  The universal behavior of magnetic impurities in a metal is proved with the
help of skeleton diagrams. The energy scales are derived from the structure of
the skeleton diagrams. A minimal set of skeleton diagrams is sorted out that
scales exactly. For example, the non-crossing approximation for the Anderson
impurity model can describe the crossover phenomenon. The universal
Wilson-number is calculated within the non-crossing approximation. The method
allows for an assessment of various approximations for impurity Hamiltonians.
