CANTOR DISPROOF <<<<<<<<<<<<<<<<
in [Logic]
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From: Sylvia Else on 24 Jun 2010 00:06 On 24/06/2010 1:11 PM, Graham Cooper wrote: > 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! You mean a "Marshall"? For once, I agree with you. Sylvia.
From: Graham Cooper on 24 Jun 2010 00:17 On Jun 24, 2:01 pm, Sylvia Else <syl...(a)not.here.invalid> wrote: > 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 was0.111111.... > > > 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. This sounds like George Greene's argument that the permutations are only finite length. It's not something I'm likely to sway you on. But 11 could just as well be 111... And the induction holds. You prove a set is oo wide and you complain the elements were built in finite steps. Herc
From: Graham Cooper on 24 Jun 2010 00:19 On Jun 24, 2:06 pm, Sylvia Else <syl...(a)not.here.invalid> wrote: > On 24/06/2010 1:11 PM, Graham Cooper wrote: > > > 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! > > You mean a "Marshall"? > > For once, I agree with you. > > Sylvia. I accidently quoted his name. But Marshall and poppycock are both terms to make an address. Herc
From: Sylvia Else on 24 Jun 2010 00:32 On 24/06/2010 2:17 PM, Graham Cooper wrote: > On Jun 24, 2:01 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: >> 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 was0.111111.... >> >>> 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. > > > This sounds like George Greene's argument that the > permutations are only finite length. > > It's not something I'm likely to sway you on. But > > 11 > > could just as well be 111... And the induction holds. Hardly. How are you going to append digits to 111.....? Clearly, you can amend the algorithm so as to put any particular infinite sequence near the beginning. But each time you do so, I can ask about a different infinite sequence. You cannot use that process to arrive at an algorithm that will work without further modification. > > You prove a set is oo wide and you complain the elements > were built in finite steps. No, that's not the complaint at all. The complaint is that the algorithm does not assign finite element numbers to all of the permutations, and thus does not list them. Sylvia.
From: Graham Cooper on 24 Jun 2010 02:31
On Jun 24, 2:32 pm, Sylvia Else <syl...(a)not.here.invalid> wrote: > On 24/06/2010 2:17 PM, Graham Cooper wrote: > > > > > > > On Jun 24, 2:01 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: > >> 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 was0.111111.... > > >>> 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. > > > This sounds like George Greene's argument that the > > permutations are only finite length. > > > It's not something I'm likely to sway you on. But > > > 11 > > > could just as well be 111... And the induction holds. > > Hardly. How are you going to append digits to 111.....? > > Clearly, you can amend the algorithm so as to put any particular > infinite sequence near the beginning. But each time you do so, I can ask > about a different infinite sequence. You cannot use that process to > arrive at an algorithm that will work without further modification. > > > > > You prove a set is oo wide and you complain the elements > > were built in finite steps. > > No, that's not the complaint at all. The complaint is that the algorithm > does not assign finite element numbers to all of the permutations, and > thus does not list them. > > Sylvia. You don't choose what digits to append each indexed computation is deterministic every complete permutation set HAS infinite repetitions. You only need 10 repetitions to prove there is no maximum digit width. By noticing each of 0..9 are joined to the end, in that CPS or some duplicate CPS with or without some further digits. Let's define the scope. Can we show that sufficient permutations are listable such that modifying the diagonal won't produce anything new? Herc |