Date: Dec 28, 2012 7:16 PM
Author: Graham Cooper
Subject: CHANGING THE DIAGONAL!
+----->

| 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)