no need to worry over this slowness issue, i've the same situation so i understand entirely.
so the comment about not asking more questions of this nature (fingers crossed behind back) was in no way meant as a punishment, but i felt as if my questions were actually redundant and would make it appear i was to lazy to figure it out for myself. most likely my questions on the issue of infinity would be infinite ad nauseum if we let them. but i think you've hit upon an issue that probably steered me away from a life time of devotion to mathematics (ie. finding work in the field and feeding my self that way :). it was during my education with
respect to calculus that i hit this brick wall and back then i don't think i really knew what it was but now i think i have a better idea of what the problem was.
your essay on your website about your experience with your math professor and the question of the infinite horn is similar to the issue i faced back then. the situation i think points out the issue of mathematical sense and nonsense when
mathematics is applied to the physical world. i had similar issues in the study of physics, i nearly flunked out of the portion that was more classical (especially with respect to pulleys, levers, inclined planes and friction...)
but when i reached the arena of quantum physics i was ok. it has always seemed weird to me that something like quantum physics would make more sense to me than classical physics. example, quantum mechanical tunneling makes sense to me but i can't for the life of me glean the same sense from the physics of the wheel, lever or pulleys.
i think it has to do with this question of infinity. infinity seems a legitimate
concept mathematically and from the perspective of physics. but then one is faced with the question of what is going on behind the ...--->'s ? my intuition leads me to suspect that what ever it is we do when coping with the question of infinity is applying some repetitive operation to the mathematical terms or
physical phenomenon involved. so that what we have is the certainty of what it is we are doing to the uncertainty of what it is thats behind the ...--->'s.
whats more, we not only require this known repetitive operation but we require
(at least in our minds) that what is behind the ...--->'s to follow some rule.
it brings to mind Dr. Dick's knowable and unknowable data and the required stipulation that data is the result of rules.
at any rate i find the following quote from Dr. Dick's Fundamentals of Physical Reality fitting for the idea you state with respect to use the concept of infinity or not Paul: "In short, when in Rome, do as the Romans do. And, when in
an infinite math, remain consistent with the axioms of that math."
Dr. Dick:"I am myself fairly sure that the actual number of possible explanations (each of which entirely fit the all the facts) is probably infinite"