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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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Graham Cooper

Posts: 4,253
Registered: 5/20/10
This Is *PROOF* that AD never produces a New Digit Sequence!
Posted: Dec 29, 2012 5:18 PM
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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'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!


Herc




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