On 2 Apr., 02:01, Virgil <vir...@ligriv.com> wrote: > In article > <1dd2037c-407c-49f6-afc6-e00c1d853...@w21g2000vbp.googlegroups.com>, > > > > > > WM <mueck...@rz.fh-augsburg.de> wrote: > > On 1 Apr., 22:44, Virgil <vir...@ligriv.com> wrote: > > > > > You do not believe that a sequence or list of all rational numbers can > > > > be constructed? > > > > One can "enumerate" the set of all rationals by formula, as has been > > > quite often done, but not by physically listing all of them. > > > A formula giving every entry is enough. > > > > Note that one cannot ennumerate by listing even sufficiently large > > > finite sets, so being listable other than by formula is not a relevant > > > criterion. > > > Constructing a list by a formula is enough to prove what I said. > > And enough to disprove what WM has said as well.
Then try it. What did I say? This: After every line n of the list of all rational numbers there are infinitely many rational numbers that up to digit n are identical with the anti-diagonal up to digit n.
This holds for the digits up to every finite n. And more digits cannot be expected to exist in any decimal representation of a number.