> On 4 Jan., 22:36, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > >> Clearly, the set of reals is pairwise distinguishable but not totally >> distinguishable. But so what? > > A good question. A set distinguishable by such an n would necessarily > be finite. Do you think that anybody, and in particular Zuhair, claims > that |R is finite? Or did you miss this implication?
After posting, I came to that conclusion as well. Thus, I've no idea what Zuhair means when he says that distinguishability implies countability. (He said that it means the set of finite initial segments is countable, but since this does not contradict the uncountability of R, I don't know why he thinks this is paradoxical.)
Again, let's let Zuhair clarify precisely what his argument is. I just don't see it.
-- "This is based on the assumption that the difference in set size is what makes the important difference between finite and infinite sets, but I think most people -- even the mathematicians -- will agree that that probably isn't the case." -- Allan C Cybulskie explains infinite sets