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Topic: The Diagonal Argument
Replies: 28   Last Post: Dec 29, 2012 12:11 AM

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Graham Cooper

Posts: 4,280
Registered: 5/20/10
Re: The Diagonal Argument
Posted: Dec 27, 2012 10:56 PM
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On Dec 28, 12:58 pm, "Ross A. Finlayson" <ross.finlay...@gmail.com>
wrote:
> On Dec 27, 6:37 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
>
>
>
>
>
>
>
>

> > On Dec 28, 10:03 am, Virgil <vir...@ligriv.com> wrote:
>
> > > In article
> > > <dc67df4d-c740-4c07-b66d-24dc52f8c...@pd8g2000pbc.googlegroups.com>,
> > >  Graham Cooper <grahamcoop...@gmail.com> wrote:

>
> > > > > Try to Visualise an example.
>
> > > > > L(x,y)
> > > > > +---------------->
> > > > > | 0. 2 3 4 5 6 7 ..
> > > > > | 0. 9 8 7 6 5 5 ..
> > > > > | 0. 1 2 3 1 2 3 ..
> > > > > | 0. 9 8 9 8 9 8 ..
> > > > > | 0. 6 5 6 5 6 5 ..
> > > > > | 0. 5 6 5 6 5 6 ..
> > > > > |
> > > > > v

>
> > > > > Now apply your FLIP(d) function to the whole plane
>
> > > > > T(x,y)
> > > > > +---------------->
> > > > > | 0. 6 6 6 6 5 5 ..
> > > > > | 0. 5 5 5 5 6 6 ..
> > > > > | 0. 6 6 6 6 6 6 ..
> > > > > | 0. 5 5 5 5 5 5 ..
> > > > > | 0. 5 6 5 6 5 6 ..
> > > > > | 0. 6 5 6 5 6 5 ..
> > > > > |
> > > > > v

>
> > > > > Your claim is that is you take any path from
>
> > > > > T(1,?)
> > > > > T(2,?)
> > > > > T(3,?)
> > > > > ...

>
> > > > > and repeat that process you must end up with an infinite string absent
> > > > > from L?

>
> > > > i.e.   ANTIDIAG = T(1,1) T(2,2) T(3,3) T(4,4) ...
>
> > > > But Obviously  T(1,1) T(2,99) T(3,10110) T(4,7) ...
>
> > > > is not provably absent from L.
>
> > > > Remember Given a Stack of ESSAYS with every possible sentence written
> > > > in every possible order, taking the 1st word of Essay 1, changing it,
> > > > then the 2nd word of Essay 2, changing it, never produces a unique
> > > > sentence or any original writing at all!  Similarly the ANTIDIAG
> > > > PROCESS never conjures a Unique Digit Sequence!

>
> > > > In fact, using a Symmetric FLIP(d) Function
>
> > > >  L(x,y)
> > > >  +---------------->
> > > >  | 0. 2 3 4 5 6 7 ..
> > > >  | 0. 9 8 7 6 5 5 ..
> > > >  | 0. 1 2 3 1 2 3 ..
> > > >  | 0. 9 8 9 8 9 8 ..
> > > >  | 0. 6 5 6 5 6 5 ..
> > > >  | 0. 5 6 5 6 5 6 ..
> > > >  |
> > > >  v

>
> > > > FLIP(d) = 9-d
>
> > > > Minor Problem with:
>
> > > > 0.49999...
> > > > <=FLIP=>
> > > > 0.50000...

>
> > > >  T(x,y) = FLIP(L(x,y))
> > > >  +---------------->
> > > >  | 0. 7 6 5 4 3 2 ..
> > > >  | 0. 0 1 2 3 4 4 ..
> > > >  | 0. 8 7 6 8 7 6 ..
> > > >  | 0. 0 1 0 1 0 1 ..
> > > >  | 0. 3 4 3 4 3 4 ..
> > > >  | 0. 4 3 4 3 4 3 ..
> > > >  |
> > > >  v

>
> > > > NOW  DIAGONAL(T)  is supposedly proven absent from L
>
> > > > 0.716133..  NOT COUNTED??
>
> > > > yet  if L is the Computable Reals  then
>
> > > > T=L
>
> > > > PROOF:  For every computable real there is another computable real for
> > > > all digit changing functions.

>
> > > > which proves the DIGIT FLIP Operation is a NULL OPERATION
> > > > THERFORE  ANTIDIAGONAL(L) is no more provably absent from L than
> > > > DIAGONAL(L).

>
> > > > QED
>
> > > > Herc
>
> > > Not even as near to being right as WM is, and WM isn't near at all.
> > > --

>
> > then post your correction FOOL!
>
> > Herc
> > --
> > P: If Halts(P) Then Loop Else Halt.
> > is obviously a paradoxical program if Halts() exists.

>
> > BUT IF IT WEREN'T NAMED P then it might not be:
>
> > Q: If Halts(P) Then Loop Else Halt.
> > is NOT paradoxical.

>
> > ~ GEORGE GREEN (sci.logic)
>
> Gray,
>
> It's one thing to prove that said item isn't absent, another to prove
> it's there.
>
> I suggest you inspect EF, the antidiagonal is at the end.
>
> This is as I proved EF and compositions of EF unique among functions
> re the otherwise-uncountability of reals via functions from naturals,
> and as well that the range satisfies properties of being the unit
> interval of real numbers.
>
> Then re Halts() I'd review the discussion of this last year on "Sketch
> of a Disproof of Rice's Theorem."
>
> Regards,
>
> Ross Finlayson
>


one must consider the audience Virgil!

SWAPPING DIGITS DOWN THE DIAGONAL

seems to be the only mathematics he can grasp!

"ITS DIFFERENT! ITS DIFFERENT! 'COS ITS
DEFINED THAT WAY!" ~ VIRGIL

"MORE_THAN_INFINITY REALS IN ANY LINE SEGMENT!"
~ VIRGIL

X>oo
~ VIRGIL

Yet he seems incapable of using his beloved proof on this (semi-
decidable) computable set of

All - Subsets - Of - N.


TM1(1) Halts => 1 e POWERSET_1
TM1(2) Loops => 2 !e POWERSET_1
TM1(3) Halts => 3 e POWERSET_1
TM2(1) Halts => 1 e POWERSET_2
TM2(2) Halts => 2 e POWERSET_2
TM2(3) Halts => 3 e POWERSET_2
...

POWERSET(N) = { {1,3,...} {1,2,3...} ... }
1 <=> {1,3,..}
2 <=> {1,2,3,...}
...


---------------

With no end in sight, perhaps if Virgil could SEE

the futility of changing the Diagonal..

T(x,y)
+---------------->
| 0. 6 6 6 6 5 5 ..
| 0. 5 5 5 5 6 6 ..
| 0. 6 6 6 6 6 6 ..
| 0. 5 5 5 5 5 5 ..
| 0. 5 6 5 6 5 6 ..
| 0. 6 5 6 5 6 5 ..
|
v

then it's trivial to see the CONSTRUCTABLE PATHS


T(x,y)
+---------------->
| 0. X X X X X X ..
| 0. 5 X X X X X..
| 0. X 6 X X X X ..
| 0. X X X X 5 X ..
| 0. X X X 6 X X ..
| 0. X X 6 X X X ..
|
v

0.56665 ...

are just as easily constructed from the Original L!

I.E CHANGING DIGITS DOES NOTHING to an infinite SET
except change which Permutation you're looking at

It's safe to assume Virgil is an idiot with no mathematical grasp to
apply anything on his own, he's just stuck on arguing via text book
parroting and cannot engage the topic at all. Explaining any new
insight is certainly lost on him he is in his own world like George
Greene with their EXIST(SZ) SZ>oo

Herc




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