CANTOR DISPROOF <<<<<<<<<<<<<<<<
in [Logic]
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From: Sylvia Else on 24 Jun 2010 02:52 On 24/06/2010 4:31 PM, Graham Cooper wrote: > 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 "indexed computation"? It's that a thinly veiled attempt to get away with calling the results computable? > > 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. We know there is no maximum digit width. How often are you going to seek to prove that when it's not disputed? > > Let's define the scope. I'm not sure we can define the scope - it's already defined isn't it - all reals? > Can we show that > sufficient permutations are listable such > that modifying the diagonal won't produce > anything new? I won't even discuss that, because it's clear that you're now looking for a new way to prove that the all permutations are listable, when the previous way was already supposed to do the job. Your claim throughout numerous threads has been, albeit in expressed in different ways, that you could prove that all permutations can be listed. Now is not the time to be embarking on the development of yet another alleged proof. Let's stick with the ones you've already proposed. Even in the unlikely event that you found one that worked, unless you can show that your previous proofs were correct, your previous claims were false. How many proofs should people be asked to examine when the previous ones from the same author have failed? Sylvia.
From: Graham Cooper on 24 Jun 2010 03:22 On Jun 24, 4:52 pm, Sylvia Else <syl...(a)not.here.invalid> wrote: > On 24/06/2010 4:31 PM, Graham Cooper wrote: > > > > > > > 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 > > "indexed computation"? It's that a thinly veiled attempt to get away > with calling the results computable? > > > > > 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. > > We know there is no maximum digit width. How often are you going to seek > to prove that when it's not disputed? > > > > > Let's define the scope. > > I'm not sure we can define the scope - it's already defined isn't it - > all reals? > > > Can we show that > > > sufficient permutations are listable such > > that modifying the diagonal won't produce > > anything new? > > I won't even discuss that, because it's clear that you're now looking > for a new way to prove that the all permutations are listable, when the > previous way was already supposed to do the job. > > Your claim throughout numerous threads has been, albeit in expressed in > different ways, that you could prove that all permutations can be > listed. Now is not the time to be embarking on the development of yet > another alleged proof. Let's stick with the ones you've already > proposed. Even in the unlikely event that you found one that worked, > unless you can show that your previous proofs were correct, your > previous claims were false. How many proofs should people be asked to > examine when the previous ones from the same author have failed? > > Sylvia. So where's the color of your money now you backed down moral issues? The scope was always to prove no new permutation can be constructed. That is the functional meaning of ALL. You're the ones using that technique.
From: Graham Cooper on 24 Jun 2010 03:29 On Jun 24, 4:52 pm, Sylvia Else <syl...(a)not.here.invalid> wrote: > On 24/06/2010 4:31 PM, Graham Cooper wrote: > > > > > > > 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 > > "indexed computation"? It's that a thinly veiled attempt to get away > with calling the results computable? > > > > > 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. > > We know there is no maximum digit width. How often are you going to seek > to prove that when it's not disputed? > > > > > Let's define the scope. > > I'm not sure we can define the scope - it's already defined isn't it - > all reals? > > > Can we show that > > > sufficient permutations are listable such > > that modifying the diagonal won't produce > > anything new? > > I won't even discuss that, because it's clear that you're now looking > for a new way to prove that the all permutations are listable, when the > previous way was already supposed to do the job. > > Your claim throughout numerous threads has been, albeit in expressed in > different ways, that you could prove that all permutations can be > listed. Now is not the time to be embarking on the development of yet > another alleged proof. Let's stick with the ones you've already > proposed. Even in the unlikely event that you found one that worked, > unless you can show that your previous proofs were correct, your > previous claims were false. How many proofs should people be asked to > examine when the previous ones from the same author have failed? > > Sylvia. If you think the proof isnt about indexed computations you have serious comprehension issues in this field the reason I suggested the scope was to make your complaint more tractable in line with GGs idea eg the proof works with all finite sequences too therefore it doesn't imply all reals are listed. Now you attack a still valid proof and dismiss your need to defend your complaint based on the author having possibly erred at one point. Just amazing. I refuse to argue with any woman ever again including you. Pardon me for not responding to your posts in future. But you are a hornets nest of self contradictions Herc would you believe the CAPTCHA for this post is WISEST?
From: Graham Cooper on 24 Jun 2010 03:36 On Jun 24, 5:29 pm, Graham Cooper <grahamcoop...(a)gmail.com> wrote: > On Jun 24, 4:52 pm, Sylvia Else <syl...(a)not.here.invalid> wrote: > > > On 24/06/2010 4:31 PM, Graham Cooper wrote: > > > > 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 > > > "indexed computation"? It's that a thinly veiled attempt to get away > > with calling the results computable? > > > > 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. > > > We know there is no maximum digit width. How often are you going to seek > > to prove that when it's not disputed? > > > > Let's define the scope. > > > I'm not sure we can define the scope - it's already defined isn't it - > > all reals? > > > > Can we show that > > > > sufficient permutations are listable such > > > that modifying the diagonal won't produce > > > anything new? > > > I won't even discuss that, because it's clear that you're now looking > > for a new way to prove that the all permutations are listable, when the > > previous way was already supposed to do the job. > > > Your claim throughout numerous threads has been, albeit in expressed in > > different ways, that you could prove that all permutations can be > > listed. Now is not the time to be embarking on the development of yet > > another alleged proof. Let's stick with the ones you've already > > proposed. Even in the unlikely event that you found one that worked, > > unless you can show that your previous proofs were correct, your > > previous claims were false. How many proofs should people be asked to > > examine when the previous ones from the same author have failed? > > > Sylvia. > > If you think the proof isnt about indexed computations > you have serious comprehension issues in this field > > the reason I suggested the scope was to make your > complaint more tractable in line with GGs idea > eg the proof works with all finite sequences too > therefore it doesn't imply all reals are listed. > > Now you attack a still valid proof and dismiss your need > to defend your complaint based on the author having > possibly erred at one point. Just amazing. I refuse to argue > with any woman ever again including you. Pardon me > for not responding to your posts in future. But you are a > hornets nest of self contradictions > > Herc > > would you believe the CAPTCHA for this post is WISEST? Final word. When YOU are pinned down you change faces from topic oriented to person or method oriented. I've never seen someone with so many excuses to evade being corrected time and time again. I preferred it when you shut up every time you were proven wrong. Herc
From: Sylvia Else on 24 Jun 2010 04:27
On 24/06/2010 5:36 PM, Graham Cooper wrote: > On Jun 24, 5:29 pm, Graham Cooper<grahamcoop...(a)gmail.com> wrote: >> On Jun 24, 4:52 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: >> >>> On 24/06/2010 4:31 PM, Graham Cooper wrote: >> >>>> 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 >> >>> "indexed computation"? It's that a thinly veiled attempt to get away >>> with calling the results computable? >> >>>> 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. >> >>> We know there is no maximum digit width. How often are you going to seek >>> to prove that when it's not disputed? >> >>>> Let's define the scope. >> >>> I'm not sure we can define the scope - it's already defined isn't it - >>> all reals? >> >>> > Can we show that >> >>>> sufficient permutations are listable such >>>> that modifying the diagonal won't produce >>>> anything new? >> >>> I won't even discuss that, because it's clear that you're now looking >>> for a new way to prove that the all permutations are listable, when the >>> previous way was already supposed to do the job. >> >>> Your claim throughout numerous threads has been, albeit in expressed in >>> different ways, that you could prove that all permutations can be >>> listed. Now is not the time to be embarking on the development of yet >>> another alleged proof. Let's stick with the ones you've already >>> proposed. Even in the unlikely event that you found one that worked, >>> unless you can show that your previous proofs were correct, your >>> previous claims were false. How many proofs should people be asked to >>> examine when the previous ones from the same author have failed? >> >>> Sylvia. >> >> If you think the proof isnt about indexed computations >> you have serious comprehension issues in this field >> >> the reason I suggested the scope was to make your >> complaint more tractable in line with GGs idea >> eg the proof works with all finite sequences too >> therefore it doesn't imply all reals are listed. >> >> Now you attack a still valid proof and dismiss your need >> to defend your complaint based on the author having >> possibly erred at one point. Just amazing. I refuse to argue >> with any woman ever again including you. Pardon me >> for not responding to your posts in future. But you are a >> hornets nest of self contradictions >> >> Herc >> >> would you believe the CAPTCHA for this post is WISEST? > > > Final word. When YOU are pinned down you change faces > from topic oriented to person or method oriented. I've never > seen someone with so many excuses to evade being corrected > time and time again. I preferred it when you shut up every > time you were proven wrong. > Given the number of replies from you that my one post generated, I must conclude that you're quite upset that I'm insisting that you stand by your existing alleged proofs rather than letting you play the game of supporting a position with an endless series of them. Sylvia. |