  Within the set of schemes defined by generalized, manifestly gauge invariant
exact renormalization groups for QED, it is argued that the beta-function in
the four dimensional massless theory cannot possess any nonperturbative power
corrections. Consequently, the perturbative expression for the beta-function
must be resummable. This argument cannot be extended to flows of the other
couplings or to the anomalous dimension of the fermions and so perturbation
theory does not define a unique trajectory in the critical surface of the
Gaussian fixed point. Thus, resummability of the beta-function is not
inconsistent with the expectation that a non-trivial fixed point does not
exist.
