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

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From: Graham Cooper on 23 Jun 2010 21:17

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

Herc

From: Sylvia Else on 23 Jun 2010 21:18

On 24/06/2010 11:12 AM, Graham Cooper 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.

No it doesn't. At most, it shows how to construct them (but not compute
them in the sense of their being computable).

>
> What do you think the list of computable reals is? A list!

It's a list yes, but that doesn't mean the set of permutations of
infinite digits can be expressed as a list.

You need to prove that constructable implies computable, or that
constructable implies countable. You have done neither.

Sylvia.

From: Graham Cooper on 23 Jun 2010 21:20

On Jun 24, 10:22 am, Sylvia Else <syl...(a)not.here.invalid> wrote:
> On 24/06/2010 7:47 AM, Transfer Principle wrote:
>
> > So I agree with Nguyen that we shouldn't support inconsistency
> > in reasoning, but until Herc claims that he accepts enough
> > axioms and logic from which to derive Cantor, he hasn't posted
> > any inconsistency in reasoning yet.
>
> That's largely because his posts are devoid of reasoning. He just
> asserts things, and them blames the reader for not recognising the truth
> of the things asserted.
>
> Sylvia.

You better described someone devoid of EXPRESSING reasoning
which is mostly due to ignorance of the listener.

Herc

From: Sylvia Else on 23 Jun 2010 21:28

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.

From: Graham Cooper on 23 Jun 2010 21:41

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

Herc