Date: Feb 6, 2013 6:40 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology 203
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

andsoon

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.

Regards, WM