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Topic: Matheology § 154: Consistency Proof!
Replies: 101   Last Post: Nov 25, 2012 5:08 PM

 Messages: [ Previous | Next ]
 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 154: Consistency Proof!
Posted: Nov 23, 2012 1:36 AM

On 22 Nov., 22:38, William Hughes <wpihug...@gmail.com> wrote:
> On Nov 22, 5:22 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>
>
>

> > On 22 Nov., 22:09, William Hughes <wpihug...@gmail.com> wrote:
>
> > > On Nov 22, 4:54 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > > > On 22 Nov., 20:22, William Hughes <wpihug...@gmail.com> wrote:
>
> > > > > Note that I was able to handle your
> > > > > "simple" case using induction.

>
> > > > > I consider the following case easy.
> > > > > If you disagree maybe you can say
> > > > > why?

>
> > > > > Consider the sequence of real numbers
>
> > > > > 1.0
> > > > > 10.0
> > > > > 100.0
> > > > > ...

>
> > > > > The limit is oo (unbounded)
>
> > > > > According to set theory, the number of 1's in the limit
> > > > > is 0.  (The limit of the set of positions at which we
> > > > > have a 1 is the empty set).

>
> > > > Why should the 1 disappear completely?
>
> > > The limit of the set of positions at which we
> > > have a 1 is the empty set.  If there is a 1 it has to
> > > be a one without a position.

>
> > Iff infinity can be finished.
>
> Nope.  We can establish that each integer
> has the property that it is not the index
> of a position with a 1 without using
> completed infinity.
>
> P(n): n is not the index of a position with a 1.
>
> P(1) is true.
> If P(n) is true then P(n+1) is true.
>
> For each natural number n, P(n) is true.-

Great! What about the digits in the sequence
1.
12.
123.
...

Of course, this sequence is a little bit more sophisticated than
yours. In order to avoid complications with numbers > 9 consider the
indices only. Here induction shows:
n is not the index of a position with a finite index.
According to set theory all digits vanish in the infinite.
Set theory is really a theory of spirit.
But analysis runs differently.
And say, why is the anti-diagonal determined in such a boring way? We
could make it vanish completely. Then Cantorian disciples would come
to rest.

Regards, WM

Date Subject Author
11/18/12 mueckenh@rz.fh-augsburg.de
11/18/12 Vurgil
11/18/12 William Hughes
11/18/12 Vurgil
11/19/12 mueckenh@rz.fh-augsburg.de
11/19/12 Vurgil
11/19/12 mueckenh@rz.fh-augsburg.de
11/19/12 William Hughes
11/19/12 mueckenh@rz.fh-augsburg.de
11/19/12 Vurgil
11/20/12 mueckenh@rz.fh-augsburg.de
11/20/12 Virgil
11/21/12 William Hughes
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
11/21/12 mueckenh@rz.fh-augsburg.de
11/21/12 William Hughes
11/22/12 mueckenh@rz.fh-augsburg.de
11/22/12 William Hughes
11/22/12 mueckenh@rz.fh-augsburg.de
11/22/12 William Hughes
11/22/12 mueckenh@rz.fh-augsburg.de
11/22/12 William Hughes
11/22/12 mueckenh@rz.fh-augsburg.de
11/22/12 William Hughes
11/22/12 mueckenh@rz.fh-augsburg.de
11/22/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 William Hughes
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12
11/23/12 Virgil
11/24/12 mueckenh@rz.fh-augsburg.de
11/24/12 Virgil
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11/23/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12 Virgil
11/23/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
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11/23/12 Virgil
11/23/12 Virgil
11/22/12 Virgil
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11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/22/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
11/23/12 mueckenh@rz.fh-augsburg.de
11/23/12 Virgil
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11/22/12 mueckenh@rz.fh-augsburg.de
11/19/12 Vurgil
11/20/12 mueckenh@rz.fh-augsburg.de
11/20/12 Virgil
11/22/12 David Valdez