reflexive relation
A relation👁 Mathworld
👁 Planetmath
👁 Planetmath
on a set
is reflexive👁 Mathworld
👁 Planetmath
👁 Planetmath
👁 Planetmath
👁 Planetmath
if and only if for all .
For example, let . Then is a reflexive relation on , because it contains for all . However, is not reflexive because it does not contain .
On a finite set👁 Mathworld
👁 Planetmath
with elements there are relations,
of which are reflexive.
| Title | reflexive relation |
| Canonical name | ReflexiveRelation |
| Date of creation | 2013-03-22 12:15:36 |
| Last modified on | 2013-03-22 12:15:36 |
| Owner | yark (2760) |
| Last modified by | yark (2760) |
| Numerical id | 17 |
| Author | yark (2760) |
| Entry type | Definition |
| Classification | msc 03E20 |
| Related topic | Symmetric👁 Planetmath 👁 Planetmath 👁 Planetmath |
| Related topic | Transitive3 |
| Related topic | Antisymmetric |
| Related topic | Irreflexive👁 Mathworld 👁 Planetmath |
| Defines | reflexivity |
| Defines | reflexive |