```Date: Mar 10, 2013 4:35 PM
Author: Virgil
Subject: Re: Matheology � 222 Back to the roots

In article <53c0e229-49f3-496e-9de4-18c9f81edad1@14g2000vbr.googlegroups.com>, WM <mueckenh@rz.fh-augsburg.de> wrote:> On 9 Mrz., 23:53, William Hughes <wpihug...@gmail.com> wrote:> > On Mar 9, 5:57 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> >> > > What do you understand by the not changeable function (d)?> >> > If x is a potentially infinite sequence of 0's and 1's> > then we say (x) is associated to x, if (x) is an algorithm> > which given a natural number produces a finite string> > of 0's and 1's, such that for every natural number n,> > (x) produces the nth FIS of x.> > Ok. So it is clear that a finite number has to be given and a finite> string is produced.That defines a functional relationship between the number and the string, but does not limit the number of number-to-string pairings to only a finite number of such pairings.> >> > 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.> > "Every given n" is tantamount to "there is a last given n".Not outside Wolkenmuekenheim!> This maximum is the same for line l_max and max FIS of d.Not outside Wolkenmuekenheim!Only inside Wolkenmuekenheim can one have natural numbers without successors.> >> > Some comments.> >> > We can never have more than a limited number of the strings> > produced by (x) existing at any time, since we can never> > have more that a limited number of natural numbers.> > Correct.> >> > We cannot show that x is coFIS to (y) by using (x)> > and (y) to produce "all possible strings" and> > comparing them, since "all possible natural numbers"> > does not exist.  However, we may be able to use induction> > to show "For every n, (x) and (y) produce the same finite> > string"> > Induction is fine, but also restricted to the (variable) maximum.Requiring the existence of a natural number with no successor!> >> > To show that x is coFIS to (y), it is not enough> > to show that  every existing FIS of x, is equal to an> > existing FIS of y.> > More cannot be shown.Then such coFISm cannot be shown at all, at lest inside Wolkenmuekenheim. > >> > d, the diagonal of the list L, is a potentially infinite> > sequence of 0's and 1's with associated (d):> > for any natural number n produce> > a sequence of n ones.> > This sequence is identical to a line l_max of the list L, by> construction of d_max.But outside of Wolkenmuekenheim there is no such alleged d_max possible, as every member of d has a successor.--
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