
Re: Matheology § 233
Posted:
Apr 2, 2013 4:17 PM


On 2 Apr., 02:01, Virgil <vir...@ligriv.com> wrote: > In article > <1dd2037c407c49f6afc6e00c1d853...@w21g2000vbp.googlegroups.com>, > > > > > > WM <mueck...@rz.fhaugsburg.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 antidiagonal 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.
Regards, WM

