 Frege actually proves the Principle of Mathematical Induction from a more general principle that governs any \(R\)-series whatsoever. We will call the latter the General Principle of Induction. It asserts that whenever a falls under \(F\), and \(F\) is hereditary on the \(R\)-series beginning with \(a\), then every member of that \(R\)-series falls under \(F\). We can formalize the General Principle of Induction with the help of a strict understanding of ‘hereditary on the \(R\)-series beginning with \(a\)’. Here is a definition: