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

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From: Sylvia Else on 23 Jun 2010 22:12

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.

From: Sylvia Else on 23 Jun 2010 22:13

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.

From: Graham Cooper on 23 Jun 2010 22:33

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

From: Graham Cooper on 23 Jun 2010 22:36

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

From: Graham Cooper on 23 Jun 2010 23:02

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.

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!

Herc