How Wide Do All The Possible Computed Digit Sequences Go?
in [Logic]
|
Prev: Question about the complexity of a sentence
Next: Is Borel determinacy true in the recursive reals?
From: Sylvia Else on 25 Jun 2010 00:25 On 25/06/2010 2:20 PM, Graham Cooper wrote: > On Jun 25, 12:55 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: >> On 25/06/2010 6:10 AM, Graham Cooper wrote: >> >> >> >> >> >>> On Jun 24, 11:35 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: >>>> On 24/06/2010 5:09 PM, Graham Cooper wrote: >> >>>>> On Jun 24, 5:00 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: >>>>>> On 24/06/2010 1:12 PM, Tim Little wrote: >> >>>>>>> On 2010-06-23, Sylvia Else<syl...(a)not.here.invalid> wrote: >>>>>>>> On 23/06/2010 5:00 PM, Tim Little wrote: >>>>>>>>> It can't be conceded, as it is simply false. The predicate "list L >>>>>>>>> contains x" means exactly that there exists n in N such that L_n = x. >>>>>>>>> The list does not contain pi since there is no such n. It really is >>>>>>>>> that simple. >> >>>>>>>> Well, OK. Though I can't see how it makes any difference to Herc's >>>>>>>> argument, since I could never see what role it played anyway. >> >>>>>>> It is the very core of his argument: if pi were "contained in" the >>>>>>> infinite list >> >>>>>>> 3 >>>>>>> 3.1 >>>>>>> 3.14 >>>>>>> 3.141 >>>>>>> ... >> >>>>>>> then it would also be "contained in" any other list sharing the "all >>>>>>> prefixes" property, such as >> >>>>>>> 3.0000000 >>>>>>> 3.1000000 >>>>>>> 3.1428571. . . >>>>>>> 3.1414141 >>>>>>> ... >> >>>>>>> It would even be "contained in" any list having that as a sublist, e.g. >> >>>>>>> 0.0000000 >>>>>>> 3.0000000 >>>>>>> 3.1000000 >>>>>>> 1.0000000 >>>>>>> 3.1428571. . . >>>>>>> 2.0934953 >>>>>>> 0.5829345 >>>>>>> 3.1414141 >>>>>>> ... >> >>>>>>> The list of all computable reals is exactly such a list. Most >>>>>>> importantly, no property specific to pi is used here. Every real >>>>>>> would be "contained in" that list if we were to use Herc's broken idea >>>>>>> of "contained in". >> >>>>>> Ok, but his next step - all finite prefixes implies all infinite >>>>>> sequences - is false. So all it means is that his 'proof' contains two >>>>>> invalid steps rather than just one. >> >>>>>> Sylvia. >> >>>>> I've told you atleast 3 times specifically that is NOT an implication >>>>> of hc3. I put it in a implication formula -> are you amnesiac? >> >>>> I never said it was an implication *of* hc3. I say it's an implication >>>> *in* hc3. >> >>>>> As long as all permutations oo wide are in the set, (segmented, >>>>> appended to hitlers number, inverted, imputed, with any other >>>>> numbers you can think of) I don't care! >> >>>> You need to prove that they're all in the set, or you have nothing. >> >>>>> But one of these days >>>>> one of is going to confirm oo digits of every sequence are ALL THERE >> >>>> Sylvia. >> >>> That is no excuse you are still wrong. Something that is implied >>> is implied. You corrected the correction in place of admitting >>> you have been told >> >>> all finite prefixes -> all oo long sequences >> >>> is N O T hc3 >> >>> you've been told 5 times now plus I explained it several >>> more times in this thread and you still carry on. >> >>> Learn to read! >> >>> Herc >> >> I think it's best if we kill this subthread, and instead try to deal >> with the entire issue in the subthread where I've questioned your step 1. >> >> Sylvia. > > > Mike Terry countered your objections to step 1 He most certainly did not. Sylvia.
From: Graham Cooper on 25 Jun 2010 01:24 On Jun 25, 2:25 pm, Sylvia Else <syl...(a)not.here.invalid> wrote: > On 25/06/2010 2:20 PM, Graham Cooper wrote: > > > > > > > On Jun 25, 12:55 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: > >> On 25/06/2010 6:10 AM, Graham Cooper wrote: > > >>> On Jun 24, 11:35 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: > >>>> On 24/06/2010 5:09 PM, Graham Cooper wrote: > > >>>>> On Jun 24, 5:00 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: > >>>>>> On 24/06/2010 1:12 PM, Tim Little wrote: > > >>>>>>> On 2010-06-23, Sylvia Else<syl...(a)not.here.invalid> wrote: > >>>>>>>> On 23/06/2010 5:00 PM, Tim Little wrote: > >>>>>>>>> It can't be conceded, as it is simply false. The predicate "list L > >>>>>>>>> contains x" means exactly that there exists n in N such that L_n = x. > >>>>>>>>> The list does not contain pi since there is no such n. It really is > >>>>>>>>> that simple. > > >>>>>>>> Well, OK. Though I can't see how it makes any difference to Herc's > >>>>>>>> argument, since I could never see what role it played anyway. > > >>>>>>> It is the very core of his argument: if pi were "contained in" the > >>>>>>> infinite list > > >>>>>>> 3 > >>>>>>> 3.1 > >>>>>>> 3.14 > >>>>>>> 3.141 > >>>>>>> ... > > >>>>>>> then it would also be "contained in" any other list sharing the "all > >>>>>>> prefixes" property, such as > > >>>>>>> 3.0000000 > >>>>>>> 3.1000000 > >>>>>>> 3.1428571. . . > >>>>>>> 3.1414141 > >>>>>>> ... > > >>>>>>> It would even be "contained in" any list having that as a sublist, e.g. > > >>>>>>> 0.0000000 > >>>>>>> 3.0000000 > >>>>>>> 3.1000000 > >>>>>>> 1.0000000 > >>>>>>> 3.1428571. . . > >>>>>>> 2.0934953 > >>>>>>> 0.5829345 > >>>>>>> 3.1414141 > >>>>>>> ... > > >>>>>>> The list of all computable reals is exactly such a list. Most > >>>>>>> importantly, no property specific to pi is used here. Every real > >>>>>>> would be "contained in" that list if we were to use Herc's broken idea > >>>>>>> of "contained in". > > >>>>>> Ok, but his next step - all finite prefixes implies all infinite > >>>>>> sequences - is false. So all it means is that his 'proof' contains two > >>>>>> invalid steps rather than just one. > > >>>>>> Sylvia. > > >>>>> I've told you atleast 3 times specifically that is NOT an implication > >>>>> of hc3. I put it in a implication formula -> are you amnesiac? > > >>>> I never said it was an implication *of* hc3. I say it's an implication > >>>> *in* hc3. > > >>>>> As long as all permutations oo wide are in the set, (segmented, > >>>>> appended to hitlers number, inverted, imputed, with any other > >>>>> numbers you can think of) I don't care! > > >>>> You need to prove that they're all in the set, or you have nothing. > > >>>>> But one of these days > >>>>> one of is going to confirm oo digits of every sequence are ALL THERE > > >>>> Sylvia. > > >>> That is no excuse you are still wrong. Something that is implied > >>> is implied. You corrected the correction in place of admitting > >>> you have been told > > >>> all finite prefixes -> all oo long sequences > > >>> is N O T hc3 > > >>> you've been told 5 times now plus I explained it several > >>> more times in this thread and you still carry on. > > >>> Learn to read! > > >>> Herc > > >> I think it's best if we kill this subthread, and instead try to deal > >> with the entire issue in the subthread where I've questioned your step 1. > > >> Sylvia. > > > Mike Terry countered your objections to step 1 > > He most certainly did not. > > Sylvia. I can't quote a long post on my iPhone but search "definite index position" and "bona-fide list" kudos to Mike the first person to Take action to end my torture. Could be a sign!!!!! Herc
From: David Bernier on 25 Jun 2010 01:57 Tim Little wrote: > On 2010-06-24, Sylvia Else<sylvia(a)not.here.invalid> wrote: >> On 24/06/2010 1:12 PM, Tim Little wrote: >>> The list of all computable reals is exactly such a list. Most >>> importantly, no property specific to pi is used here. Every real >>> would be "contained in" that list if we were to use Herc's broken idea >>> of "contained in". >> >> Ok, but his next step - all finite prefixes implies all infinite >> sequences - is false. So all it means is that his 'proof' contains two >> invalid steps rather than just one. > > I think they're both examples of the same invalid use of "L contains x". > > If you replaced Herc's incorrect statements of "L contains x" with > "L contains a sequence with limit x" then both steps would be true. > If L "contains" all finite prefixes in the above broken sense, then it > provably does "contain" all infinite sequences in the same sense. > > True, but irrelevant to Cantor's proof (which uses the ordinary > mathematical meaning) and everything else he's ranting about though. I have this analogy between chess concepts and mathematics concepts which occurred to me not long ago. Those who have done publishable research in mathematics (as well as others with aptitude) may or seem to be working with high-level math. concepts For example, even having mastery over "function with domain A and co-domain B" in the greatest generality might have some medium to high-level ideas: a mapping can be illustrated but with no "rule", as f(n) = n!, it might be hard to grasp. In chess, there are the Laws of chess. This I associate to formal deductions in FOL ZFC. Anybody can check a proof of Cantor's result that there is no bijection between omega and P(omega); this would be tedious and probably un-enlightening. No argument for the uncountability of the reals presented in sci.math is likely to be in formal FOL ZFC. So ultimately it must rest on English sentences and some math. symbols. These evoke in the understanders ideas and concepts, with logical connections and the argument is understood, eventually. When I look at papers on Langlands functoriality, I'm left in a very foggy state of mind. Perhaps some of the non-understanders are in some kind of foggy state too... In chess, there are many high-level concepts including cramped position, king safety, key squares, weak pawns, strong knights, blockade, etc. etc. David Bernier
From: Mike Terry on 25 Jun 2010 14:09 "Graham Cooper" <grahamcooper7(a)gmail.com> wrote in message news:deeb13f2-175e-4afd-b132-7c1ce1f9a0e8(a)g19g2000yqc.googlegroups.com... > On Jun 25, 2:25 pm, Sylvia Else <syl...(a)not.here.invalid> wrote: > > On 25/06/2010 2:20 PM, Graham Cooper wrote: > > > > > > > > > > > > > On Jun 25, 12:55 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: > > >> On 25/06/2010 6:10 AM, Graham Cooper wrote: > > > > >>> On Jun 24, 11:35 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: > > >>>> On 24/06/2010 5:09 PM, Graham Cooper wrote: > > > > >>>>> On Jun 24, 5:00 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: > > >>>>>> On 24/06/2010 1:12 PM, Tim Little wrote: > > > > >>>>>>> On 2010-06-23, Sylvia Else<syl...(a)not.here.invalid> wrote: > > >>>>>>>> On 23/06/2010 5:00 PM, Tim Little wrote: > > >>>>>>>>> It can't be conceded, as it is simply false. The predicate "list L > > >>>>>>>>> contains x" means exactly that there exists n in N such that L_n = x. > > >>>>>>>>> The list does not contain pi since there is no such n. It really is > > >>>>>>>>> that simple. > > > > >>>>>>>> Well, OK. Though I can't see how it makes any difference to Herc's > > >>>>>>>> argument, since I could never see what role it played anyway. > > > > >>>>>>> It is the very core of his argument: if pi were "contained in" the > > >>>>>>> infinite list > > > > >>>>>>> 3 > > >>>>>>> 3.1 > > >>>>>>> 3.14 > > >>>>>>> 3.141 > > >>>>>>> ... > > > > >>>>>>> then it would also be "contained in" any other list sharing the "all > > >>>>>>> prefixes" property, such as > > > > >>>>>>> 3.0000000 > > >>>>>>> 3.1000000 > > >>>>>>> 3.1428571. . . > > >>>>>>> 3.1414141 > > >>>>>>> ... > > > > >>>>>>> It would even be "contained in" any list having that as a sublist, e.g. > > > > >>>>>>> 0.0000000 > > >>>>>>> 3.0000000 > > >>>>>>> 3.1000000 > > >>>>>>> 1.0000000 > > >>>>>>> 3.1428571. . . > > >>>>>>> 2.0934953 > > >>>>>>> 0.5829345 > > >>>>>>> 3.1414141 > > >>>>>>> ... > > > > >>>>>>> The list of all computable reals is exactly such a list. Most > > >>>>>>> importantly, no property specific to pi is used here. Every real > > >>>>>>> would be "contained in" that list if we were to use Herc's broken idea > > >>>>>>> of "contained in". > > > > >>>>>> Ok, but his next step - all finite prefixes implies all infinite > > >>>>>> sequences - is false. So all it means is that his 'proof' contains two > > >>>>>> invalid steps rather than just one. > > > > >>>>>> Sylvia. > > > > >>>>> I've told you atleast 3 times specifically that is NOT an implication > > >>>>> of hc3. I put it in a implication formula -> are you amnesiac? > > > > >>>> I never said it was an implication *of* hc3. I say it's an implication > > >>>> *in* hc3. > > > > >>>>> As long as all permutations oo wide are in the set, (segmented, > > >>>>> appended to hitlers number, inverted, imputed, with any other > > >>>>> numbers you can think of) I don't care! > > > > >>>> You need to prove that they're all in the set, or you have nothing. > > > > >>>>> But one of these days > > >>>>> one of is going to confirm oo digits of every sequence are ALL THERE > > > > >>>> Sylvia. > > > > >>> That is no excuse you are still wrong. Something that is implied > > >>> is implied. You corrected the correction in place of admitting > > >>> you have been told > > > > >>> all finite prefixes -> all oo long sequences > > > > >>> is N O T hc3 > > > > >>> you've been told 5 times now plus I explained it several > > >>> more times in this thread and you still carry on. > > > > >>> Learn to read! > > > > >>> Herc > > > > >> I think it's best if we kill this subthread, and instead try to deal > > >> with the entire issue in the subthread where I've questioned your step 1. > > > > >> Sylvia. > > > > > Mike Terry countered your objections to step 1 > > > > He most certainly did not. > > > > Sylvia. > > > I can't quote a long post on my iPhone but > search "definite index position" and "bona-fide list" > > kudos to Mike the first person to Take action to > end my torture. Could be a sign!!!!! Herc, I wouldn't count on that :-) All I have done is point out that you have a "bona-fide" list of strings of finite length. (Assuming I have understood your construction.) Everyone agrees these are countable in any case! I'm not in any way supporting your argument that this implies anything about strings of infinite length... (and I can't remember what Sylvia's objection to step 1 was, but I expect she was right :-) Mike. > Herc
From: Jesse F. Hughes on 25 Jun 2010 17:53
"Mike Terry" <news.dead.person.stones(a)darjeeling.plus.com> writes: >> kudos to Mike the first person to Take action to >> end my torture. Could be a sign!!!!! > > Herc, I wouldn't count on that :-) Well, to be honest, Herc has rather more experience seeing signs than you do. -- "This is based on the assumption that the difference in set size is what makes the important difference between finite and infinite sets, but I think most people -- even the mathematicians -- will agree that that probably isn't the case." -- Allan C Cybulskie explains infinite sets |