How Wide Do All The Possible Computed Digit Sequences Go?
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From: Sylvia Else on 24 Jun 2010 09:35 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. >
From: George Greene on 24 Jun 2010 11:08 On Jun 24, 2:16 am, Graham Cooper <grahamcoop...(a)gmail.com> wrote: > It's the digit width of a SET of numbers. It IS NOT, DUMBASS. ONLY an INDIVIDUAL real GETS TO HAVE a width! If you have A SET of them then they COULD ALL HAVE DIFFERENT widths and there IS NO OBVIOUS way of defining the width of the SET! The set can have a SIZE (or, since the list runs DOWN the page, in this case, A LENGTH), but the SET *does*NOT*have* a WIDTH! > > I know the wording can be manipulated but my proof > in CANTORS PROOF <<<<<< cannot. You have never written a proof. We doubt you ever will.
From: George Greene on 24 Jun 2010 11:13 On Jun 24, 2:16 am, Graham Cooper <grahamcoop...(a)gmail.com> wrote: > It's the digit width of a SET of numbers. IT *IS*NOT*. In the first place, THIS IS A *LIST*, NOT a mere SET, of numbers! In the second place, you are still refusing to do this with THE RIGHT list, which is the list OF ALL FINITE sequences. Doing it with all computable will UNDERcut your claim because EVERY sequence in THAT list has wdith w (so you might get away with abusing language long enough to claim that "the list" had width w). But in THE ACTUALLY RELEVANT CASE, individual (finite) sequences-on-the-list have DIFFERENT widths and THERE IS NO MAXIMUM width!
From: Graham Cooper on 24 Jun 2010 16:01 On Jun 25, 1:13 am, George Greene <gree...(a)email.unc.edu> wrote: > On Jun 24, 2:16 am, Graham Cooper <grahamcoop...(a)gmail.com> wrote: > > > It's the digit width of a SET of numbers. > > IT *IS*NOT*. IT IS TOO! It's my definition it's my theorem. All you have to do is put in your own words the corrollery of this short proof. Assumption. There exists a real number with a finite sequence of digits that is not computable. Contradiction. Therefore...... <take it away George!> Herc
From: Graham Cooper on 24 Jun 2010 16:07
On Jun 25, 6:01 am, Graham Cooper <grahamcoop...(a)gmail.com> wrote: > On Jun 25, 1:13 am, George Greene <gree...(a)email.unc.edu> wrote: > > > On Jun 24, 2:16 am, Graham Cooper <grahamcoop...(a)gmail.com> wrote: > > > > It's the digit width of a SET of numbers. > > > IT *IS*NOT*. > > IT IS TOO! > > It's my definition it's my theorem. I called them Complete Permutation Sets and there are many subsets of the comp reals that are CPS of many digit widths. Herc |