hi Paul,
i've got to apologize. i was being very loose when i used "...--->" . it is not proper mathematical terminology that i know of.
i made "...--->" up to use it as a representation of the collection of the ending
... terms we so often see in the terms of a mathematical expression when dealing with infinity, such as infinite series, ect.
so what i meant by "but then one is faced with the question of what is going on behind the ...--->'s ?" was in other words but then one is faced with the question of what is going on behind the ...'s ? i'm not so sure i was meaning the limiting process (although i guess i was refering to that process later in the post when i wrote about repetitive known operation to what we don't know) but i think i was refering to what is not known (ie. perhaps infinity) or the stuff going on after or during the ...'s.
i'm (i think like you) in that i don't trust that notation, i just have this primal or archaic doubt or need to wonder about just what does happen after or during the ...'s. the truth is we don't really know. physics, at least the physics of the present physical phase or state of the universe leads us to believe that a so called infinite series would be affected by entropy. let us take to identical series and isloate each one in two separate physical systems, say the minds of two mathematicians. let the mathematicians work the series in their minds. on their death bed we have each one give us the result of their calculations. will the answer be the same? i'd say know never, especially since simultaineous phenomeneon are hard or impossible to produce. so are the two identical series identical? well as far as actually conducting the series and producing identical results in the case above the answer is no. this is similar to your declaration above when you say "That's the assumption I balk at. I think there is an implicit question here of exactly to what extent is some consciousness required to be involved in this process. It seems to me that the conventional view holds that consciousness can somehow disengage after a while and let the process proceed on its own in order to finally "reach infinity"."
thank you for your response Paul, i shall read your essay.
regards, tim