Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Topic: This Is *PROOF* that AD never produces a New Digit Sequence!
Replies: 12   Last Post: Jan 2, 2013 11:38 AM

 Search Thread: Advanced Search

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
This Is *PROOF* that AD never produces a New Digit Sequence!
Posted: Dec 29, 2012 5:18 PM
 Plain Text Reply

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

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

© The Math Forum at NCTM 1994-2017. All Rights Reserved.