Virgil
Posts:
4,483
Registered:
1/6/11
|
|
Re: Matheology � 154: Consistency Proof!
Posted:
Nov 23, 2012 4:39 PM
|
|
In article
<7e92096f-b31a-41fd-8f4e-ee611b00ef52@o30g2000vbu.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:
> On 23 Nov., 08:25, Virgil <vir...@ligriv.com> wrote:
> > In article
> > <caaeacd6-40ef-4d48-8efc-c1932fe1f...@k6g2000vbr.googlegroups.com>,
> >
> >
> >
> >
> >
> > 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! What about the digits in the sequence
> > > 1.
> > > 12.
> > > 123.
> > > ...
> >
> > Your "sequence" is not well defined, since there is no obvious successor
> > to 1232456789.
>
> That's the good news: The successor question is irrelevant. Matheology
> fails with every possible successor. But of course,
>
> Ther's no con-
> tra-dic-tion!
> Ther's no con-
> tra-dic-tion!
> Ther's no con-
> tra-dic-tion!
> ...
Other than in your Wolkenmuekenheim, quite true!
--
|
|
