Definition:Transitive Closure (Relation Theory)/Union of Compositions
Jump to navigation
Jump to search
Definition
Let $\RR$ be a relation on a set $S$.
Let:
- $\RR^n := \begin{cases}
\RR & : n = 1 \\ \RR^{n-1} \circ \RR & : n > 1 \end{cases}$
where $\circ$ denotes composition of relations.
Finally, let:
- $\ds \RR^+ = \bigcup_{i \mathop = 1}^\infty \RR^i$
Then $\RR^+$ is called the transitive closure of $\RR$.
Also see
- Results about transitive closures can be found here.
There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page. |