity or transitive may refer to: Transitivity (grammar), a property regarding
Transitivity
Mathematical set with an ordering
Formally, a partial order is a homogeneous binary relation that is reflexive, antisymmetric, and transitive. A partially ordered set (poset for short) is
Partially_ordered_set
Reversal of the order of elements of a binary relation
of relations by inclusion. If a relation is reflexive, irreflexive, symmetric, antisymmetric, asymmetric, transitive, connected, trichotomous, a partial
Converse_relation
CA-groups are also called commutative-transitive groups (or CT-groups for short) because commutativity is a transitive relation amongst the non-identity elements
CA-group
Copy of a directed graph with redundant edges removed
reachability relation as D. Equivalently, D and its transitive reduction should have the same transitive closure as each other, and the transitive reduction
Transitive_reduction
also co-transitive if it is symmetric, left or right Euclidean, transitive, or quasitransitive. If incomparability w.r.t. R is a transitive relation, then
Pseudo-order
Mathematical result on order relations
{\displaystyle xRy.} A relation is reflexive if x R x {\displaystyle xRx} holds for every element x ∈ X ; {\displaystyle x\in X;} it is transitive if x R y and
Szpilrajn_extension_theorem
Logical paradox from vague predicates
more red than Y. The relation ≥ is the disjoint union of the symmetric relation ≈ and the transitive relation >. Using the transitivity of >, the knowledge
Sorites_paradox
Reflexive and transitive binary relation
in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. The name preorder is meant to suggest that preorders
Preorder
Generalization of equivalence classes to scheme theory
R)\to X(T)\times X(T)} is an equivalence relation; that is, a reflexive, symmetric and transitive relation. The basic case in practice is when C is the
Quotient by an equivalence relation
Quotient_by_an_equivalence_relation
Connected series of neighbouring populations
the issue is that interfertility (ability to interbreed) is not a transitive relation; if A breeds with B, and B breeds with C, it does not mean that A
Ring_species
Physical law for definition of temperature
consequence of equivalence is that thermal equilibrium is described as a transitive relation: If A is in thermal equilibrium with B and if B is in thermal equilibrium
Zeroth_law_of_thermodynamics
Randomized transitivity in paired comparisons
comparisons, specifically in scenarios where transitivity is expected, however, empirical observations of the binary relation is probabilistic. For example, players'
Stochastic_transitivity
quasitransitivity is a weakened version of transitivity that is used in social choice theory and microeconomics. Informally, a relation is quasitransitive if it is symmetric
Quasitransitive_relation
Directed graph with no directed cycles
ordered as u ≤ v ≤ w. The transitive closure of a DAG is the graph with the most edges that has the same reachability relation as the DAG. It has an edge
Directed_acyclic_graph
Set whose elements all belong to another set
Given any set A {\displaystyle A} , A ⊆ A {\displaystyle A\subseteq A} Transitivity: If A ⊆ B {\displaystyle A\subseteq B} and B ⊆ C {\displaystyle B\subseteq
Subset
Property of elements related by inequalities
redirect targets, a partial ordering in which incomparability is a transitive relation Trotter, William T. (1992), Combinatorics and Partially Ordered Sets:Dimension
Comparability
Logical quantifier
{\displaystyle a+2=5{\text{ and }}b+2=5.} Then since equality is a transitive relation, a + 2 = b + 2. {\displaystyle a+2=b+2.} Subtracting 2 from both
Uniqueness_quantification
Any interpersonal relationship between two or more conspecifics between/within groups
A social relation is the fundamental unit of analysis within the social sciences, and describes any voluntary or involuntary interpersonal relationship
Social_relation
Type of binary relation
right Euclidean relation is always quasitransitive, as is a left Euclidean relation. A connected right Euclidean relation is always transitive; and so is a
Euclidean_relation
Directed graph where each vertex pair has one arc
called transitive. In other words, in a transitive tournament, the vertices may be (strictly) totally ordered by the edge relation, and the edge relation is
Tournament_(graph_theory)
Observational basis of thermodynamics
empirical parameter in thermodynamic systems and establishes the transitive relation between the temperatures of multiple bodies in thermal equilibrium
Laws_of_thermodynamics
(3,3),(4,4)\}.} Symmetric closure Transitive closure – Smallest transitive relation containing a given binary relation Franz Baader and Tobias Nipkow, Term
Reflexive_closure
Index of articles associated with the same name
types of binary relation. One specific variation of weak ordering, a total preorder (= a connected, reflexive and transitive relation), is also sometimes
Preference_relation
Directed graph representing dependencies
dependency graph. Given a set of objects S {\displaystyle S} and a transitive relation R ⊆ S × S {\displaystyle R\subseteq S\times S} with ( a , b ) ∈ R
Dependency_graph
Property regarding whether a lexical item denotes a transitive object
Transitivity is a linguistics property that relates to whether a verb, participle, or gerund denotes a transitive object. It is closely related to valency
Transitivity_(grammar)
membership relation ∈, is an intuitive example of a class model that is standard transitive. To better illustrate the concepts of "standard" and "transitive",
Standard_model_(set_theory)
Result in mathematics and set theory
every such R there exists a unique transitive class (possibly proper) whose structure under the membership relation is isomorphic to (X, R), and the isomorphism
Mostowski_collapse_lemma
Type of binary relation
x is called a well-founded set if the set membership relation is well-founded on the transitive closure of x. The axiom of regularity, which is one of
Well-founded_relation
Study of parts and the wholes they form
This thesis is controversial, since parthood may not seem to be a transitive relation (as claimed by GEM) in some cases, such as the parthood between organisms
Mereology
Mathematical ordering of a partial order
of their product order. A partial order is a reflexive, transitive and antisymmetric relation. Given any partial orders ≤ {\displaystyle \,\leq \,} and
Linear_extension
Syllogism with conditional premise(s)
R} (from (3) and (4) by modus ponens) Plausible reasoning Transitive relation Type of syllogism (disjunctive, hypothetical, legal, poly-, prosleptic
Hypothetical_syllogism
Order whose elements are all comparable
corresponding total preorder on that subset. A binary relation that is antisymmetric, transitive, and reflexive (but not necessarily total) is a partial
Total_order
Semantic relations involving the type-of property
then X is a hyponym of Y and Y is a hypernym of X. Hyponymy is a transitive relation: if X is a hyponym of Y, and Y is a hyponym of Z, then X is a hyponym
Hypernymy_and_hyponymy
mathematical logic, the ancestral relation (often shortened to ancestral) of a binary relation R is its transitive closure, however defined in a different
Ancestral_relation
Integer that divides another integer
then a ∣ c ; {\displaystyle a\mid c;} that is, divisibility is a transitive relation. If a ∣ b {\displaystyle a\mid b} and b ∣ a , {\displaystyle b\mid
Divisor
Pattern relating to the subject and object of verbs
intransitive verb behaves like the object of a transitive verb, and differently from the agent of a transitive verb. In ergative–absolutive languages with
Ergative–absolutive_alignment
Concept in metaphysics and philosophy
counterpart relation (C-relation) differs from the notion of identity. Identity is a reflexive, symmetric, and transitive relation. The counterpart relation is
Counterpart_theory
Ways how entities stand to each other
and strict partial order. An equivalence relation is a relation that is reflexive, symmetric, and transitive, like equality expressed through the symbol
Relation_(philosophy)
State of no net thermal energy flow between two connected systems
the "zeroth law of thermodynamics", that thermal equilibrium is a transitive relation. They comment that the equivalence classes of systems so established
Thermal_equilibrium
Theorem in economics
A\succ B} . Not every preference-relation has a utility-function representation. For example, if the relation is not transitive (the agent prefers A to B, B
Utility representation theorem
Utility_representation_theorem
Any binary relation equal to its composition with itself
R = S. Equivalently, relation R is idempotent if and only if the following two properties are true: R is a transitive relation, meaning that R ∘ R ⊆ R
Idempotent_relation
Relation used in geometry
is a transitive relation. However, in case l = n, the superimposed lines are not considered parallel in Euclidean geometry. The binary relation between
Parallel_(geometry)
Concept in economics
preference relation ⪰ {\displaystyle \succeq } is complete if all pairs a , b {\displaystyle a,b\;} can be ranked. The relation is a transitive relation if whenever
Indifference_curve
Mathematical relation inside orderings
which the covering relation is empty is called "dense." If a partially ordered set is finite, its covering relation is the transitive reduction of the partial
Covering_relation
Graph linking pairs of comparable elements in a partial order
orientation of the graph) such that the adjacency relation of the resulting directed graph is transitive: whenever there exist directed edges (x,y) and (y
Comparability_graph
Type of binary relation
In mathematics, a binary relation R {\displaystyle R} on a set X {\displaystyle X} is antisymmetric if there is no pair of distinct elements of X {\displaystyle
Antisymmetric_relation
Subgroup invariant under conjugation
group need not be normal in the group. That is, normality is not a transitive relation. The smallest group exhibiting this phenomenon is the dihedral group
Normal_subgroup
Self-replicating objects or patterns
Phrase separating reality from fiction or social media Transitive relation – Type of binary relation Tony D. Sampson – British critical theorist (born 1964)
Viral_phenomenon
Maximal biconnected subgraph
if f is related in the same way to e. Less obviously, this is a transitive relation: if there exists a simple cycle containing edges e and f, and another
Biconnected_component
Overview of and topical guide to discrete mathematics
Antisymmetric relation – Type of binary relation Transitivity (mathematics) – Type of binary relation Transitive closure – Smallest transitive relation containing
Outline of discrete mathematics
Outline_of_discrete_mathematics
Linguistic theory giving noun phrases semantic roles
sometimes Force rather than Agent). In syntax, the agent is the argument of a transitive verb that corresponds to the subject in English. Experiencer The entity
Thematic_relation
Partition of vertices of a directed graph
{\displaystyle \asymp } is a transitive relation (because it is a transitive closure). As with any equivalence relation, it can be used to partition the
Weak_component
Transformation of one computational problem to another
reduction. Reducibility is a preordering, that is, a reflexive and transitive relation, on P(N)×P(N), where P(N) is the power set of the natural numbers
Reduction_(complexity)
utility function. In particular, it does not have to correspond to a transitive relation. An equilibrium in a generalized abstract economy is a vector of
Abstract_economy
Branch of mathematics
preorder is a relation that is reflexive and transitive, but not necessarily antisymmetric. Each preorder induces an equivalence relation between elements
Order_theory
Human contact that exists because of a mutual friend
connection. But the fact that friendship is not automatically a transitive relation produces some social dynamics. In some social sciences, the phrase
Friend_of_a_friend
Kind of transfinite induction
{\displaystyle \in } -transitive means ∀ ( x ∈ Σ ) . x ⊆ Σ {\displaystyle \forall (x\in \Sigma ).x\subseteq \Sigma } There are many transitive sets, in particular
Epsilon-induction
converse relation, R T . {\displaystyle R^{\operatorname {T} }.} Transitive closure – Smallest transitive relation containing a given binary relation Reflexive
Symmetric_closure
Theories in cognitive psychology
must be able to represent two entities and one relation between them. To understand a transitive relation one must be able to represent at least three entities
Neo-Piagetian theories of cognitive development
Neo-Piagetian_theories_of_cognitive_development
Level of database normalization
states that a relation R is in 3NF if and only if it is in second normal form (2NF) and every non-prime attribute of R is non-transitively dependent on
Third_normal_form
Zero-sum game where competitions between strategies contain a cycle
beats A, then the binary relation "to beat" is intransitive, since transitivity would require that A beat C. The terms "transitive game" or "intransitive
Intransitive_game
Describes approximate behavior of a function
g = o ( F + G ) {\displaystyle f+g=o(F+G)} It also satisfies a transitivity relation: if f = o ( g ) {\displaystyle f=o(g)} and g = o ( h ) {\displaystyle
Big_O_notation
Glossary of terms used in branch of mathematics
R S T U V W X Y Z Acyclic. A binary relation is acyclic if it contains no "cycles": equivalently, its transitive closure is antisymmetric. Adjoint. See
Glossary_of_order_theory
Sequence of propositions which constitute a sequence of overlapping syllogisms
- the rhetorical grounds of polysyllogism. Philosophical realism Transitive relation Type of syllogism (disjunctive, hypothetical, legal, poly-, prosleptic
Polysyllogism
Canadian-born American philosopher
predicate Q {\displaystyle Q} and if R {\displaystyle R} is an entire transitive relation, then by a formal analysis as above, predicate logic negates the
Stephen_Yablo
Property of a relation on a set
a transitive asymmetrical relation, we can express connection by the condition that any two terms of our series are to have the generating relation. — Bertrand
Connected_relation
Basic notion of sameness in mathematics
not be an equivalence relation, due to its not being transitive. This is the case even when it is modeled as a fuzzy relation. In computer science, equality
Equality_(mathematics)
Overview of and topical guide to logic
relation Serial relation Surjective function Symmetric relation Ternary relation Transitive relation Trichotomy (mathematics) Well-founded relation Mathematical
Outline_of_logic
ordinals transitive 1. A transitive relation 2. The transitive closure of a set is the smallest transitive set containing it. 3. A transitive set or
Glossary_of_set_theory
Equivalence relation in algebra
In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector
Congruence_relation
Mathematical relation making a non-equal comparison
(non-strict) partial order is a binary relation ≤ over a set P which is reflexive, antisymmetric, and transitive. That is, for all a, b, and c in P, it
Inequality_(mathematics)
Law (all real numbers are positive, negative, or 0)
x<y, x=y, y<x. A relation is trichotomous if, and only if, it is asymmetric and connected. If a trichotomous relation is also transitive, then it is a strict
Law_of_trichotomy
Any one of the distinct objects that make up a set in set theory
membership only, and "includes" for the subset relation only. For the relation ∈ , the converse relation ∈T may be written A ∋ x {\displaystyle A\ni x}
Element_of_a_set
Concept in game design
In case of transitivity given A beats B and B beats C, A beats C. This means that A is the best element of those three. A transitive relation is especially
Game_balance
Given a binary relation R, its rewrite closure is the smallest rewrite relation containing R. A transitive and reflexive rewrite relation that contains
Rewrite_order
Formal system for transcribing expressions into equivalent terms
\rightarrow } , i.e. the transitive closure of ( → ) ∪ ( = ) {\displaystyle (\rightarrow )\cup (=)} , where = is the identity relation. Equivalently, → ∗ {\displaystyle
Abstract_rewriting_system
Vertices connected in pairs by edges
other graphs with large automorphism groups: vertex-transitive, arc-transitive, and distance-transitive graphs; strongly regular graphs and their generalizations
Graph_(discrete_mathematics)
is a symmetric and transitive relation. Its domain is the set of elements a of M n such that φ(a, a); it is an equivalence relation on its domain. An imaginary
Imaginary_element
Number of arguments required by a function
the number of arguments or operands taken by a function, operation or relation. In mathematics, arity may also be called rank, but this word can have
Arity
Variant of heap data structure
children (11 > 5; if 15 > 11, and 11 > 5, then 15 > 5, because of the transitive relation). The procedure for deleting the root from the heap (effectively
Binary_heap
Property that assigns truth values to k-tuples of individuals
relation is called the arity, adicity or degree of the relation. A relation with n "places" is variously called an n-ary relation, an n-adic relation
Finitary_relation
lending them emphasis. ancestral In logic and mathematics, the transitive closure of a relation, capturing the idea of indirect relationships across generations
Glossary_of_logic
British Mathematician
Project Robinson, Derek J. S. (1964). "Groups in which normality is a transitive relation". Mathematical Proceedings of the Cambridge Philosophical Society
Derek_J._S._Robinson
TRANSITIVE RELATION
TRANSITIVE RELATION
Boy/Male
Hindu, Indian
Age of Transition; New Age
Boy/Male
Tamil
Jasevaraj | ஜஸேவாராஜ
Heart of relation
Jasevaraj | ஜஸேவாராஜ
Girl/Female
Tamil
Bhandhavi | பாநà¯à®¤à®µà¯€
Who loves friends & family members, Friendship, Relationship
Bhandhavi | பாநà¯à®¤à®µà¯€
Surname or Lastname
English
English : variant spelling of Brook, which preserves a trace of the Old English dative singular case, originally used after a preposition (e.g. ‘at the brook’).In 1650, Robert and Mary Mainwaring Brooke brought ten children and a number of servants with them from England to MD, where Robert became governor. Although the fourteen known contemporary Brooke immigrants in VA included Robert’s brothers Richard and Humphrey, the relationships of the others are unknown. Brooke family memorials remain in the Anglican church at Whitchurch, Hampshire, England.
Boy/Male
Tamil
Transition
Boy/Male
Muslim
Of Husain, Nisba relation
Boy/Male
Hindu
Vimoktre detacher of all relationship
Surname or Lastname
English
English : variant of Feather.North German, Dutch, and Danish : from the Frisian personal name Vetter, meaning ‘relative’. Relationship terms were commonly used as personal names in Friesland.
Girl/Female
Indian
Who loves friends & family members, Friendship, Relationship
Girl/Female
Muslim
Relation, Way, Sake
Boy/Male
Indian
Of Husain, Nisba relation
Surname or Lastname
English
English : variant spelling of Messenger.German and Jewish (Ashkenazic) : occupational name for a brazier, from an agent derivative of Middle High German messinc ‘brass’, German Messing, from Greek mossynoikos (khalkos) ‘Mossynoecan bronze’, named after the people of northeastern Asia Minor who first produced the alloy.German : habitational name from Mössingen in Baden-Württemberg (Messingen in the local dialect), which is recorded as Masginga in 789, probably from the personal name Masco + ingen, suffix of relationship.
Surname or Lastname
North German
North German : probably from a derivative of Pille 1.Dutch : relationship name from Middle Dutch pil(le) ‘godchild’.English : possibly a variant of Pilling.
Girl/Female
Indian
Who loves friends & family members, Friendship, Relationship
Surname or Lastname
French
French : perhaps a variant of Parrain, relationship name from parrain ‘godfather’.English : possibly a variant of Parent.
Boy/Male
Tamil
Sarvabandha | ஸரà¯à®µà®ªà®‚தா
Vimoktre detacher of all relationship
Sarvabandha | ஸரà¯à®µà®ªà®‚தா
Boy/Male
Tamil
Relation
Surname or Lastname
English
English : from the Middle English personal name Hick + Middle English maugh, mough ‘relative’ (from Old Norse mágr or Old English magu). The exact nature of the relationship is not clear; the Middle English word meant ‘relative by marriage’, but was also used occasionally of a female blood relation.
Girl/Female
Tamil
Who loves friends & family members, Friendship, Relationship
Boy/Male
Hindu
Transition
TRANSITIVE RELATION
TRANSITIVE RELATION
Girl/Female
Arabic, Muslim, Sindhi
Mystic; Following
Girl/Female
British, English
The Lord Remembers
Male
Spanish
Spanish form of Latin Gervasius, GERVASI means "spear servant."
Girl/Female
American, Australian, British, English, French
Desired; Longed for; Variant of French Desiree
Girl/Female
Indian, Punjabi, Sikh
Meditative Mind
Girl/Female
Tamil
Sayantini | ஸயாநà¯à®¤à¯€à®¨à¯€Â
Evening
Boy/Male
Hindu
Battle maiden
Biblical
slender; sharp
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Marathi, Telugu
Victorious
Boy/Male
Tamil
A crane
TRANSITIVE RELATION
TRANSITIVE RELATION
TRANSITIVE RELATION
TRANSITIVE RELATION
TRANSITIVE RELATION
a.
Of or pertaining to transition; involving or denoting transition; as, transitional changes; transitional stage.
n.
An intransitive verb.
a.
Intransitive; as, a neuter verb.
adv.
Without an object following; in the manner of an intransitive verb.
n.
Transition.
n.
A passing from one subject to another.
a.
tropical; figurative; as, a translative sense.
a.
Effected by transference of signification.
a.
Passing over to an object; expressing an action which is not limited to the agent or subject, but which requires an object to complete the sense; as, a transitive verb, for example, he holds the book.
n.
A transition from one subject to another.
a.
Applied to verbs which assert that the subject acts upon or affects something else; transitive.
n.
A direct or indirect passing from one key to another; a modulation.
n.
Change from one form to another.
a.
Transmitted or transmissible from father to son, or from age, by oral communication; traditional.
n.
Passage from one place or state to another; charge; as, the transition of the weather from hot to cold.
a.
Not passing farther; kept; detained.
v. t.
To require to be in a particular case; as, a transitive verb governs a noun in the objective case; or to require (a particular case); as, a transitive verb governs the objective case.
a.
Not transitive; not passing over to an object; expressing an action or state that is limited to the agent or subject, or, in other words, an action which does not require an object to complete the sense; as, an intransitive verb, e. g., the bird flies; the dog runs.
a.
Having the power of making a transit, or passage.