The transitive closure R* of a relation R is defined by

        x R y => x R* y
        x R y  and  y R* z => x R* z

I.e. elements are related by R* if they are related by R directly or through some sequence of intermediate related elements.

E.g. in graph theory, if R is the relation on nodes "has an edge leading to" then the transitive closure of R is the relation "has a path of zero or more edges to". See also Reflexive transitive closure.