Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Graham Cooper

Posts: 4,280
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
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Dec 30, 1:15 pm, Virgil <vir...@ligriv.com> wrote:
> In article
> <c5b60ef5-2f84-4a6d-811c-373c2a3b1...@vb8g2000pbb.googlegroups.com>,
>  Graham Cooper <grahamcoop...@gmail.com> wrote:
>
>
>
>
>
>
>
>
>

> > On Dec 30, 9:31 am, Virgil <vir...@ligriv.com> wrote:
> > > In article
> > > <d95b3181-5372-47ca-8cc9-f2d6ee9bb...@po6g2000pbb.googlegroups.com>,
> > >  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?

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)




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.