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...

is a relation that is reflexive, antisymmetric, and transitive, an equivalence relation is a relation that is reflexive, symmetric, and transitive, a function...

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...

mathematics, an equivalence relation is a binary relation that is reflexive, symmetric, and transitive. The equipollence relation between line segments in...

Antitransitivity is a stronger property which describes a relation where, for any three values, the transitivity condition never holds. Some authors use the term...

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...

reflexive. An asymmetric relation is necessarily irreflexive. A transitive and irreflexive relation is necessarily asymmetric. left quasi-reflexive if whenever...

Symmetry, along with reflexivity and transitivity, are the three defining properties of an equivalence relation. "is equal to" (equality) (whereas "is...

{\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...

{\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...

partially ordered sets in which incomparability is a transitive relation), as total preorders (transitive binary relations in which at least one of the two...

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...

Look up transitivity or transitive in Wiktionary, the free dictionary. Transitivity or transitive may refer to: Transitivity (grammar), a property regarding...

transitive dependency is an indirect dependency relationship between software components. This kind of dependency is held by virtue of a transitive relation...

theory, a branch of mathematics, a set A {\displaystyle A} is called transitive if either of the following equivalent conditions holds: whenever x ∈ A...

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...

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...

is symmetric and transitive. If the relation is also reflexive, then the relation is an equivalence relation. Formally, a relation R {\displaystyle R}...

types of binary relation. One specific variation of weak ordering, a total preorder (= a connected, reflexive and transitive relation), is also sometimes...

Formally, a partial order is a homogeneous binary relation that is reflexive, antisymmetric, and transitive. A partially ordered set (poset for short) is...

Phrase separating reality from fiction or social media Transitive relation – Type of binary relation Tony D. Sampson – British critical theorist (born 1964)...

CA-groups are also called commutative-transitive groups (or CT-groups for short) because commutativity is a transitive relation amongst the non-identity elements...

reachability relation as D. Equivalently, D and its transitive reduction should have the same transitive closure as each other, and the transitive reduction...

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...

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...

thermal equilibrium between systems is a transitive relation. Two systems are said to be in the relation of thermal equilibrium if they are linked by...

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...

of relations by inclusion. If a relation is reflexive, irreflexive, symmetric, antisymmetric, asymmetric, transitive, connected, trichotomous, a partial...

consequence of equivalence is that thermal equilibrium is described as a transitive relation:: 56  If A is in thermal equilibrium with B and if B is in thermal...

more red than Y. The relation ≥ is the disjoint union of the symmetric relation ≈ and the transitive relation >. Using the transitivity of >, the knowledge...