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

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...

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

alternating group is (n − 2)-transitive but not (n − 1)-transitive. The action of the general linear group of a vector space V on the set V ∖ {0} of non-zero vectors...

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 sets,...

In the mathematical field of graph theory, a transitive reduction of a directed graph D is another directed graph with the same vertices and as few edges...

which is a subset of the power set of L α {\displaystyle L_{\alpha }} . Consequently, this is a tower of nested transitive sets. But L {\displaystyle L} itself...

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 class...

defined as transitive sets of transitive sets. The induction situation in the first infinite ordinal ω {\displaystyle \omega } , the set of natural numbers...

In mathematical set theory, a transitive model is a model of set theory that is standard and transitive. Standard means that the membership relation is...

a set x: x is a (von Neumann) ordinal, x is a transitive set, and set membership is trichotomous on x, x is a transitive set totally ordered by set inclusion...

is the largest superset of X that has the same rank as X. The transitive closure of a set. The algebraic closure of a field. The integral closure of an...

V_{\alpha }} for some ordinal α {\displaystyle \alpha } . Any stage is a transitive set, hence every y ∈ x {\displaystyle y\in x} is already y ∈ V α {\displaystyle...

antisymmetric, and transitive. A partially ordered set (poset for short) is an ordered pair P = ( X , ≤ ) {\displaystyle P=(X,\leq )} consisting of a set X {\displaystyle...

the extension property. In other words, for all U ⊂ Vκ there exists a transitive set X with κ ∈ X, and a subset S ⊂ X, such that (Vκ, ∈, U) is an elementary...

where transitive ( x ) {\displaystyle {\text{transitive}}(x)} asserts that x {\displaystyle x} is transitive. Starting with the observation that set parameters...

subtle cardinal ≤ κ {\displaystyle \leq \kappa } if and only if every transitive set S {\displaystyle S} of cardinality κ {\displaystyle \kappa } contains...

a set of dice is intransitive if the binary relation – X rolls a higher number than Y more than half the time – on its elements is not transitive. More...

In set theory, a discipline within mathematics, an admissible set is a transitive set A {\displaystyle A\,} such that ⟨ A , ∈ ⟩ {\displaystyle \langle...

coordinates, draw a point at (x,y) whenever (x,y) ∈ R. A transitive relation R on a finite set X may be also represented as Hasse diagram: Each member...

is a cardinal κ in a model of Zermelo–Fraenkel set theory with the property that for every transitive set M that includes κ and α < κ, there is a nontrivial...

(transitive). Each equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are...

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

nor 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...

In set theory, a supertransitive class is a transitive class which includes as a subset the power set of each of its elements. Formally, let A be a transitive...

relation. In this way, every finite partially ordered set can be represented as a DAG. The transitive reduction of a DAG is the graph with the fewest edges...

A group G {\displaystyle G} acts 2-transitively on a set S {\displaystyle S} if it acts transitively on the set of distinct ordered pairs { ( x , y ) ∈...

the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories...

In set theory, the complement of a set A, often denoted by A ∁ {\displaystyle A^{\complement }} (or A′), is the set of elements not in A. When all elements...

O r d {\displaystyle Ord} of all ordinals is a set. Then O r d {\displaystyle Ord} is a transitive set well-ordered by ∈ {\displaystyle \in } . So, by...