Full Idea
Frege was operating with a successor relation, rather than a successor function.
Gist of Idea
For Frege, successor was a relation, not a function
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.2
Book Reference
Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.13
A Reaction
That is, succession is a given fact, not a construction. 4 may be the successor of 3 in natural numbers, but not in rational or real numbers, so we can't take the relation for granted.