Date: Feb 19, 2013 10:42 AM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots

On Feb 19, 4:15 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 19 Feb., 14:10, William Hughes <wpihug...@gmail.com> wrote:
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> > On Feb 19, 12:41 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > On 18 Feb., 23:08, William Hughes <wpihug...@gmail.com> wrote:
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> > > > On Feb 18, 10:40 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
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> > > > > On 18 Feb., 19:19, William Hughes <wpihug...@gmail.com> wrote:
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> > > > > > > > Is there a potentially infinite sequence,
> > > > > > > > x, such that the nth FIS of x consists of
> > > > > > > > n 1's

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> > > > > 1
> > > > > 11
> > > > > 111
> > > > > ...

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> > > > > > > Yes, of course
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> > > > > > Let y be a potentially infinite sequence
> > > > > > where the nth FIS of y consists of a 1 followed
> > > > > > by n-1 0's

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> > > > > 1
> > > > > 10
> > > > > 100
> > > > > 1000
> > > > > ...

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> > > > > > Are x and y coFIS?
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> > > > > No.
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> > > > Is y the first line of the potentially
> > > > infinite list of potentially infinite
> > > > sequences

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> > > > L=
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> > > > 1000...
> > > > 11000...
> > > > 111000...
> > > > ...

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> > > > ?-
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> > > The n-th term of y and of the first line of L are coFIS up to every n.
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> > If two potentially infinite sequences have the same FIS's
> > up to every n then they are coFIS.

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> > The concept "coFIS up to n" has not been and need not be defined.
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> It is self-evident that "for every natural number" is identical with
> "up to every natural number". More than "up to number n" with n a
> natural number not fixed though is not a meaningful expression in this
> connection.
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> > Are y and the first line of L coFIS?-
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> Yes, obviously.
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> Regards, WM


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?