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Topic: This Is *PROOF* that AD never produces a New Digit Sequence!
Replies: 12   Last Post: Jan 2, 2013 11:38 AM

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: This Is a Failed *PROOF* that AD never produces a New Digit Sequence!
Posted: Dec 29, 2012 10:29 PM

On Dec 30, 1:15 pm, Virgil <vir...@ligriv.com> wrote:
> In article
>  Graham Cooper <grahamcoop...@gmail.com> wrote:
>
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>

> > On Dec 30, 9:31 am, Virgil <vir...@ligriv.com> wrote:
> > > In article
> > >  Graham Cooper <grahamcoop...@gmail.com> wrote:

>
> > > > AD METHOD (binary version)
> > > >   Choose the number 0.a_1a_2a_3...., where a_i = 1 if the i-th
> > > >   number in your list had zero in its i-position, a_i = 0 otherwise.

>
> > > > LIST
> > > >   R1= < <314><15><926><535><8979><323> ... >
> > > >   R2= < <27><18281828><459045><235360> ... >
> > > >   R3= < <333><333><333><333><333><333> ... >
> > > >   R4= < <888888888888888888888><8><88> ... >
> > > >   R5= < <0123456789><0123456789><01234 ... >
> > > >   R6= < <1><414><21356><2373095><0488> ... >
> > > > ....

>
> > > > By breaking each infinite expansion into arbitrary finite length
> > > > segments

>
> > > > [3]  The anti-Diagonal never produces a unique segment
> > > >       (all finite segments are computable)

>
> > > > [4]  The anti-Diagonal never produces a unique sequence
> > > >        of segments (all segment sequences are computable)

>
> > > It easily produces a sequence which does not already exist in any
> > > countable seqeunce of sequences since it can be made to differ in at
> > > least one place with each sequence, the place depending on the listed
> > > position of that sequence.

>
> > > > It's just like the infinite STACK of ESSAYS!  They contain every
> > > > possible sentence in every possible order!  By changing one word at a
> > > > time it's Still IMPOSSIBLE to construct a New Essay!

>
> > > But your essays are all of finite length but each is a string of words
> > > taken from an infinite dictionary, which is not at all the same thing.

>
> > > Even so any infinite essay will differ from a of you essays, so you
> > > analogy fails.

>
> > NO VIRGIL!
>
> > You are  MAKING UP BULLSHIT
>
> On the contrary, I am merely trying to dig myself out of yours.
>

If you disagree with a numbered point then which one?

Choose the number 0.a_1a_2a_3...., where a_i = 1 if the i-th
number in your list had zero in its i-position, a_i = 0 otherwise.

LIST
R1= < <314><15><926><535><8979><323> ... >
R2= < <27><18281828><459045><235360> ... >
R3= < <333><333><333><333><333><333> ... >
R4= < <888888888888888888888><8><88> ... >
R5= < <0123456789><0123456789><01234 ... >
R6= < <1><414><21356><2373095><0488> ... >
....

By breaking each infinite expansion into arbitrary finite length
segments

[3] The anti-Diagonal never produces a unique segment
(all finite segments are computable)

[4] The anti-Diagonal never produces a unique sequence
of segments (all segment sequences are computable)

Date Subject Author
12/29/12 Graham Cooper
12/29/12 Virgil
12/29/12 Graham Cooper
12/29/12 Virgil
12/29/12 Graham Cooper
12/30/12 Virgil
12/30/12 INFINITY POWER
12/30/12 Virgil
12/30/12 Graham Cooper
1/1/13 INFINITY POWER
1/1/13 Shmuel (Seymour J.) Metz
1/2/13 Graham Cooper