  More generally, if given a series of facts of the form \(aRb\), \(bRc\), \(cRd\), and so on, Frege showed how to define the relation \(R^*\), i.e., x is an ancestor of y in the R-series, which Frege referred to as: \(y\) follows \(x\) in the \(R\)-series. To exploit this definition in the case of natural numbers, Frege had to define both the relation \(x\) precedes \(y\) and the ancestral of this relation, namely, \(x\) is an ancestor of \(y\) in the predecessor-series. He first defined the relational concept \(x\) precedes \(y\) as follows (1884, §76):