CANTOR DISPROOF <<<<<<<<<<<<<<<< [Math]

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From: Marshall on 23 Jun 2010 23:06

On Jun 23, 2:30 pm, Transfer Principle <lwal...(a)lausd.net> wrote:
> More often than
> not, one abuses the word "troll" to mean someone with whom one
> disagrees, and thus "feeding the trolls" means giving any
> attention to the poster with the alternate viewpoint.

Bullshit.

Marshall

From: Graham Cooper on 23 Jun 2010 23:11

On Jun 24, 1:06 pm, Marshall <marshall.spi...(a)gmail.com> wrote:
> On Jun 23, 2:30 pm, Transfer Principle <lwal...(a)lausd.net> wrote:
>
> > More often than
> > not, one abuses the word "troll" to mean someone with whom one
> > disagrees, and thus "feeding the trolls" means giving any
> > attention to the poster with the alternate viewpoint.
>
> Bullshit.
>
> Marshall

Tis the proper term to express an alternate viewpoint!

Herc

From: Graham Cooper on 23 Jun 2010 23:23

On Jun 24, 12:36 pm, Graham Cooper <grahamcoop...(a)gmail.com> wrote:
> On Jun 24, 12:33 pm, Graham Cooper <grahamcoop...(a)gmail.com> wrote:
>
>
>
>
>
> > On Jun 24, 12:12 pm, Sylvia Else <syl...(a)not.here.invalid> wrote:
>
> > > On 24/06/2010 11:41 AM, Graham Cooper wrote:
>
> > > > On Jun 24, 11:28 am, Sylvia Else<syl...(a)not.here.invalid> wrote:
> > > >> On 24/06/2010 11:17 AM, Graham Cooper wrote:
>
> > > >>> On Jun 24, 11:12 am, Graham Cooper<grahamcoop...(a)gmail.com> wrote:
> > > >>>> On Jun 24, 10:20 am, Sylvia Else<syl...(a)not.here.invalid> wrote:
>
> > > >>>>> On 24/06/2010 12:01 AM, Graham Cooper wrote:
>
> > > >>>>>> On Jun 23, 11:45 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
> > > >>>>>>> On 23/06/2010 11:04 PM, Graham Cooper wrote:
>
> > > >>>>>>>> On Jun 23, 10:02 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
> > > >>>>>>>>> On 23/06/2010 8:28 PM, Graham Cooper wrote:
>
> > > >>>>>>>>>> On Jun 23, 8:12 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
> > > >>>>>>>>>>> On 23/06/2010 7:50 PM, Graham Cooper wrote:
>
> > > >>>>>>>>>>>> On Jun 23, 7:41 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
> > > >>>>>>>>>>>>> On 23/06/2010 7:32 PM, Graham Cooper wrote:
>
> > > >>>>>>>>>>>>>>>> start with an assumption the computable
> > > >>>>>>>>>>>>>>>> reals has a finite maximum to the digit
> > > >>>>>>>>>>>>>>>> width of COMPLETE permutation set.
>
> > > >>>>>>>>>>>>>>> That's garbled. Try again.
>
> > > >>>>>>>>>>>>>>> Sylvia.
>
> > > >>>>>>>>>>>>>> Dingo can comprehend it. You try again.
>
> > > >>>>>>>>>>>>> I can find no evidence that Dingo can comprehend it.
>
> > > >>>>>>>>>>>>> Anyway, you're trying to prove something to me, and I cannot parse that
> > > >>>>>>>>>>>>> sentence.
>
> > > >>>>>>>>>>>>> Sylvia.
>
> > > >>>>>>>>>>>> Ok let's define complete permutation set.
>
> > > >>>>>>>>>>>> With an example!!
>
> > > >>>>>>>>>>>> 00
> > > >>>>>>>>>>>> 01
> > > >>>>>>>>>>>> 10
> > > >>>>>>>>>>>> 11
>
> > > >>>>>>>>>>>> this is a complete permutation set of digit width 2.
>
> > > >>>>>>>>>>>> Does that help?
>
> > > >>>>>>>>>>> It's all the different ways in which the digits 0 and 1 can be placed
> > > >>>>>>>>>>> into a sequence of length 2. If you're confining yourself to just those
> > > >>>>>>>>>>> two digits (which you can do without loss of generality), then I can
> > > >>>>>>>>>>> accept that as the definition of "complete permutation set of digit
> > > >>>>>>>>>>> width 2". That is, the expression "complete permutation set of digit
> > > >>>>>>>>>>> width n" is all the combinations of 0 and 1 in a sequence of length n.
> > > >>>>>>>>>>> Indeed there are 2^n of them.
>
> > > >>>>>>>>>>> Conversely, if the complete permutation set contains 2^n sequences, then
> > > >>>>>>>>>>> the digit width is defined to be n.
>
> > > >>>>>>>>>>> So far so good.
>
> > > >>>>>>>>>>> Next...
>
> > > >>>>>>>>>>> Sylvia.
>
> > > >>>>>>>>>> Is there a complete permutation set with digit width 1,000,000
> > > >>>>>>>>>> in the list of computable reals? Use base 10.
>
> > > >>>>>>>>> I take that to mean: Is the complete permutation set (using digits 0
> > > >>>>>>>>> thru 9) of digit width 1,000,000 a subset of the set of computable reals?
>
> > > >>>>>>>>> The answer is yes.
>
> > > >>>>>>>>> I'll add that it's also yes if any other finite positive integer is
> > > >>>>>>>>> substituted for 1,000,000.
>
> > > >>>>>>>>> Next....
>
> > > >>>>>>>>> Sylvia.
>
> > > >>>>>>>> Is the maximum digit width finite?
>
> > > >>>>>>> No.
>
> > > >>>>>>> I'm beginning to get bad feelings about this. This is another proof
> > > >>>>>>> (well, pretty much the same one, actually) of the undisputed fact that
> > > >>>>>>> the width is infinite isn't it?
>
> > > >>>>>>> Anyway, next....
>
> > > >>>>>>> Sylvia.
>
> > > >>>>>> Can you parse 'start with the assumption' paragraph yet?
>
> > > >>>>>> If you can compute all permutations infinitely wide then
> > > >>>>>> isn't that all reals?
>
> > > >>>>> <sigh> I was right.
>
> > > >>>>> All permutations infinitely wide is all reals. But that was not the
> > > >>>>> issue. The question was whether they could be listed, which you still
> > > >>>>> haven't proved. I'm at a loss to understand why you think that proving
> > > >>>>> they're infinitely wide proves that they can be listed.
>
> > > >>>>>> That's all from me I'm homeless in a few hours so I'll need
> > > >>>>>> my iPhone battery to check my bank account.
>
> > > >>>>> With all that income from camgirls.com, your bank account shouldn't be a
> > > >>>>> problem.
>
> > > >>>>> Sylvia.
>
> > > >>>> For the 10th time the proof shows how to list all
> > > >>>> permutations of digits oo wide.
>
> > > >>>> What do you think the list of computable reals is? A list!
>
> > > >>>> Herc
>
> > > >>> how to list computable reals
>
> > > >>> take the first Turing machine, input 1, ouptut L(1,1)
> > > >>> multitasking on all TMs and all inputs will output all
> > > >>> computable outputs
> > > >>> the computable reals is a subset of those rows
>
> > > >> It's not been disputed that the computable reals are listable.
>
> > > >> You persist in seeking to prove things that are not in dispute, while
> > > >> ignoring the core issue, which is proving that all permutations of
> > > >> infinite digits can be expressed as a list.
>
> > > >> Sylvia.
>
> > > > What are you going on about?
>
> > > > What DID I prove about all permutations of infinite digits?
>
> > > > Hint: I made a list of them and an algorithm to list them
>
> > > No you didn't. Your algorithm doesn't put them into a list. For example
> > > in what element does 1/9 appear? If the permutations are in a list, the
> > > answer should be a finite number.
>
> > > Sylvia.
>
> > The only way to answer that would be to give you the
> > program in some 3GL say of a Universal Turing Machine
> > and plug in increasing Natural inputs in unary say and
> > wait until the output was0.111111....
>
> > I Dont see what that would accomplish.
>
> > Herc
>
> Also you could manually program the output to be 1/9
> and use some translation algorithm to find the 'godel number'
> of that program. Depending how you enumerate all programs.
>
> Herc

START --- 0 / 1 / R ---> START

There you go! 1/9th! There should be a computer program listed
somewhere early on to do that!

Herc

From: Sylvia Else on 24 Jun 2010 00:01

On 24/06/2010 12:33 PM, Graham Cooper wrote:
> On Jun 24, 12:12 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
>> On 24/06/2010 11:41 AM, Graham Cooper wrote:
>>
>>
>>
>>
>>
>>> On Jun 24, 11:28 am, Sylvia Else<syl...(a)not.here.invalid> wrote:
>>>> On 24/06/2010 11:17 AM, Graham Cooper wrote:
>>
>>>>> On Jun 24, 11:12 am, Graham Cooper<grahamcoop...(a)gmail.com> wrote:
>>>>>> On Jun 24, 10:20 am, Sylvia Else<syl...(a)not.here.invalid> wrote:
>>
>>>>>>> On 24/06/2010 12:01 AM, Graham Cooper wrote:
>>
>>>>>>>> On Jun 23, 11:45 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
>>>>>>>>> On 23/06/2010 11:04 PM, Graham Cooper wrote:
>>
>>>>>>>>>> On Jun 23, 10:02 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
>>>>>>>>>>> On 23/06/2010 8:28 PM, Graham Cooper wrote:
>>
>>>>>>>>>>>> On Jun 23, 8:12 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
>>>>>>>>>>>>> On 23/06/2010 7:50 PM, Graham Cooper wrote:
>>
>>>>>>>>>>>>>> On Jun 23, 7:41 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
>>>>>>>>>>>>>>> On 23/06/2010 7:32 PM, Graham Cooper wrote:
>>
>>>>>>>>>>>>>>>>>> start with an assumption the computable
>>>>>>>>>>>>>>>>>> reals has a finite maximum to the digit
>>>>>>>>>>>>>>>>>> width of COMPLETE permutation set.
>>
>>>>>>>>>>>>>>>>> That's garbled. Try again.
>>
>>>>>>>>>>>>>>>>> Sylvia.
>>
>>>>>>>>>>>>>>>> Dingo can comprehend it. You try again.
>>
>>>>>>>>>>>>>>> I can find no evidence that Dingo can comprehend it.
>>
>>>>>>>>>>>>>>> Anyway, you're trying to prove something to me, and I cannot parse that
>>>>>>>>>>>>>>> sentence.
>>
>>>>>>>>>>>>>>> Sylvia.
>>
>>>>>>>>>>>>>> Ok let's define complete permutation set.
>>
>>>>>>>>>>>>>> With an example!!
>>
>>>>>>>>>>>>>> 00
>>>>>>>>>>>>>> 01
>>>>>>>>>>>>>> 10
>>>>>>>>>>>>>> 11
>>
>>>>>>>>>>>>>> this is a complete permutation set of digit width 2.
>>
>>>>>>>>>>>>>> Does that help?
>>
>>>>>>>>>>>>> It's all the different ways in which the digits 0 and 1 can be placed
>>>>>>>>>>>>> into a sequence of length 2. If you're confining yourself to just those
>>>>>>>>>>>>> two digits (which you can do without loss of generality), then I can
>>>>>>>>>>>>> accept that as the definition of "complete permutation set of digit
>>>>>>>>>>>>> width 2". That is, the expression "complete permutation set of digit
>>>>>>>>>>>>> width n" is all the combinations of 0 and 1 in a sequence of length n.
>>>>>>>>>>>>> Indeed there are 2^n of them.
>>
>>>>>>>>>>>>> Conversely, if the complete permutation set contains 2^n sequences, then
>>>>>>>>>>>>> the digit width is defined to be n.
>>
>>>>>>>>>>>>> So far so good.
>>
>>>>>>>>>>>>> Next...
>>
>>>>>>>>>>>>> Sylvia.
>>
>>>>>>>>>>>> Is there a complete permutation set with digit width 1,000,000
>>>>>>>>>>>> in the list of computable reals? Use base 10.
>>
>>>>>>>>>>> I take that to mean: Is the complete permutation set (using digits 0
>>>>>>>>>>> thru 9) of digit width 1,000,000 a subset of the set of computable reals?
>>
>>>>>>>>>>> The answer is yes.
>>
>>>>>>>>>>> I'll add that it's also yes if any other finite positive integer is
>>>>>>>>>>> substituted for 1,000,000.
>>
>>>>>>>>>>> Next....
>>
>>>>>>>>>>> Sylvia.
>>
>>>>>>>>>> Is the maximum digit width finite?
>>
>>>>>>>>> No.
>>
>>>>>>>>> I'm beginning to get bad feelings about this. This is another proof
>>>>>>>>> (well, pretty much the same one, actually) of the undisputed fact that
>>>>>>>>> the width is infinite isn't it?
>>
>>>>>>>>> Anyway, next....
>>
>>>>>>>>> Sylvia.
>>
>>>>>>>> Can you parse 'start with the assumption' paragraph yet?
>>
>>>>>>>> If you can compute all permutations infinitely wide then
>>>>>>>> isn't that all reals?
>>
>>>>>>> <sigh> I was right.
>>
>>>>>>> All permutations infinitely wide is all reals. But that was not the
>>>>>>> issue. The question was whether they could be listed, which you still
>>>>>>> haven't proved. I'm at a loss to understand why you think that proving
>>>>>>> they're infinitely wide proves that they can be listed.
>>
>>>>>>>> That's all from me I'm homeless in a few hours so I'll need
>>>>>>>> my iPhone battery to check my bank account.
>>
>>>>>>> With all that income from camgirls.com, your bank account shouldn't be a
>>>>>>> problem.
>>
>>>>>>> Sylvia.
>>
>>>>>> For the 10th time the proof shows how to list all
>>>>>> permutations of digits oo wide.
>>
>>>>>> What do you think the list of computable reals is? A list!
>>
>>>>>> Herc
>>
>>>>> how to list computable reals
>>
>>>>> take the first Turing machine, input 1, ouptut L(1,1)
>>>>> multitasking on all TMs and all inputs will output all
>>>>> computable outputs
>>>>> the computable reals is a subset of those rows
>>
>>>> It's not been disputed that the computable reals are listable.
>>
>>>> You persist in seeking to prove things that are not in dispute, while
>>>> ignoring the core issue, which is proving that all permutations of
>>>> infinite digits can be expressed as a list.
>>
>>>> Sylvia.
>>
>>> What are you going on about?
>>
>>> What DID I prove about all permutations of infinite digits?
>>
>>> Hint: I made a list of them and an algorithm to list them
>>
>> No you didn't. Your algorithm doesn't put them into a list. For example
>> in what element does 1/9 appear? If the permutations are in a list, the
>> answer should be a finite number.
>>
>> Sylvia.
>
>
> The only way to answer that would be to give you the
> program in some 3GL say of a Universal Turing Machine
> and plug in increasing Natural inputs in unary say and
> wait until the output was 0.111111....
>
> I Dont see what that would accomplish.
>
> Herc

It would provide the element number for 1/9 in a list of computable
reals. And you're right, it would accomplish nothing, due to the absence
of a proof that the computable reals include all inifinite sequences.

But you appear to have segwayed onto a different algorithm.

The algorithm you described, which I copied from another posting of
yours was

---
>
> Given a set of complete permutations w digits wide
>
> eg
>
> 00
> 01
> 10
> 11
>
> make 2 copies and append each of 0,1
>
> 00+0
> 01+0
> 10+0
> 11+0
>
> 00+1
> 01+1
> 10+1
> 11+1
> ----
>
> and extended indefinitely.

The last three words are mine.

If you follow that algorithm, you cannot assign a finite element number
to 1/9 because 1/9, which is an infinitely recurring decimal, must be
prededed by infinitely many finite sequences. Since 1/9 is not assigned
a finite element number, the algorithm does not list all the reals.

Sylvia.

From: Sylvia Else on 24 Jun 2010 00:04

On 24/06/2010 1:02 PM, Graham Cooper wrote:
> On Jun 24, 12:13 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
>> On 24/06/2010 11:14 AM, Graham Cooper wrote:
>>
>>> On Jun 24, 11:10 am, Ars ne Lupin<deten...(a)gmail.com> wrote:
>>>> Why people bother replying?
>>
>>> The more important question is why the proof that
>>> computable reals contain all digit permutations oo long
>>> is ignored.
>>
>> Because no such proof has been offered.
>>
>> Sylvia.
>
> I gave a valid proof that computable reals contain all
> permutations oo digits wide.
>
> You say you accept computable reals can be listed but your
> line of questioning suggests the opposite.

The computable reals can be listed.

You have not proved that the computable reals contained all permutations
of infinite width.

>
> When a contradiction to the results of the diagonal proof is given
> you backtrack to disputing fundamental properties of computable
> reals. Saying I haven't "shown how to list the permutations" is
> poppycock!

I have addressed that claim in the thread where we are discussing you
claimed method of listing the permutations.

Sylvia.