Great post! I believe I totally follow your explanations.
A set is denumerable (contains a denumerable amount of members) if its members can be mapped by some rule or rules, one to one, with the positive integers, and that set can contain either a finite or infinite amount of members.
So now I see that the definition I would have given you for "innumerable" would have been inconsistent with at least one of the mathematical definitions you provided. This means my definition was wrong. I won't bother to post it.
Thanks for taking the time to create that explanation. BTW, sets must be a girl thing, otherwise Sue wouldn't have gotten it first.
---Al
