You might want to take a look at some of Ehrlich's work.
Here is a view of an anthology:
http://projecteuclid.org/DPubS/Repos...rml/1081878082
It is has an article by Conway on the surreal numbers, and Erhlich's work on infinity is based on Conway's earlier studies. Some essays into into the matter of infinite real numbers, infinitesimals, and their reciprocals. As an alternative to the surreal numbers (of which the reals are a part) there is a paper by H. Jerome Keisler on the hyperreals which also have infinite and infinitesimal numbers.
For some sense of what the course I took from Ehrlich was like see this:
http://www.pitt.edu/~pittcntr/Being_...pr_11_2006.htm