In article <firstname.lastname@example.org>, WM <email@example.com> 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.