  The superconducting pairing instability---as determined by a divergence of
the two-particle susceptibility---is obtained in the mean field (BCS)
approximation in the thermodynamic limit. The usual practice is to examine this
property for a finite lattice. We illustrate that, while the conclusions remain
unchanged, the technical features are very different in the thermodynamic limit
and conform more closely with the usual treatment of phase transitions
encountered in, for example, the mean-field paramagnetic-ferromagnetic
transition. Furthermore, by going to the extreme dilute limit, one can
distinguish three dimensions from one and two dimensions, in which a pairing
instability occurs even for two particles.
