transitivity set

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• Transitivity — The term transitivity may refer to:In grammar * Transitivity (grammatical category) * Transitive verb, when a verb takes an object * Intransitive verbIn logic and mathematics * Transitive relation, a binary relation * Transitive group action *… …   Wikipedia

• set theory — the branch of mathematics that deals with relations between sets. [1940 45] * * * Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its… …   Universalium

• Transitivity (mathematics) — In mathematics, the word transitive admits at least three distinct meanings:* A group G acts transitively on a set S if for any x , y ∈ S , there is some g ∈ G such that gx = y . See group action. A somewhat related meaning is explained at… …   Wikipedia

• Partially ordered set — The Hasse diagram of the set of all subsets of a three element set {x, y, z}, ordered by inclusion. In mathematics, especially order theory, a partially ordered set (or poset) formalizes and generalizes the intuitive concept of an ordering,… …   Wikipedia

• Implementation of mathematics in set theory — This article examines the implementation of mathematical concepts in set theory. The implementation of a number of basic mathematical concepts is carried out in parallel in ZFC (the dominant set theory) and in NFU, the version of Quine s New… …   Wikipedia

• Directed set — In mathematics, a directed set (or a directed preorder or a filtered set) is a nonempty set A together with a reflexive and transitive binary relation ≤ (that is, a preorder), with the additional property that every pair of elements has an upper… …   Wikipedia

• Transitive set — In set theory, a set (or class) A is transitive, if * whenever x ∈ A , and y ∈ x , then y ∈ A , or, equivalently, * whenever x ∈ A , and x is not an urelement, then x is a subset of A .The transitive closure of a set A is the smallest (with… …   Wikipedia

• Cyclic order — In mathematics, a cyclic order is a way to arrange a set of objects in a circle.[nb] Unlike most structures in order theory, a cyclic order cannot be modeled as a binary relation a < b . One does not say that east is more clockwise than west.… …   Wikipedia

• Arrow's impossibility theorem — In social choice theory, Arrow’s impossibility theorem, the General Possibility Theorem, or Arrow’s paradox, states that, when voters have three or more distinct alternatives (options), no voting system can convert the ranked preferences of… …   Wikipedia

• Strict weak ordering — The 13 possible strict weak orderings on a set of three elements {a, b, c}. The only partially ordered sets are coloured, while totally ordered ones are in black. Two orderings are shown as connected by an edge if they differ by a single… …   Wikipedia

• Hasse diagram — In the mathematical discipline known as order theory, a Hasse diagram (pronEng|ˈhɑːsə HAHS uh ), named after Helmut Hasse (1898 ndash;1979)) is a simple picture of a finite partially ordered set, forming a drawing of the transitive reduction of… …   Wikipedia