> In article > <b76b5101-f3f2-4b86-91b5-75792335690d@k8g2000yqn.googlegroups.com>, > WM <mueckenh@rz.fh-augsburg.de> wrote: > >> On 13 Jun., 19:26, Virgil <virg...@nowhere.com> wrote: >> >> >> We agree that in Cantor's diagonal argument, applied to real numbers, >> the numbers are represented and identified solely by their digits. No >> further information is available. >> >> We assume that a real number p can be distinguished from a set Q of >> real numbers q by general considerations, for instance, if p is a >> transcendental number and Q consists of rational numbers q only. > > Then one can then distinguish between any real number whose binary or > decimal or other base expansion is eventually periodic and those whose > expansions are not eventually periodic. >> >> >> Of course it would be impossible to distinguish p from all q, because >> for every digit d_n of p, there is a number q that shares all digits >> up to d_n with p. > > Thus one can distingish any number with a non-eventually-periodic > expansion from all rationals.
What the hell has the diagonal argument to do with "distinguishing" numbers from one another? This is nothing but one more of Mueckenheim's red herrings.
