In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> 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.
The "god" of WMytheology, namely WM himself, will insist that every such potential string must have a finite definition in order to be thought about at all. > > Regards, WM
Actually, real math suggests that there are reals so incredibly inaccessible that finding the digit sequence representing one of them is not possible.
In which case such numbers may well not be "finitely distinguishable". --