Reflexive transitive closure ($R^{\ast }={\bigcup }_{n\ge 0}{R}^n$)

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.