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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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Registered: 1/6/11
Re: This Is a Failed *PROOF* that AD never produces a New Digit Sequence!
Posted: Dec 29, 2012 6:31 PM
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In article
Graham Cooper <> 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.
> 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.
> Herc


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