  At energies above a few TeV, no measurements of the cosmic-ray electron
spectrum exist yet. By considering the similarity of air showers induced by
electrons and gamma rays as seen by ground-based arrays, we use published
limits on isotropic gamma-ray fluxes to place first constraints on the >10 TeV
electron spectrum. We demonstrate that, due the proximity of known sources, the
flux of such electrons (and positrons) can be large. We show how these smoothly
connect to lower-energy positrons measured by PAMELA and relate to exciting new
indications from Fermi.
