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Topic: Matheology � 300
Replies: 27   Last Post: Jul 9, 2013 2:50 PM

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Posts: 8,833
Registered: 1/6/11
Re: Matheology � 300
Posted: Jul 9, 2013 2:50 PM
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In article <>, wrote:

> On Tuesday, 9 July 2013 00:59:26 UTC+2, Virgil wrote:

> > Consider the strictly increasing sequence f(n) = (n-1)/n.
> > While there is never a last term to that sequence, but when one has
> > increases to 1, one has past by all the terms of that sequence.

> The limit 1 will never be reached by passing through infinitely many terms.
> The limit 1 only says that no term will be 1 but many terms will come as
> close as you like.

When one has passed every n in (n-1)/n, the difference from 1 will be 0.
> It is impossible to reach pi by its rational approximations. It is impossible
> to define Cantor's diagonal by digits.

It is outside of WM's wild weird world of WMytheology.

> All its digits belong to rational
> approximations.

All its digits belong to {0,1,2,3,4,5,6,7,8,9}, but it does not belong
to the list from which it was derived.

> But all rational approximations can be in a
> rationals-complete list.

That is irrelevant!
The point is that no list (countable set) of reals can contain all reals.
> For every index n exist infinitely many lines

> Since it is impossible to find

any logic in WMytheology

None of WM's arguments in any way repudiate EITHER of Cantor's proofs
that there is no ennumeration (listing) or reals containing all reals.

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