Date: Mar 10, 2013 3:20 PM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots
On Mar 10, 7:12 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

> On 10 Mrz., 18:24, William Hughes <wpihug...@gmail.com> wrote:

>

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> > On Mar 10, 6:05 pm, WM <mueck...@rz.fh-augsburg.de> wrote:

>

> > > On 10 Mrz., 17:40, William Hughes <wpihug...@gmail.com> wrote:

>

> > > > There is no findable line that is

> > > > coFIS to (d)

>

> > > (d) is *not* an actual infinite sequence but only a description in

> > > letters.

>

> > > > g is a findable line.

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> > > > Do you agree with the statement

>

> > > > g is not coFIS to (d)

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> > > Of course. The number m = max is not findable or fixable.

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> > So do you agree with the statement.

>

> > If G is a set of lines of L with a findable

> > last element, then there is no line s of

> > G such that s is coFIS to (d)

>

> Yes. How often will you ask?

> (d) is a prescription to find or to construct FIS d_1, ..., d_n.

>

> Would you expect that

> "write 0. and then add the digit 1 with no end" is coFIS with a line

> of

> 0.1

> 0.11

> 0.111

> ...

>

No, the other way round.

Recall

We will say x is coFIS to (y) iff

i. We have (x) associated to x and

(y) associated to y

ii. For every n, (x) and (y) produce the same

finite string.

The statement x is coFIS to (y) means approximately

that x and the potentially infinite sequence described

by (y) are COFIS.

Do you agree with the statement

For every n, the nth FIS of x is

contained in g iff

g is coFIS to (x)