Reflexive transitive closure
= Reflexive transitive closure
{title2=$R^*=\bigcup_{n\geq0}R^n$}
The least <reflexive relation> and <transitive relation> containing $R$. Here $R^0$ is the identity relation. Membership means that a finite sequence of zero or more $R$-steps connects the ordered pair. Adding paths can create reverse connections that were absent in $R$, so initial <antisymmetry> need not be preserved.