 In spite of that, Peano elaborated a formal solution. He tried to get rid of vagueness and reference to \(E\), the set of finitely definable reals in the unit interval, by fixing an explicit “Gödel-numbering”: given a natural number \(n\), write \(n\) in base \(B\), for sufficiently large \(B\) (so as to include the number of alphabet letters plus punctuation marks). Then each number is assigned a finite string of symbols in the natural language, and in certain cases the string will define a number, \(\Val(n) =\) “the decimal number which is determined by the expression encoded by \(n\) and interpreted according to the rules of the natural language”. Now, in order to get the paradox, one has to prove that there exists a unique number \(N\) in (0, 1), satisfying the condition given by Richard (see  2.5  above), but this condition, and hence \(N\) itself, depends on \(\Val\), which is possibly obscure and cannot be defined exactly according to the rules of mathematics (p. 352, p. 358). The conclusion is that no such a real can exist and Richard’s definition is defective in the same way that “the greatest prime number” is.