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Topic: CHANGING THE DIAGONAL!
Replies: 6   Last Post: Dec 29, 2012 4:14 AM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: CHANGING THE DIAGONAL!
Posted: Dec 29, 2012 2:27 AM

In article
Graham Cooper <grahamcooper7@gmail.com> wrote:

> On Dec 29, 3:18 pm, Virgil <vir...@ligriv.com> wrote:
> > In article
> >  Graham Cooper <grahamcoop...@gmail.com> wrote:
> >
> >
> >
> >
> >
> >
> >
> >
> >

> > > On Dec 29, 11:37 am, Virgil <vir...@ligriv.com> wrote:
> > > > In article
> > > >  Graham Cooper <grahamcoop...@gmail.com> wrote:

> >
> > > > > +----->
> > > > > | 0. 542..
> > > > > | 0. 983..
> > > > > | 0. 143..
> > > > > | 0. 543..
> > > > > | ...
> > > > > v
> > > > > OK - THINK - don't back explain to me.
> > > > > You run down the Diagonal  5 8 3 ...
> > > > > IN YOUR MIND -

> >
> > > > > [1]
> > > > > you change each digit ONE AT A TIME
> > > > > 0.694...
> > > > > but this process NEVER STOPS

> >
> > > > > [2]
> > > > > so you NEVER CONSTRUCT A NEW DIGIT SEQUENCE!

> >
> > > > That is like saying that the function f+ |N -> |N : x \_--> x^2
> > > > never ends.

> >
> > > Right!  but since it has no free variable input to apply it's safe to
> > > extrapolate results toward infinity.

> >
> > > > As soon as one has a completed rule by which values of the function are
> > > > determined from its domain to its codomain, the function is defined.

> >
> > > > E.g., f:|N --> |N : 2 |--> 2*x+1
> > > > is  completed function

> >
> > > > Thus a rule or function for determining anti-diagonal digits creates the
> > > > entire anti-diagonal list of digits in one step.

> >
> > > dependent on the input.
> >
> > As a function of the input certainly, but one theat function is defined
> > the process is essentially completed.
> >
> >
> >

> > > In this case, you cannot ANTI-DIAGONALISE an infinite set.
> >
> > > Every digit you change is substitutable by another digit in another
> > > permutation.

> >
> > I have defined a function which does it automatically for any and every
> > list of endless sequences of decimal digits, giving a resulting sequence
> > not listed in that list.
> >

>
> It has a parameter that only works given LIST format.
>
> It doesn't prove a SET of reals is in-complete.

The set of all reals is not complete, but it also cannot be listed.
>
> Here is the SET of all reals.
>
> UTM( real , digit ) [mod 10]
>
>
> that is a complete specification of the set.
>
> However, there are infinitely many permutations, due to there being
> infinitely many universal turing machines in infinitely many different
> languages.
>
> Since your process has a free variable, the never ending cross-
> sequence you compute is dependent on your own selected free variable,
> the permutation you must select for listable format for your process
> to work.
>
> IF you got out of your corner and examined the other methods put forth
> you would see this.
>
> IS 0. T(2,1) T(1,2) T(3,3) T(4,4) ...
>
> absent from L?
>
> T is the list of all reals with the digit changing function applied to
> all digits of every real.

You are assuming that there can be a list of all real as a step in
trying to prove that there can be such a list.
Such argiuments, being circular, are invalid.
>
> If you cannot address the posts in the group you should stop yourself
> from arguing against them.

I am well able to spot you flaws.
--

Date Subject Author
12/28/12 Graham Cooper
12/28/12 Virgil
12/28/12 Graham Cooper
12/29/12 Virgil
12/29/12 Graham Cooper
12/29/12 Virgil
12/29/12 Graham Cooper