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6 QUESTIONS That No LOGICIAN Can Answer!!!!!!

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Graham Cooper

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Jul 12, 2012, 7:54:01 PM7/12/12
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Q1
What are 2 missing reals from this List using Cantor's method?

LIST
0.100..
0.000..
0.001..
..
LIST'
0.000.. (Old Row 2)
0.100.. (Old Row 1)
0.001..
..

*****************************************************
*****************************************************


Q2
Why is this GODEL NUMBER BARRED from a theory?

20032104211598200321042105
a00(a10,a11)=!a00(a10,a10)
x e y <-> NOT(x e x)
RUSSELL'S SET

*****************************************************
*****************************************************


Q3
And this GODEL NUMBER is a prerequisite of all theories > PA?

8203215
!a0(a1)
NOT(PROOF(GN#))
GODEL'S STATEMENT

*****************************************************
*****************************************************


Q4
How can there be uncountable many GODEL NUMBERS like this?

20130415
a01(0,1)
MIDPOINT(0,1)
A CHOICE FUNCTION

*****************************************************
*****************************************************


Q5
Which 1 of these does not hold?

a) N <-BIJECTS-> GODEL NUMBERS
b) GODEL NUMBERS <-BIJECT-> FUNCTIONS
c) CHOICE FUNCTIONS <-BIJECT-> SETS
d) |SETS| > |N|

Q6
Does this Anti-Diagonal Method produce any unique digit segment not
listed?

AD METHOD
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> ... >
....

G. Cooper (BInfTech)
--

http://tinyURL.com/BLUEPRINTS-THEOREM
http://tinyURL.com/BLUEPRINTS-TURING
http://tinyURL.com/BLUEPRINTS-GODEL
http://tinyURL.com/BLUEPRINTS-PROOF
http://tinyURL.com/BLUEPRINTS-MATHS
http://tinyURL.com/BLUEPRINTS-LOGIC
http://tinyURL.com/BLUEPRINTS-REAL
http://tinyURL.com/BLUEPRINTS-SETS
http://tinyURL.com/BLUEPRINTS-HALT
http://tinyURL.com/BLUEPRINTS-P-NP
http://tinyURL.com/BLUEPRINTS-MIND
http://tinyURL.com/BLUEPRINTS-GUT

The 12 Feats Of |-|erc

William Hughes

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Aug 17, 2012, 7:53:25 PM8/17/12
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On Jul 12, 8:54 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> Q1
> What are 2 missing reals from this List using Cantor's method?
>
> LIST
> 0.100..
> 0.000..
> 0.001..

A real that begins 0.010...
(also missing from LIST')

> ..
> LIST'
> 0.000..    (Old Row 2)
> 0.100..    (Old Row 1)
> 0.001..
> ..
>

A real that begins 0.110..
(also missing from LIST).


Graham Cooper

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Aug 17, 2012, 10:17:03 PM8/17/12
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So just by examining

LIST
0.100..
0.000..
0.001..
..


you can calculate

0.010..
0.110..

are BOTH missing?

[X] stands for NOT X.

LIST
0.[1]00..
0.0[0]0..
0.00[1]..
..
==> 0.010..

LIST
0.1[0]0..
0.[0]00..
0.00[1]..
..
==> 0.110..

because you can flip the first digit (of some row)
and flip the second digit (of some row)
(without missing any rows)?

So some real beginning

0.000...
0.001...
0.010...
0.011...
0.100...
0.101...
0.110...
0.111...

are all missing too right?


Herc

William Hughes

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Aug 17, 2012, 10:49:25 PM8/17/12
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Indeed (in the sense that at least two real numbers
one starting .010 and one starting .110 are missing)
Yes, (although you have not shown this
for all cases, eg. 0.100...)
Note however that there are reals
starting 0.100... 0.000... and 0.001..
that are not missing and are not the antidiagonal
of the main diagonal of any *permutation* of the list.


Graham Cooper

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Aug 17, 2012, 11:05:02 PM8/17/12
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what list?

This is an infinite list

LIST
0.100..
0.000..
0.001..
..


with more than 3 prefixes.

So if we examine the list further

LIST
0.100..
0.000..
0.001..
0.111..
0.000..
0.000..
..

all 8 prefixes are DIAGONALS of some permutation and ANTI-DIAGONALS of
some permutation.

0.000... IS A DIAGONAL
0.000... IS AN ANTIDIAGONAL

0.001... IS A DIAGONAL
0.001... IS AN ANTIDIAGONAL
...
0.111... IS A DIAGONAL
0.111... IS AN ANTIDIAGONAL

That can be deduced just by inspecting the list.

LIST
0.100..
0.000..
0.001..
0.111..
0.000..
0.000..
..

Herc
--
http://microPROLOG.com

[mP]-FACT ADDED
[mP]-[happy Dude] if [rich Dude].

William Hughes

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Aug 17, 2012, 11:26:54 PM8/17/12
to
On Aug 18, 12:05 am, Graham Cooper <grahamcoop...@gmail.com> wrote:

<snip>

> all 8 prefixes are DIAGONALS of some permutation and ANTI-DIAGONALS of
> some permutation.
>

> 0.000... IS A DIAGONAL

Yes there is a real number starting 0.000... which is a diagonal
of some permutation.

> 0.000... IS AN ANTIDIAGONAL

Yes there is a real number starting 0.000... which is an antidiagonal
of some permutation.

Note there is also a real number starting 0.000 which is not the
antidiagonal
of any permutation of the list.

Graham Cooper

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Aug 17, 2012, 11:30:46 PM8/17/12
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On Aug 18, 1:26 pm, William Hughes <wpihug...@gmail.com> wrote:
> Note there is also a real number starting 0.000 which is not the
> antidiagonal
> of any permutation of the list.

Is that true for every digit of this mystery number 0.000..?

LIST
0.100..
0.000..
0.001..
0.111..
0.000.. could be this one?
0.000.. might be this one??
..


Herc

William Hughes

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Aug 17, 2012, 11:44:08 PM8/17/12
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On Aug 18, 12:30 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Aug 18, 1:26 pm, William Hughes <wpihug...@gmail.com> wrote:
>
> > Note there is also a real number starting 0.000 which is not the
> > antidiagonal
> > of any permutation of the list.
>
> Is that true for every digit of this mystery number 0.000..?

Certainly, for any digit, x_i, of the "mystery number"
you can find a permutation, p(x_i), such that the digit
is in the correct place in the antidiagonal of the
permutation p(x_i).
However, you cannot find one permutation, q, such that *all*
the digits of the mystery number are in the correct place
in the antidiagonal of the permutation q.



Virgil

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Aug 17, 2012, 11:57:19 PM8/17/12
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In article
<6f938a6b-0a8c-4897...@f4g2000pbq.googlegroups.com>,
For any n in N, any list of n n-place binaries is incomplete.

And, as it happens, any list of |N| |N|-place binaries is incomplete.
--


Virgil

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Aug 17, 2012, 11:59:15 PM8/17/12
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Graham Cooper

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Aug 18, 2012, 12:11:48 AM8/18/12
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On Aug 18, 1:59 pm, Virgil <vir...@ligriv.com> wrote:
> In article
> <827cd15d-cac1-451a-b16f-13298c918...@k9g2000pbr.googlegroups.com>,
>  Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > On Aug 18, 1:26 pm, William Hughes <wpihug...@gmail.com> wrote:
> > > Note there is also a real number starting 0.000 which is not the
> > > antidiagonal
> > > of any permutation of the list.
>
> > Is that true for every digit of this mystery number 0.000..?
>
> > LIST
> > 0.100..
> > 0.000..
> > 0.001..
> > 0.111..
> > 0.000..    could be this one?
> > 0.000..    might be this one??
> > ..
>
> > Herc
>
> For any n in N, any list of n n-place binaries is incomplete.
>
> And, as it happens, any list of |N| |N|-place binaries is incomplete.
> --

You made 2 statements when only 1 was required.

Herc

Graham Cooper

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Aug 18, 2012, 12:10:56 AM8/18/12
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So after seeing 0.000.. *IS* in the list..

there is a real number starting 0.000 which is not the
antidiagonal of any permutation of the list.

so for ANY-REAL-IN-THE-LIST
THAT-REAL is not the antidiagonal

Why is that?

Self referential evident truth?
Extra reals that cannot be listed?

Herc

William Hughes

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Aug 18, 2012, 12:47:49 AM8/18/12
to
On Aug 18, 1:10 am, Graham Cooper <grahamcoop...@gmail.com> wrote:

> So after seeing 0.000..  *IS* in the list..
>
>   there is a real number starting 0.000 which is not the
>   antidiagonal of any permutation of the list.
>
> so for ANY-REAL-IN-THE-LIST
> THAT-REAL is not the antidiagonal
>
> Why is that?

Because ANY-REAL-IN-THE-LIST must be at some
row, say i, and any permutation, q, must put
row i somewhere, thus ANY-REAL-IN-THE-LIST
is not the antidiagonal of permutation q,



Virgil

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Aug 18, 2012, 1:40:20 AM8/18/12
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In article
<764a086a-e970-4301...@oq8g2000pbc.googlegroups.com>,
Just logorrhea, I guess!
--


Graham Cooper

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Aug 18, 2012, 4:27:16 AM8/18/12
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So ANY-REAL-IN-THE-LIST
is not the anti-diagonal of the SET.

William Hughes

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Aug 18, 2012, 8:12:35 AM8/18/12
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On Aug 18, 5:27 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Aug 18, 2:47 pm, William Hughes <wpihug...@gmail.com> wrote:
>
>
>
>
>
>
>
>
>
> > On Aug 18, 1:10 am, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > > So after seeing 0.000..  *IS* in the list..
>
> > >   there is a real number starting 0.000 which is not the
> > >   antidiagonal of any permutation of the list.
>
> > > so for ANY-REAL-IN-THE-LIST
> > > THAT-REAL is not the antidiagonal
>
> > > Why is that?
>
> > Because ANY-REAL-IN-THE-LIST must be at some
> > row, say i, and any permutation, q, must put
> > row i somewhere, thus ANY-REAL-IN-THE-LIST
> > is not the antidiagonal of permutation q,
>
> So ANY-REAL-IN-THE-LIST
> is not the anti-diagonal of the SET.
>
> Why is that?

Because any anti-diagonal of the SET
must be the anti-diagonal of some permutation
q.

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