is not equal to
. Various subtleties arise in identifying this form of our assumption with the form that asserts the existence of infinite collections; but we will leave these out of account until, in a later chapter, we come to consider the axiom of infinity on its own account. For the present we shall merely assume that, if
is an inductive number,
is not equal to
. This is involved in Peano's assumption that no two inductive numbers have the same successor; for, if
