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

 Messages: [ Previous | Next ]
 William Hughes Posts: 2,330 Registered: 12/7/10
Re: Matheology § 154: Consistency Proof!
Posted: Nov 23, 2012 7:27 AM

On Nov 23, 2:36 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> 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!

So to summarize:

Analysis:
limit in real numbers: unbounded
(oo in extended reals)

limit of set of 1's: not estimated

Set Theory
limit in real numbers: not estimated
limit of set of 1's: {}

by finite terms)

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
11/23/12 Virgil
11/24/12 mueckenh@rz.fh-augsburg.de
11/24/12 Virgil
11/25/12 mueckenh@rz.fh-augsburg.de
11/25/12 Virgil
11/25/12 mueckenh@rz.fh-augsburg.de
11/25/12 Virgil
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
11/23/12 Virgil
11/23/12 Virgil
11/23/12 Virgil
11/22/12 Virgil
11/22/12 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
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
11/22/12 Virgil
11/21/12 Virgil
11/21/12 Virgil
11/21/12 Virgil
11/21/12 Virgil
11/21/12 Virgil
11/21/12 Virgil
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