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Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: VIRGIL CANNOT ANTI-DIAGONALISE THIS POWERSET(N)! <<<<<
Replies: 5   Last Post: Dec 30, 2012 2:10 AM

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camgirls@hush.com

Posts: 12
Registered: 4/8/11
VIRGIL CANNOT ANTI-DIAGONALISE THIS POWERSET(N)! <<<<<
Posted: Dec 29, 2012 7:27 PM
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USE YOUR ANTI-DIAGONAL METHOD
ON THIS SET OF *ALL* SUBSETS OF N!


tinyurl.com/blueprints-powerset

INPUT 1 2 3 4 5 6 7 8 9 10 ...
===========================
TM1 H L H H H L L L L L ...
TM2 H H H H H H H H H H ...
TM3 H L L L L L L L L L ...
TM4 L H L H L H L H L H ...
...

If TM1(1) Halts then 1 e POWERSET_1
If TM1(2) Loops then 2 !e POWERSET_1
If TM2(1) Halts then 1 e POWERSET_2
If TM2(2) Halts then 2 e POWERSET_2
...

TAKEN FROM THE HALTING VALUES OF THIS EXAMPLE
INPUT 1 2 3 4 5 6 7 8 9 10 11 12 13 14...
TM1 H L
TM2 H H
...

POWERSET(N) = { {1,...} {1,2,...} ... }



CAN YOU SEE THE BIJECTION TO N VIRGIL?????


1 <=> {1,3,4,5...}
2 <=> {1,2,3,4,5,6,7,8,9,10...}
3 <=> {1}
4 <=> {2,4,6,8,10,...}

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