There is at least one proposal as to how to extend the rational numbers
(already in common lisp), to include denominators of 0; adding objects
0/0, 1/0, and -1/0. They correspond in most respects to the floating-point
objects in the IEEE standard of NotANumber, Infinity, and negative Infinity.
As a consequence, one can look in the literature for reasonable definitions
for (say) expt, log, cosine, addition, multiplication, ... of these objects.
Unfortunately this does not always lead to consistency (in IEEE .. as
well).
Just patching one spot to leave 1/0 alone may have some momentary appeal,
but if you think about it a little, it requires a lot of work and
considerable thought
to make such a feature work.
RJF
ps
www.cs.berkeley.edu/~*fateman*/papers/extrat.ps