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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