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?