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 ]
 INFINITY POWER Posts: 117 Registered: 11/1/11
Re: This Is a Failed *PROOF* that AD never produces a New Digit Sequence!
Posted: Dec 30, 2012 1:35 AM

"Virgil" wrote in message...

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

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

Which is correct for a list of infinite binary sequences, but the "list"
below is not a list of infinite binary sequences to which the above can
be applied.

>
> 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)

Depends on what you call an antidiagonal.

If R1(1) = <314>, R1(2) = <15>, R1(3) = <926>, ...
And R2(1) = <27>, R2(2) = ,18281828>, R2(3) = <459045>, ...
and so on, then any Roo such that
Roo(1) <> R1(1), Roo(2) <> R2(2) and generally Roo(n) <> Rn(n)
will be a sequence that is not listed in your listing..
>
> [4] The anti-Diagonal never produces a unique sequence
> of segments (all segment sequences are computable)

But given any list of such sequences whose terms appear to be natural
numbers, it is quite easy to show that there are such sequences not
listed in that list.

Note that for two sequences to be equal, they must agree at EVERY
position, not just a few positions.

***********HERC************

It's a normal Decimal List!

LIST
R1= 0.314159265358979323> ...
R2= 0.2718281828459045235360 ...
R3= 0.333333333333333333 ...
R4= 0.888888888888888888888888 ...
R5= 0.0123456789012345678901234 ...
R6= 0.14142135623730950488 ...
....

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> ... >
....

What is missing? <in segment notation>

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