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...

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...

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

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...

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...

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

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

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

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...

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...

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...

other sets. A set may have a finite number of elements or be an infinite set. There is a unique set with no elements, called the empty set; a set with...