Date: Feb 20, 2013 5:27 PM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots

On Feb 20, 10:52 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 20 Feb., 17:44, William Hughes <wpihug...@gmail.com> wrote:
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> > On Feb 20, 5:29 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > On 20 Feb., 13:31, William Hughes <wpihug...@gmail.com> wrote:
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> > > > On Feb 20, 12:37 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > 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)

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

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

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

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

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

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> > true?-
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> True



Is the statement

There is no natural number m
such that the mth line of L and x
are coFIS

true?