Date: Feb 6, 2013 4:31 PM
Subject: Re: Matheology 203
WM <firstname.lastname@example.org> 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
> 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
If 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