It has been observed that Frege’s formal system is an interpreted system: it assigns invariant meanings to its primitive functional constants and assumes that the quantifiers have a fixed and universal domain. This implies that its definitions and theorems are also supposed to have invariant meanings. These meanings depend, however, on how one conceives value-ranges. Frege never tells us explicitly how he conceives of them and whether there are objects that are not value-ranges. It follows that the invariant meanings that Frege seems to assign to his definitions and theorems are not, in fact, as precise as would be expected. The aim of this chapter is to illustrate this ambiguity by focusing on the system of definitions that leads to the definition of Anzahlen that Frege presents in the Grundgesetze.