## You are here

Hometransitive relation

## Primary tabs

# transitive relation

A relation $\mathcal{R}$ on a set $A$ is *transitive* if and only if
$\forall x,y,z\in A$, $(x\mathcal{R}y\land y\mathcal{R}z)\rightarrow(x\mathcal{R}z)$.

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

Defines:

transitivity, transitive

Related:

Reflexive, Symmetric, Antisymmetric

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

03E20*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections