Date: Feb 6, 2013 6:40 AM
Subject: Re: Matheology 203

On 6 Feb., 10:08, Virgil <> 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

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