Date: Feb 20, 2013 11:44 AM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots

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.
>
>
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>
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>
> > <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?