  We review the concept of infinity as applied to regularization procedures in
Quantum Electrodynamics. A clear distinction that is lacking in current
literature is made between the physical contents of renormalization, and the
mathematical aspects of regularization. Robinson's non-standard analysis is
offered as a means to settle the ambiguities of the theory, in the spirit of
Paul Dirac's well known comments concerning the weak status of the mathematics
used in traditional regularization schemes. As a case study we consider the
Casimir effect
