Date: Feb 20, 2013 7:28 PM
Author: Virgil
Subject: Re: WMytheology � 222 Back to the hoots

In article 
<cfa32dfa-046d-49f8-b134-fe030cb487c1@u20g2000yqj.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 20 Feb., 17:44, William Hughes <wpihug...@gmail.com> wrote:
> > On Feb 20, 5:29 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> >
> >
> >
> >

> > > On 20 Feb., 13:31, William Hughes <wpihug...@gmail.com> wrote:
> >
> > > > On Feb 20, 12:37 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> >
> > > > > On 20 Feb., 11:30, William Hughes <wpihug...@gmail.com> wrote:
> > > > <snip>
> > > > > > A  statement you can make is that there
> > > > > > is no line of the list with the property
> > > > > > that it is coFIS to d.
> > > > > > (you do not need every line or every FIS to "actually
> > > > > > exist" to make this statement)

> >
> > > > > You need all FISs of d to make this statement.
> >
> > > > No, for each line of L you only need some
> > > > of the FISs.  For every line you need every
> > > > not all.

> >
> > > Then you have a statement for finitely many lines and none for
> > > infinitely many lines.

> >
> > > > <snip>
> >
> > > > > > Let z be a potentially infinite sequence such that
> > > > > > for some natural number m, the mth FIS of
> > > > > > z contains a zero.

> >
> > > > > > Are z and x coFIS?
> >
> > > > > No.
> >
> > > > Is the following statement true
> >
> > > > For every natural number n we have
> >
> > > >     the (n+1)st FIS of the nth line
> > > >     of L contains a 0.

> >
> > > Of course.
> >
> > Is the statement
> >
> > For every natural number n we have
> >     the nth line of L and x
> >     are not coFIS
> >
> > true?-

>
> True but irrelevant.


Perhaps irrelevant in WMytheology, but quite relevant in mathematics.
>
> Relevant is only this: For every natural number n we have a line that
> is identical with d_1, ..., d_n.



All lines belong to the set of those lines for which we have FIS of d
longer than that line.
>
> You try and try to have a one-sided look onto the infinite.


It is WM who has a one-sided look that never sees far enough.
>
> For every natural number n we have a FIS 1,2,3,...,n, ..., m that is
> longer and contains n.


And vice versa, for every FISn of d there is a {1,2,3,...,m} with more
elements in it.

But in mathematics, even if not in WMytheology, one may have the set of
all FISs and the set of all n's.

Note that without an inductive set like |N, induction is impossible, so
to work only in WMytheology one must give up induction.
--