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A "WEAK DIAGONAL" - A WEAKER VERSION OF CANTOR'S PROOF
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Graham Cooper
Nov 25, 2011, 3:05:07 PM11/25/11
to
You can get the same result using an equivalent technique as the
DIAGONAL -> ANTIDIAGONAL method in Cantor's Proof with a wDIAGONAL
that can use a single digit position to cover/match multiple rows in
the List.
This is all you need to construct a wDIAGONAL.
r1 has a common digit to wDIAGONAL anywhere in it's expansion
r2 has a common digit to wDIAGONAL ...
r3 has a common digit to wDIAGONAL ...
...
Before I post my critique of Cantor's Proof, which will only be
ignored..
can anyone confirm that ANTI(wDIAGONAL) as defined above
will be #missing from the List r1, r2, r3,... ?
# according to conventional theory
not all digits of wDIAGONAL need to be specified
Herc
DIAGONAL -> ANTIDIAGONAL method in Cantor's Proof with a wDIAGONAL
that can use a single digit position to cover/match multiple rows in
the List.
This is all you need to construct a wDIAGONAL.
r1 has a common digit to wDIAGONAL anywhere in it's expansion
r2 has a common digit to wDIAGONAL ...
r3 has a common digit to wDIAGONAL ...
...
Before I post my critique of Cantor's Proof, which will only be
ignored..
can anyone confirm that ANTI(wDIAGONAL) as defined above
will be #missing from the List r1, r2, r3,... ?
# according to conventional theory
not all digits of wDIAGONAL need to be specified
Herc
William Hughes
Nov 25, 2011, 3:24:54 PM11/25/11
to
On Nov 25, 4:05 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> You can get the same result using an equivalent technique as the
>
> DIAGONAL -> ANTIDIAGONAL method in Cantor's Proof with a wDIAGONAL
> that can use a single digit position to cover/match multiple rows in
> the List.
>
> This is all you need to construct a wDIAGONAL.
>
> r1 has a common digit to wDIAGONAL anywhere in it's expansion
> r2 has a common digit to wDIAGONAL ...
> r3 has a common digit to wDIAGONAL ...
> ...
>
> Before I post my critique of Cantor's Proof, which will only be
> ignored..
>
> can anyone confirm that ANTI(wDIAGONAL) as defined above
> will be #missing from the List r1, r2, r3,... ?
Yes, if you specify each digit of a wDIAGONAL then ANTI(wDIAGONAL)
> You can get the same result using an equivalent technique as the
>
> DIAGONAL -> ANTIDIAGONAL method in Cantor's Proof with a wDIAGONAL
> that can use a single digit position to cover/match multiple rows in
> the List.
>
> This is all you need to construct a wDIAGONAL.
>
> r1 has a common digit to wDIAGONAL anywhere in it's expansion
> r2 has a common digit to wDIAGONAL ...
> r3 has a common digit to wDIAGONAL ...
> ...
>
> Before I post my critique of Cantor's Proof, which will only be
> ignored..
>
> can anyone confirm that ANTI(wDIAGONAL) as defined above
> will be #missing from the List r1, r2, r3,... ?
will
be a real number that is not in the list.
If you do not specify each digit of a wDIAGONAL,
then ANTI(wDIAGONAL) is not a real number.
Graham Cooper
Nov 25, 2011, 5:04:17 PM11/25/11
to
LIST
0.02468...
0.12345...
0.22222...
0.32198...
0.82828...
0.33333...
0.44444...
0.12345...
...
LIST
0.[0]2468...
0.1[2]345...
0.2[2]222...
0.3[2]198...
0.8[2]828...
0.33[3]33...
0.444[4]4...
0.1234[5]...
...
wDIAGONAL = 0.02345...
missing real = 0.57890...
The 1st digit of mr =/= r1
the 2nd digit of mr =/= r2
the 3rd digit of mr =/= r3
...
You only need a wDIAGONAL to prove the same result as Cantor's Proof.
THEOREM1: Cantor's Main Diagonal is a special type of wDIAGONAL
Herc
Graham Cooper
Nov 25, 2011, 9:23:01 PM11/25/11
to prize.p...@clay.org, gen...@clay.org, graham...@gmail.com
On Nov 26, 11:00 am, William Hughes <wpihug...@gmail.com> wrote:
> On Nov 25, 6:24 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > On Nov 26, 8:11 am, William Hughes <wpihug...@gmail.com> wrote:
> > > Actually the third line should read
>
> > > the 2rd digit of mr =/= r3
>
> > > Have I pulled enough teeth yet?
>
> > E(d): r1_d = wDIAGONAL_d
>
> Note that this puts a constraint on wDIAGONAL
> We cannot have for all n in N, wDIAGONAL_n =/= r1_n
Right! This also holds in Cantor's proof for the MainDiagonal.
>
> > E(e): r2_e = wDIAGONAL_e
> > E(f): r3_f = wDIAGONAL_f
> > ...
>
> > A(o): wDIAGONAL_o = 0 OTHERWISE
>
> Clearly I have not pulled enough teeth yet.
> Please get to the point.
Let's call THE wDIAGONAL PROOF the following deduction sequence:
[1] Given any list of reals: r1, r2, r3...
[2] Construct a wDIAGONAL
E(d): r1_d = wDIAGONAL_d
E(e): r2_e = wDIAGONAL_e
E(f): r3_f = wDIAGONAL_f
...
A(o): wDIAGONAL_o = 0 OTHERWISE
[3] Construct ANTI(wDIAGONAL) .... add 5 mod 10 to each digit
[4]
E(d): r1_d =/= ANTI(wDIAGONAL)_d
E(e): r2_e =/= ANTI(wDIAGONAL)_e
E(f): r3_f =/= ANTI(wDIAGONAL)_f
...
[5] A(n): rn =/= ANTI(wDIAGONAL)
[6] ANTI(wDIAGONAL) is not in the list r1, r2, r3...
[7] The list r1, r2, r3... is incomplete
[8] By Universal Generalisation, since rn is any arbitrary real
no list of reals can be the complete set of reals.
OK 1 more step if you agree with the above proof!
Herc
> On Nov 25, 6:24 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > On Nov 26, 8:11 am, William Hughes <wpihug...@gmail.com> wrote:
>
> > > the 2rd digit of mr =/= r3
>
> > > > You only need a wDIAGONAL to prove the same result as Cantor's Proof.
>
> > > Yep (but you do need every digit specified)
> > > > You only need a wDIAGONAL to prove the same result as Cantor's Proof.
>
>
> > > > THEOREM1: Cantor's Main Diagonal is a special type of wDIAGONAL
>
> > > Yes, in particular every element of the main diagonal is specified.
> > > > THEOREM1: Cantor's Main Diagonal is a special type of wDIAGONAL
>
>
> > > Have I pulled enough teeth yet?
>
> > E(d): r1_d = wDIAGONAL_d
>
> Note that this puts a constraint on wDIAGONAL
> We cannot have for all n in N, wDIAGONAL_n =/= r1_n
Right! This also holds in Cantor's proof for the MainDiagonal.
>
> > E(e): r2_e = wDIAGONAL_e
> > E(f): r3_f = wDIAGONAL_f
> > ...
>
> > A(o): wDIAGONAL_o = 0 OTHERWISE
>
> Clearly I have not pulled enough teeth yet.
> Please get to the point.
Let's call THE wDIAGONAL PROOF the following deduction sequence:
[1] Given any list of reals: r1, r2, r3...
[2] Construct a wDIAGONAL
E(d): r1_d = wDIAGONAL_d
E(e): r2_e = wDIAGONAL_e
E(f): r3_f = wDIAGONAL_f
...
A(o): wDIAGONAL_o = 0 OTHERWISE
[3] Construct ANTI(wDIAGONAL) .... add 5 mod 10 to each digit
[4]
E(d): r1_d =/= ANTI(wDIAGONAL)_d
E(e): r2_e =/= ANTI(wDIAGONAL)_e
E(f): r3_f =/= ANTI(wDIAGONAL)_f
...
[5] A(n): rn =/= ANTI(wDIAGONAL)
[6] ANTI(wDIAGONAL) is not in the list r1, r2, r3...
[7] The list r1, r2, r3... is incomplete
[8] By Universal Generalisation, since rn is any arbitrary real
no list of reals can be the complete set of reals.
OK 1 more step if you agree with the above proof!
Herc
William Hughes
Nov 25, 2011, 9:42:52 PM11/25/11
to
as there are certain strings (that depend on the list, so given
two different lists, there are different possible wDIAGONAL's)
that cannot be the wDIAGONAL I agree with the above proof.
Graham Cooper
Nov 25, 2011, 10:28:59 PM11/25/11
to prize.p...@claymath.org
On Nov 26, 12:42 pm, William Hughes <wpihug...@gmail.com> wrote:
> On Nov 25, 10:23 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> >
> > THE wDIAGONAL PROOF
> On Nov 25, 10:23 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> >
>
> > [1] Given any list of reals: r1, r2, r3...
>
> > [2] Construct a wDIAGONAL
>
> > E(d): r1_d = wDIAGONAL_d
> > E(e): r2_e = wDIAGONAL_e
> > E(f): r3_f = wDIAGONAL_f
> > ...
>
> > A(o): wDIAGONAL_o = 0 OTHERWISE
>
> > [3] Construct ANTI(wDIAGONAL) .... add 5 mod 10 to each digit
>
> > [4]
>
> > E(d): r1_d =/= ANTI(wDIAGONAL)_d
> > E(e): r2_e =/= ANTI(wDIAGONAL)_e
> > E(f): r3_f =/= ANTI(wDIAGONAL)_f
> > ...
>
> > [5] A(n): rn =/= ANTI(wDIAGONAL)
>
> > [6] ANTI(wDIAGONAL) is not in the list r1, r2, r3...
>
> > [7] The list r1, r2, r3... is incomplete
>
> > [8] By Universal Generalisation, since rn is any arbitrary real
> > no list of reals can be the complete set of reals.
>
> > OK 1 more step if you agree with the above proof!
>
> > Herc
>
> Noting that the wDIAGONAL constructed in step 2 is not arbitrary
> as there are certain strings (that depend on the list, so given
> two different lists, there are different possible wDIAGONAL's)
> that cannot be the wDIAGONAL I agree with the above proof.
Every non-trivial# List of Reals has the wDIAGONAL 0.0000...
> > [1] Given any list of reals: r1, r2, r3...
>
> > [2] Construct a wDIAGONAL
>
> > E(d): r1_d = wDIAGONAL_d
> > E(e): r2_e = wDIAGONAL_e
> > E(f): r3_f = wDIAGONAL_f
> > ...
>
> > A(o): wDIAGONAL_o = 0 OTHERWISE
>
> > [3] Construct ANTI(wDIAGONAL) .... add 5 mod 10 to each digit
>
> > [4]
>
> > E(d): r1_d =/= ANTI(wDIAGONAL)_d
> > E(e): r2_e =/= ANTI(wDIAGONAL)_e
> > E(f): r3_f =/= ANTI(wDIAGONAL)_f
> > ...
>
> > [5] A(n): rn =/= ANTI(wDIAGONAL)
>
> > [6] ANTI(wDIAGONAL) is not in the list r1, r2, r3...
>
> > [7] The list r1, r2, r3... is incomplete
>
> > [8] By Universal Generalisation, since rn is any arbitrary real
> > no list of reals can be the complete set of reals.
>
> > OK 1 more step if you agree with the above proof!
>
> > Herc
>
> Noting that the wDIAGONAL constructed in step 2 is not arbitrary
> as there are certain strings (that depend on the list, so given
> two different lists, there are different possible wDIAGONAL's)
> that cannot be the wDIAGONAL I agree with the above proof.
or 0.1000...
or 0.2000...
or 0.3000...
or 0.4000...
or 0.5000...
or 0.6000...
or 0.7000...
or 0.8000...
or 0.9000...
#no digit position in the list has a limited amount of any digit 0..9
000... can be replaced with any arbitrary real.
So at most 10 guesses are required to find a wDIAGONAL for any List
without inspection of the List.
Herc
Graham Cooper
Nov 25, 2011, 10:38:07 PM11/25/11
to
I only thought of wDIAGONALS this morning.
a list with 0.222.. 0.333.. 0.444..
would not fit any of those 10 wDIAGONALS.
More later.. perhaps..
Herc
Graham Cooper
Nov 25, 2011, 11:19:52 PM11/25/11
to
On Nov 26, 2:03 pm, William Hughes <wpihug...@gmail.com> wrote:
> If you want to show a string S a DIAGONAL
> or a wDIAGONAL you have to do two things.
>
> (i) For each position k, find a row m such that
> the kth digit of row m = S_k
>
> (ii) Show that every row is used.
>
> From the start your problem has been that you always concentrate
> on (i) and forget about (ii). One way of looking
> at the diagonal argument is that it is a clever way
> of exploiting (ii). (ii) is in fact more important
> than (i)
>
> - William Hughes
(1) and (ii) are kiddy nonsense.
When I have a spare $100/wk I'll send 2,000 amateur mathematicians a
day to
http://matheology.com
with Google Adwords.
Any year 8 advanced math kid can see the copious flaws in the AD
proof.
There are INFINITE possible rows (of infinite possible selections for
each of 0,1,2,3,4,5,6,7,8,9)
for AD_1
yet somehow you believe the fact R is so big explains all the
inconsistencies with the proof.
Yet none of you admit
SIZE(R) > oo
and none of you can construct an actual anti-diagonal to 10 of my
example lists.
You're in a dream Will, you're not using reason, you don't do the
examples then your theory is unsupported.
Herc
> or a wDIAGONAL you have to do two things.
>
> (i) For each position k, find a row m such that
> the kth digit of row m = S_k
>
> (ii) Show that every row is used.
>
> From the start your problem has been that you always concentrate
> on (i) and forget about (ii). One way of looking
> at the diagonal argument is that it is a clever way
> of exploiting (ii). (ii) is in fact more important
> than (i)
>
> - William Hughes
(1) and (ii) are kiddy nonsense.
When I have a spare $100/wk I'll send 2,000 amateur mathematicians a
day to
http://matheology.com
with Google Adwords.
Any year 8 advanced math kid can see the copious flaws in the AD
proof.
There are INFINITE possible rows (of infinite possible selections for
each of 0,1,2,3,4,5,6,7,8,9)
for AD_1
yet somehow you believe the fact R is so big explains all the
inconsistencies with the proof.
Yet none of you admit
SIZE(R) > oo
and none of you can construct an actual anti-diagonal to 10 of my
example lists.
You're in a dream Will, you're not using reason, you don't do the
examples then your theory is unsupported.
Herc
William Hughes
Nov 26, 2011, 12:15:22 AM11/26/11
to
Graham Cooper
Nov 26, 2011, 12:52:06 AM11/26/11
to
The fact any L1' and L2' have the SAME DIAGONAL is proof outright that
the diagonal is independent of the List.
You just copout of the fact any random digit string can be fitted to
any list with the STUPID argument that with P=0 the random diagonal
suggestion will equal an anti-row.
It's P=0 that any row will be perpetually shuffled OFF THE LIST.
but that's your argument!
And it's defeated by the 2 List independence proof.
That works FOR ALL LISTS.
You claim the diagonal is DEPENDENT on EACH PARTICULAR LIST
and it CLEARLY IS NOT!
D(L1') = D(L2') for ANY 2 ARBITRARY LISTS!
THEN you put your blinkers on AGAIN... for the 10TH TIME RUNNING...
and none of you can admit the random walk flipped is just another
random walk!
0.0100010..
0.1010000..
0.1111000..
0.0001100..
..
0. [0] 100010 ..
0. 100 [1] 000..
0. 1 [1] 11000..
0. 00 [0] 1100.. ----> 0.0101...
..
0. 010 [0] 010.. ----> 0.1010...
0. [1] 010000 ..
0. 11 [1] 1000..
0. 0 [0] 01100..
..
OH WHOOPEE DEE!
YOU CHANGED THE DIAGONAL!
---
EVEN GOD THINKS YOUR A BABY...
YOU DON'T KNOW HOW TO CHANGE A DIAPER #numerology = DIAGONAL
Herc
Graham Cooper
Nov 26, 2011, 1:23:23 AM11/26/11
to
>
> YOU DON'T KNOW HOW TO CHANGE A DIAPER #numerology = DIAGONAL
>
> Herc
Next time you CHANGE A DIAGONAL
> YOU DON'T KNOW HOW TO CHANGE A DIAPER #numerology = DIAGONAL
>
> Herc
DON'T FORGET TO GET A FRESH NEW DIAGONAL! (of the same list)
Herc
Message has been deleted
Graham Cooper
Nov 26, 2011, 4:27:42 PM11/26/11
to
On Nov 27, 6:43 am, Robert James <ElBongHuf...@Diabetics.org> wrote:
> On Fri, 25 Nov 2011 22:23:23 -0800; I imposed a declaration in opposition
> to Graham Cooper's motion to modify THE PRELIMINARY INJUNCTION in support
> of the CROSS MOTION TO VACATE THE PRELIMINARY INJUNCTION. So noted by the
> Federal Court of Usenet Justice proceeding preliminary declaration,
> 5596333d-a6bf-4dec-b550-d4c54b49d...@z22g2000prd.googlegroups.com:
> What does you diagonal changing have to do with A26, Herc?
>
I couldn't get Sunny Leone to pose for you so I thought you'd like
some free maths lessons!
Herc
> On Fri, 25 Nov 2011 22:23:23 -0800; I imposed a declaration in opposition
> to Graham Cooper's motion to modify THE PRELIMINARY INJUNCTION in support
> of the CROSS MOTION TO VACATE THE PRELIMINARY INJUNCTION. So noted by the
> Federal Court of Usenet Justice proceeding preliminary declaration,
> 5596333d-a6bf-4dec-b550-d4c54b49d...@z22g2000prd.googlegroups.com:
>
I couldn't get Sunny Leone to pose for you so I thought you'd like
some free maths lessons!
Herc
Message has been deleted
Graham Cooper
Nov 26, 2011, 5:04:58 PM11/26/11
to
On Nov 27, 7:38 am, Robert James <ElBongHuf...@Diabetics.org> wrote:
> On Sat, 26 Nov 2011 13:27:42 -0800; I imposed a declaration in opposition
> That's why my *nix OS comes with a free calculator, so I don't NEED
> lessons. But I can't flap to a calculator that worked out what 7342 plus
> 666 is. I need real 8008ies! Anywayzzzzzz, the fact you failed my quest
> just goes to prove you have no cam whores, and you never completed a D&D
> adventure in your life. Plus it was *Sunny Lane* I demanded, not that
> Indian half bread Sunny Leone!
>
I thought she looked different!
Yeh Sunny Lane is amazing, make a great character actress very
expressive face. 8^)
I must have mixed them up, been negotiating $5 Million sale for
CamGirls.com with VIVID ENTERTAINMENT all week, the company behind
Leone.
Penthouse owns Cams.com
Manwin owns Webcams.com
Vivid are very interested in my CamGirls.com!
Herc
--
http://CAMGIRLS.com
> On Sat, 26 Nov 2011 13:27:42 -0800; I imposed a declaration in opposition
> to Graham Cooper's motion to modify THE PRELIMINARY INJUNCTION in support
> of the CROSS MOTION TO VACATE THE PRELIMINARY INJUNCTION. So noted by the
> Federal Court of Usenet Justice proceeding preliminary declaration,
> d70d2d28-c21b-4449-898b-5d24ab670...@n22g2000prh.googlegroups.com:
> of the CROSS MOTION TO VACATE THE PRELIMINARY INJUNCTION. So noted by the
> Federal Court of Usenet Justice proceeding preliminary declaration,
> lessons. But I can't flap to a calculator that worked out what 7342 plus
> 666 is. I need real 8008ies! Anywayzzzzzz, the fact you failed my quest
> just goes to prove you have no cam whores, and you never completed a D&D
> adventure in your life. Plus it was *Sunny Lane* I demanded, not that
> Indian half bread Sunny Leone!
>
I thought she looked different!
Yeh Sunny Lane is amazing, make a great character actress very
expressive face. 8^)
I must have mixed them up, been negotiating $5 Million sale for
CamGirls.com with VIVID ENTERTAINMENT all week, the company behind
Leone.
Penthouse owns Cams.com
Manwin owns Webcams.com
Vivid are very interested in my CamGirls.com!
Herc
--
http://CAMGIRLS.com
Message has been deleted
Graham Cooper
Nov 26, 2011, 7:18:58 PM11/26/11
to
On Nov 27, 9:47 am, Robert James <ElBongHuf...@Diabetics.org> wrote:
> On Sat, 26 Nov 2011 14:04:58 -0800; I imposed a declaration in opposition
> herd the name "Leone".
> strange, yet I have not seen her recently since she wanted to get married.
>
> That's right Herc, first you start bitching about needing an extra $100 a
> week; and now apparently your working on a multi-million dollar deal on a
> site you don't own and are only an affiliate of... okay!
>
Ah no! Totally superfluous spending $100/week on Google Ads to my
MATHS SITE!
http://Matheology.com
Slightly different scenerio to being short on Ca$h!
Herc
--
http://CamGirls.com
> On Sat, 26 Nov 2011 14:04:58 -0800; I imposed a declaration in opposition
> to Graham Cooper's motion to modify THE PRELIMINARY INJUNCTION in support
> of the CROSS MOTION TO VACATE THE PRELIMINARY INJUNCTION. So noted by the
> Federal Court of Usenet Justice proceeding preliminary declaration,
> b3c6e430-bddf-49ff-bedc-7515d1cfe...@h37g2000pri.googlegroups.com:
> of the CROSS MOTION TO VACATE THE PRELIMINARY INJUNCTION. So noted by the
> Federal Court of Usenet Justice proceeding preliminary declaration,
>
> > I thought she looked different!
>
> And I thought my package twitched to the wrong side of my pants when I
> > I thought she looked different!
>
> herd the name "Leone".
>
> > Yeh Sunny Lane is amazing, make a great character actress very
> > expressive face. 8^)
>
> Well since she got some unneeded plastic work on her face she looks a bit
> > Yeh Sunny Lane is amazing, make a great character actress very
> > expressive face. 8^)
>
> strange, yet I have not seen her recently since she wanted to get married.
>
> > I must have mixed them up, been negotiating $5 Million sale for
> > CamGirls.com with VIVID ENTERTAINMENT all week, the company behind
> > Leone. Vivid are very interested in my CamGirls.com!
> > I must have mixed them up, been negotiating $5 Million sale for
> > CamGirls.com with VIVID ENTERTAINMENT all week, the company behind
>
> That's right Herc, first you start bitching about needing an extra $100 a
> week; and now apparently your working on a multi-million dollar deal on a
> site you don't own and are only an affiliate of... okay!
>
Ah no! Totally superfluous spending $100/week on Google Ads to my
MATHS SITE!
http://Matheology.com
Slightly different scenerio to being short on Ca$h!
Herc
--
http://CamGirls.com
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