A New Light on Minkowski'S? (X) Function

The well-known Minkowski's ?(x) function is presented as the asymptotic distribution function of an enumeration of the rationals in (0,1] based on their continued fraction representation. Besides, the singularity of ?(x) is clearly proved in two ways: by exhibiting a set of measure one in which ?'(x) = 0; and again by actually finding a set of measure one which is mapped onto a set of measure zero and viceversa. These sets are described by means of metrical properties of different systems for real number representation