User blog comment:Mh314159/Natural number recursion - first 4 rule sets/@comment-35470197-20191019143654/@comment-39585023-20191020132647

Is it a map instead of a function because of the indexing? Is it because A(x) has a natural number domain and outputs another function instead of outputting a natural number? In either case, I think the rules are now free of ambiguity and can now be recursed all the way to the end result which is a single natural number via the successor function.