> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/220-relation-theory/terms/acc-relations.md).

# Index of relations

* relations and arity
  * unary relation is a property
  * binary is the most common
  * ternary relation
  * n-ary relation
* relations (generity)
  * homogeneous
  * heterogeneous
* relations (axioms)
  * reflexivity
  * symmetry
  * transitivity
* relations (sorts)
  * reflexivity
    * reflexive relation
    * irreflexive relation
    * antireflexive relation
    * quasireflexive relation
    * (non variants)
  * symmetry
    * symmetric relation
    * asymmetric relation
    * antisymmetric relation
    * (non variants)
  * transitivity
    * transitive relation
    * antitransitive relation
    * (non variants)
  * equivalence relation
  * congruence relation
  * functional
  * uniqueness
    * left-unique
  * serial
    * right-serial
  * trichotomy

One-to-Many Relation A one-to-many relation is also referred to as: an injective relation a left-unique relation a single-rooted relation a one-many correspondence

<https://proofwiki.org/wiki/Definition:Many-to-One\\_Relation> <https://proofwiki.org/wiki/Definition:One-to-Many\\_Relation> <https://proofwiki.org/wiki/Definition:Injection>