[In reference to: (.9 + .09 + .009 + .0009 + ...)]
I am a pretty smart person. I don't try to hide this. That is not endearing. That being said, trust me when I say that if you think that I am being obtuse; it is certainly not intentional. Have you noticed that I have started approaching this in the tiniest bites possible? That is because (it seems to me) that there is a marked lack of communication between us. I don't think the problem lies on my end.
I am not trying to avoid answering your question [what it is that I mean by "innumerable"], although it certainly may seem that way. I just want to understand what you mean about things you have already said before I address this. However, this may not even be possible here. It seems distinctly possible to me that your definitions for "countable", "finite" and "infinite" may be different from mine (and most other people's here). If that is so, I am not interested in a semantical argument or interested at this time in taking the effort to learn your legitimate or otherwise differing definitions.
And THAT being said, would it be a bother to ask you to explain the difference between "infinite" and "denumerable"? (and yes, again, even if you already have, or maybe put it more succinctly, so that people who don't use the concepts everyday can understand?)
---Al
