# Transitivity (mathematics)

﻿
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 ergodic theory.

* A binary relation is transitive if whenever A is related to B and B is related to C, then A is related to C, for all A, B, and C in the domain of the relation. See transitive relation.
* A transitive set is a set A such that whenever "x" ∈ "A", and "y" ∈ "x", then "y" ∈ "A". The smallest transitive set containing a set A is called the transitive closure of A.

ee also

* intransitivity

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• 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

• transitivity — noun 1. (logic and mathematics) a relation between three elements such that if it holds between the first and second and it also holds between the second and third it must necessarily hold between the first and third • Topics: ↑logic,… …   Useful english dictionary

• Outline of discrete mathematics — The following outline is presented as an overview of and topical guide to discrete mathematics: Discrete mathematics – study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have… …   Wikipedia

• List of basic discrete mathematics topics — Discrete mathematics, also called finite mathematics, is the study of mathematical structures that are fundamentally , in the sense of not supporting or requiring the notion of continuity. Most, if not all, of the objects studied in finite… …   Wikipedia

• List of mathematics articles (T) — NOTOC T T duality T group T group (mathematics) T integration T norm T norm fuzzy logics T schema T square (fractal) T symmetry T table T theory T.C. Mits T1 space Table of bases Table of Clebsch Gordan coefficients Table of divisors Table of Lie …   Wikipedia

• Inequality (mathematics) — Not to be confused with Inequation. Less than and Greater than redirect here. For the use of the < and > signs as punctuation, see Bracket. More than redirects here. For the UK insurance brand, see RSA Insurance Group. The feasible regions… …   Wikipedia

• Forcing (mathematics) — For the use of forcing in recursion theory, see Forcing (recursion theory). In the mathematical discipline of set theory, forcing is a technique invented by Paul Cohen for proving consistency and independence results. It was first used, in 1963,… …   Wikipedia

• Category (mathematics) — In mathematics, a category is an algebraic structure that comprises objects that are linked by arrows . A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object. A …   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

• Fuzzy mathematics — Fuzzy math redirects here. For the controversies about mathematics education curricula that are sometimes disparaged as fuzzy math, see Math wars. Fuzzy mathematics form a branch of mathematics related to fuzzy logic. It started in 1965 after… …   Wikipedia