The notation for an integer must, like everything else in the hierarchy, be an instance of the class Functional . If a Functional is not a notation for an integer this member returns -1 . Class Functional represents arbitrary structures.
Integers are the finite ordinals.
This will return a null pointer if the Functional does not represent an ordinal. If it does represent an ordinal it returns a pointer to itself that can then access member functions specific to ordinals. Ordinals must be recursively well ordered. The orderings defined in a particular expansion will always have a fixed recursive ordinal as a limit. This limit does not hold for sequences of expansions.