TFF:"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."
Think about it, it's really simple. You don't need too much topology.Topologically,the numbers are simply points on a line (the real line), and as such you don't need to define addition and multiplication of points (you don't need algebraic structures like groups, semigroups or fields/korps). You only need some ordering relation between points. So nothing stpos you to include -Infty and Infty into the real line as the inf and supp of the set of points. In this way you have just compactified the real line.
TFF:"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."
That was (part) of my point. The other part of the point was that as you said (better that I did), you can define a consistent algebraic structure over the real numbers that includes Infty - the semiring - in spite of the traditional wisdom that claims that in fact Infty is not a number. It is for a semiring, it isn't for a unitary ring or a field, depends on the aplication, context, etc.
TFF:"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."
Fine by me, but hopefully the above cleared a bit what I wanted to say from the topological viewpoint.
