Search All of the Math Forum:

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

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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 30, 2012 8:05 PM

On Dec 31, 8:31 am, George Greene <gree...@email.unc.edu> wrote:
> On Dec 29, 10:29 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>

> > If you disagree with a numbered point then which one?
>
> Everybody disagrees WITH POINT 4, DUMBASS.   IT DOESN'T FOLLOW
> from anything.  YOU CAN'T PROVE IT.  We by contrast HAVE EASILY
> proved that since for EVERY n, the nth position of the diagonal
> DIFFERS from the nth R on the list AT Rn's nth position,
> THE ANTI-DIAGONAL *IS*NOT*ON* the list.  If it WERE on, it would
> have to be on it *AT* some row n. But the anti-diagonal IS NOT
> on the list at row n because Rn DIFFERS from the anti-diagonal IN
> POSITION n.
>
>
>
>
>
>
>
>
>

> > 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)

>
> MOST of the *infinitely*-long segment sequences ARE NOT computable.
> The fact that all the FINITE ones are DOES NOT IMPLY that the infinite
> ones are also.
> The mystery is why you would think it would.
>

Point 4 inductively follows from point 3.

< <sub-segment> <sub-segment> <sub-segment> >

this sequence of segments.

You opposing argument is that some sequence of sentences cannot be
written down and placed on a stack.

INFINITE STACK OF INFINITE ESSAYS OF FINITE VOCABULARY
in order to be equivalent to a BASE-|VOCAB| List of infinite
strings.

SEGMENT <=> SENTENCE

Herc

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