```Date: Feb 6, 2013 4:31 PM
Author: Virgil
Subject: Re: Matheology 203

In article <63c3dd2b-cf74-407d-a750-c6a6981b1421@fv9g2000vbb.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 6 Feb., 10:08, Virgil <vir...@ligriv.com> wrote:> > > > Everything of 0.111... that can be defined by sequences of 1's, is in> > > the list. The finite definition "s" or "o.111..." is not in the list,> > > but finite definitions have nothing to do with Cantor's diagonal> > > proof.> > > Is that really exceeding the capacity of your brain?> >> > It certainly seems beyond the capacity of WM's.> > With no doubt.> >> > 0.111... is a finite definition for Sum_(n in |N) 1/b^n,> > which is another finite definition of 1/9 and notr available for> diagonalization.> > Try to diagonalize:> > 1 divided by 9> 1 divided by circumference of the unit circle> series of Gregory-Leibniz> basis of the logarithms> Euler's constant> andsoonIf the nth term in that sequence can be expressed in some n-ary form with n >= 4, , say, decimal form, accurate to n+1 n-ary places, then forming an anti-diagonal is trivial.> > Nothing else is required by Cantor with the only exception, that for> every n the finite initial segment a_n1, ..., a_nn of entry number n> has to be expanded by digits. But as everybody knows, these finite> initial segments belong to a countable subset of the countable set of> rational numbers.The nth term need not be expanded beyond n+1 digit accuracy in order to have a well defined antidiagonal. > > Regards, WM--
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