transitive relation

A relationMathworldPlanetmath on a set A is transitiveMathworldPlanetmathPlanetmathPlanetmathPlanetmath if and only if x,y,zA, (xyyz)(xz).

For example, the “is a subset of” relation on any set of sets is transitive. The “less than” relation < on the set of real numbers is also transitive.

The “is not equal to” relation on the set of integers is not transitive, because 12 and 21 does not imply 11.

Title transitive relation
Canonical name TransitiveRelation
Date of creation 2013-03-22 12:15:52
Last modified on 2013-03-22 12:15:52
Owner yark (2760)
Last modified by yark (2760)
Numerical id 14
Author yark (2760)
Entry type Definition
Classification msc 03E20
Related topic ReflexiveMathworldPlanetmathPlanetmathPlanetmath
Related topic SymmetricPlanetmathPlanetmathPlanetmath
Related topic Antisymmetric
Defines transitivity
Defines transitive