CANTOR DISPROOF <<<<<<<<<<<<<<<<
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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 |