```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 lineof 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 fewwords. 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 list11,21,2,3...1,2,3,...,maxand 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 containedin the last line and in the sequence described by d.Is that a sufficient answer to your question? If not, don't hesitateto ask. But I would be glad, if you could stay with our example L andd.Regards, WM
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