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Re: Matheology 203
Posted:
Feb 6, 2013 6:40 AM
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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
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