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


In article <kbonb9$th7$1@dontemail.me>, "INFINITY POWER" <infinity@limited.com> wrote:
> "Virgil" wrote in message... > > In article > <1d297c9c4129474ab84e5f3cd0950803@p7g2000pbz.googlegroups.com>, > Graham Cooper <grahamcooper7@gmail.com> wrote: > > > On Dec 30, 1:15 pm, Virgil <vir...@ligriv.com> wrote: > > > In article > > > <c5b60ef52f844a6d811c373c2a3b1...@vb8g2000pbb.googlegroups.com>, > > > Graham Cooper <grahamcoop...@gmail.com> wrote: > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > On Dec 30, 9:31 am, Virgil <vir...@ligriv.com> wrote: > > > > > In article > > > > > <d95b3181537247ca8cc9f2d6ee9bb...@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 ith > > > > > > number in your list had zero in its iposition, 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 antiDiagonal never produces a unique segment > > > > > > (all finite segments are computable) > > > > > > > > > [4] The antiDiagonal 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 ith > > number in your list had zero in its iposition, 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 antiDiagonal 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 antiDiagonal 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! 

