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

+----->| 0. 542..| 0. 983..| 0. 143..| 0. 543..| ...vOK - 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 TIME0.694...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 lengthsegments[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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