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Topic: Matheology § 191
Replies: 91   Last Post: Jan 18, 2013 2:44 AM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: WMatheology § 191
Posted: Jan 15, 2013 4:18 PM

On 15 Jan., 22:03, Virgil <vir...@ligriv.com> wrote:
> In article
>
>
>
>
>
>  WM <mueck...@rz.fh-augsburg.de> wrote:

> > On 15 Jan., 19:54, Virgil <vir...@ligriv.com> wrote:
> > > In article

>
> > > WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > On 15 Jan., 08:23, Virgil <vir...@ligriv.com> wrote:
>
> > > > > > But here is the list: All finite initial segments of all decimal
> > > > > > expansions are included.

>
> > > > > That is not a list.
>
> > > > The set is countable. There exists a bijection with |N. So list-
> > > > fetishists should be able to set up a list of that set.

>
> > > Your set is not a list until that bijection, or at least a surjection,
> > > from |N to your set has been explicitly established, at which point an
> > > antidiagonal which is not listed can be shown to exist.

>
> > The set is countable with no doubt.
>
> Until it is proved so by being listed, there can be legitimate doubt.

Doubt that the terminating rationals are countable?
Doubt that the definable tails are countable?
Doubt that aleph_0 * aleph_0 = aleph_0?
Not even in matheology.
>
> > An anti-diagonal cannot differ from every number of the set because
> > the set contains all numbers.

>
> Only as finite strings so that any infinite string will differ from
> every finite string.

Not at a digit at a finite place.
>
> > Compare the Binary Tree where no anti-
> > diagonal can be found (in the finite realm).

>
> But the complete infinite binary tree itself does not exist in any
> finite realm,

The complete infinite Binary Tree exists within the infinite set of
all finite levels. There is no further place where it could exist. A
life after life belongs to theology. A definition afterall finite
definability belongs to matheology.
>
>

> > And there is no infinite realm.
>
> Maybe not in WMYTHEOLOGY, but there are more things in heaven and earth,
> WM, than are dreamt of your philosophy.

Perhaps in heaven, but mathematics does not belong to heaven.
>
> > So if there are infinitely many paths
> > in the Binary Tree, then they must cross at least one finite level
> > together.

>
> Paths of finite trees don't "cross" any level together, so why should
> any other tree differ?

All paths cross every level, but not at distinct nodes. If however a
number n of paths of the Binary Tree is claimed, then ther must be a
level with n nodes.
>
> > But that is not the case. Hence they can only become
> > infinitely many beyond every finite level. But that is the realm of
> > matheology. In mathematics there does nothing follow beyond every
> > finite level.

>
> In a sequence of levels, either there is a last level or no last level.
>
> If there is a last level then there are only finitely many levels.
>
> If there is no last level then there are infinitely many levels.
>
> In the set of naturals numbers, beyond each natural there is another
> natural, so there more than any finite number of naturals.

Nevertheless every natural n is finite and the index n can be the last
one of a finite initial segment.

Regards, WM

Date Subject Author
1/12/13 mueckenh@rz.fh-augsburg.de
1/12/13 Zaljohar@gmail.com
1/12/13 mueckenh@rz.fh-augsburg.de
1/12/13 Virgil
1/12/13 mueckenh@rz.fh-augsburg.de
1/12/13 Zaljohar@gmail.com
1/12/13 mueckenh@rz.fh-augsburg.de
1/12/13 Virgil
1/13/13 Zaljohar@gmail.com
1/13/13 mueckenh@rz.fh-augsburg.de
1/13/13 Virgil
1/13/13 mueckenh@rz.fh-augsburg.de
1/13/13 Virgil
1/14/13 mueckenh@rz.fh-augsburg.de
1/14/13 Virgil
1/15/13 mueckenh@rz.fh-augsburg.de
1/15/13 Virgil
1/15/13 mueckenh@rz.fh-augsburg.de
1/15/13 Virgil
1/15/13 mueckenh@rz.fh-augsburg.de
1/15/13 Virgil
1/15/13 mueckenh@rz.fh-augsburg.de
1/15/13 Virgil
1/16/13 mueckenh@rz.fh-augsburg.de
1/16/13 Virgil
1/16/13 mueckenh@rz.fh-augsburg.de
1/16/13 Virgil
1/16/13 mueckenh@rz.fh-augsburg.de
1/16/13 Virgil
1/17/13 Virgil
1/17/13 mueckenh@rz.fh-augsburg.de
1/17/13 fom
1/17/13 mueckenh@rz.fh-augsburg.de
1/17/13 fom
1/17/13 mueckenh@rz.fh-augsburg.de
1/17/13 Virgil
1/18/13 Virgil
1/17/13 Jesse F. Hughes
1/17/13 mueckenh@rz.fh-augsburg.de
1/17/13 Jesse F. Hughes
1/17/13 mueckenh@rz.fh-augsburg.de
1/17/13 Jesse F. Hughes
1/17/13 Virgil
1/17/13 Virgil
1/17/13 Virgil
1/17/13 Virgil
1/17/13 mueckenh@rz.fh-augsburg.de
1/17/13 Virgil
1/13/13 Zaljohar@gmail.com
1/13/13 mueckenh@rz.fh-augsburg.de
1/13/13 Virgil
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1/13/13 Virgil
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1/14/13 Virgil
1/13/13 mueckenh@rz.fh-augsburg.de
1/13/13 Virgil
1/13/13 Virgil
1/12/13 Virgil
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1/13/13 Virgil
1/13/13 mueckenh@rz.fh-augsburg.de
1/13/13 Virgil
1/14/13 mueckenh@rz.fh-augsburg.de
1/14/13 Virgil
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1/14/13 Virgil
1/15/13 mueckenh@rz.fh-augsburg.de
1/15/13 Virgil
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1/15/13 Virgil
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1/15/13 Virgil
1/12/13 Ben Bacarisse
1/12/13 mueckenh@rz.fh-augsburg.de
1/12/13 Virgil
1/13/13 mueckenh@rz.fh-augsburg.de
1/13/13 Virgil
1/12/13 David C. Ullrich
1/12/13 mueckenh@rz.fh-augsburg.de
1/12/13 Virgil
1/13/13 mueckenh@rz.fh-augsburg.de
1/13/13 Virgil
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1/14/13 Virgil
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1/14/13 Virgil
1/12/13 Virgil
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1/13/13 Virgil