Category:Reflexive Transitive Closures
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This category contains results about Reflexive Transitive Closures.
Definitions specific to this category can be found in Definitions/Reflexive Transitive Closures.
Let $\RR$ be a relation on a set $S$.
Smallest Reflexive Transitive Superset
The reflexive transitive closure of $\RR$ is denoted $\RR^*$, and is defined as the smallest reflexive and transitive relation on $S$ which contains $\RR$.
Reflexive Closure of Transitive Closure
The reflexive transitive closure of $\RR$ is denoted $\RR^*$, and is defined as the reflexive closure of the transitive closure of $\RR$:
- $\RR^* = \paren {\RR^+}^=$
Transitive Closure of Reflexive Closure
The reflexive transitive closure of $\RR$ is denoted $\RR^*$, and is defined as the transitive closure of the reflexive closure of $\RR$:
- $\RR^* = \paren {\RR^=}^+$
Subcategories
This category has only the following subcategory.