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Topic: CHANGING THE DIAGONAL!
Replies: 6   Last Post: Dec 29, 2012 4:14 AM

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Graham Cooper

Posts: 4,344
Registered: 5/20/10
CHANGING THE DIAGONAL!
Posted: Dec 28, 2012 7:16 PM
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+----->
| 0. 542..
| 0. 983..
| 0. 143..
| 0. 543..
| ...
v
OK - THINK - don't back explain to me.
You run down the Diagonal 5 8 3 ...
IN YOUR MIND -

[1]
you change each digit ONE AT A TIME
0.694...
but this process NEVER STOPS

[2]
so you NEVER CONSTRUCT A NEW DIGIT SEQUENCE!

[1]
[1]->[2]
[2]

*******
*PROOF*
*******


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)

CONCLUSION:
Changing the diagonal just changes the permutation,
every digit change is accommodated into the same set.

G Cooper (BInfTech)




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