   Russell described the next advance as taking place in the work of Frege. According to the conception of number found in Frege’s Grundgesetze der Arithmetik, a number can be regarded as an equivalence class consisting of those classes whose members can be put in 1-1 correspondence with any other member of the class. According to Russell, this conception allowed the primitives of Peano’s analysis to be defined fully in terms of the notion of a class, along with other logical notions such as identity, quantification, negation and the conditional. Similarly, Frege’s work showed how the basic principles of Peano’s analysis could be derived from logical axioms alone. However, Frege’s analysis was not in all ways successful, as the notion of a class or the extension of a concept which Frege included as a logically primitive notion lead to certain contradictions. In this regard, Russell saw his own analysis of mathematics (largely developed independently from Frege) as an improvement, with its more austere analysis that eliminates even the notion of a class as a primitive idea (see the discussion of classes in Section 2.4 above), and thereby eliminates the contradictions (see, e.g., RMDP, 276–81; LA, 325–27).