CANTOR DISPROOF <<<<<<<<<<<<<<<<
in [Logic]
|
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. |