The spectrum of cosmic ray electrons is discussed in terms of the contributions from discrete sources distributed over the Galaxy. The analysis shows that one needs sources situated within a few hundred parsecs of the solar system, in order that the radiative losses of energy do not induce a premature cutoff in the energy spectrum. If the mean spatial density of the sources is roughly uniform over the galactic plane, then there should be at least 3 x 10/sup 4/ active sources accelerating cosmic rays in the Galaxy. Therefore it is very unlikely that supernovae are the only sources of cosmic ray electrons in the energy range 1--1000 GeV.