It depends. Most people who write 1/infinity mean more precisely lim y--> infinity 1/y, so the answer is "yes" in most cases. However, I think saying "yes" for all cases would be over-restrictive, unless we add all sorts of conditions about the "rate" of approaching infinity, etc. Regardless of whether you think of infinity as some 'closed entity' (for lack of a better term) or not, (and some would argue that this is a bad interpretation, although I think it does have some merit), we can see that in this particular case 1/'infinity' and lim x--> infinity 1/x are equivalent, as both equal zero.
Yeah, that's sort of what I would have guessed.
In any case, can you elaborate on the "closed entity" or does it require a heavy background in mathematics that I don't have (yet)? It sounds like an interesting concept.
