"Three major sorts of infinities occur in quantum electrodynamics. The first, associated with the electron's infinite energy of interaction with its own electromagnetic field, is removed by redefining its mass to be the physical value, order by order, in perturbation theory. The second can be removed by demanding that a free electron produced at a given point in space be detectable with unit probability at some distant point at a later time. The third, related to the polarization of the vacuum pairs by a test charge, can be removed by redefining the electron's charge as its value as seen by a distant observer."