Date: Mar 10, 2013 3:39 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots
On 10 Mrz., 20:20, William Hughes <wpihug...@gmail.com> wrote:

> > > 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.

There is no way. This is a sequence of less than 10 words: "write 0.

and then add the digit 1 with no end". It is not coFIS with any line

of the list. But it defines the lines of the list.

>

> 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.

(x) and (y), if describing infinite sequences, are phrases of few

words. They are probably not coFIS.

>

> 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)

Let us stay in the concrete example:

L is the list

1

1,2

1,2,3

...

1,2,3,...,max

and d is the diagonal 1,2,3,...,max.

For every n, the nth FIS of d is contained in the list L and,

therefore, in the last, unfixable and unfindable, line 1,2,3,...,max.

Since the last line and the sequence 1,2,3,...,max described by (d)

are identical, every line l_n = 1,2,3,...,n of the list is contained

in the last line and in the sequence described by d.

Is that a sufficient answer to your question? If not, don't hesitate

to ask. But I would be glad, if you could stay with our example L and

d.

Regards, WM