I agree that it's largely a matter of efficacy. The only reason I'm tied up on the ring/field thing is that I know that there are certain mathematical benefits to such things.
I suppose I had thought that the issue was decided long ago. I was warned back in algebra II that using Inf as a number was an expediency that was "not technically correct." I've seen people do this in lectures and presentations before, but never in a journal article. OTOH, we often *think* this way.
Topology is something I've studied cursorily on my own. It's not something that's covered in engineering curricula. I don't recall using algebra with it, but I was reading mostly on a baby level. Regardless, I can see the advantage in regular calculus of treating Inf as a number, if no other reason than to simplify notation of more complicated problems.
I'll take your word for it till I have a chance to look into this in more detail. I'm a pretty slow guy - and I gotta work through it at my own pace.
