 By the time of the Grundgesetze, Frege had settled on an explication of cardinal numbers in class-theoretic terms, which would preserve the structure of the foregoing considerations. The number of Fs (i.e., the cardinal number of the class of all Fs) was identified as the class of all classes that are equinumerous with (i.e., in 1–1 correspondence with) the class of all  Fs.[21]  Thus the class of all Fs is a member of its own cardinal number. So too is any class that is equinumerous with the class of all Fs. Thus the cardinal number of any one-membered class is the class of all one-membered classes; the cardinal number of any two-membered class is the class of all two-membered classes; … and so on. It is easy to see that, on Frege’s class-theoretic definition of cardinal number, any two equinumerous classes have the same cardinal number. And numbers are not sui generis, but are rather classes of a very special kind. See also the Encyclopedia article on  Frege’s Theorem and Foundations for Arithmetic.  