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?
A set S of infinite strings of digits (the God of matheology may present the strings without defining them in another way) is finitely distinguishable if for all x, y in S, if x != y then there is an m in | N (i.e., a finite index) such that x_m != y_m.