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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

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Virgil

Posts: 8,833
Registered: 1/6/11
Re: This Is a Failed *PROOF* that AD never produces a New Digit Sequence!
Posted: Dec 30, 2012 2:17 AM
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In article <kbonb9$th7$1@dont-email.me>,
"INFINITY POWER" <infinity@limited.com> wrote:

> "Virgil" wrote in message...
>
> In article
> <1d297c9c-4129-474a-b84e-5f3cd0950803@p7g2000pbz.googlegroups.com>,
> Graham Cooper <grahamcooper7@gmail.com> wrote:
>

> > 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.

>
> 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> ... >
> ....


The above two partial lists of sequences of characters are clearly not
identical, but for either one one can easily provide a sequence which is
not a member of that list.
>
>
> What is missing? <in segment notation>


Your share of common sense!
--





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