How Wide Do All The Possible Computed Digit Sequences Go?
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From: Graham Cooper on 24 Jun 2010 02:16 On Jun 24, 4:02 pm, George Greene <gree...(a)email.unc.edu> wrote: > On Jun 21, 2:28 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > > > HOW WIDE ARE ALL_POSSIBLE_SEQUENCES COVERED IN THE SET OF COMPUTABLE REALS? > > We're going to try this again from the beginning: > 1) This question IS TOTALLY STUPID because Herc canNOT DEFINE > "covered". > 2) The words "all" and "possible" are just irrelevant here: > ANY real, BY DEFINITION, is w digits wide. > No other width is relevant. In particular NO finite widths are > relevant. > If, however, you want to talk about ALL the infinitely many DIFFERENT > finite widths, that is STILL NOT THE SAME THING AS > talking about THE ONE INDIVIDUAL INfinite width. It's the digit width of a SET of numbers. I know the wording can be manipulated but my proof in CANTORS PROOF <<<<<< cannot. Your evasion of giving a suitable interpretation is over. Herc
From: Graham Cooper on 24 Jun 2010 02:44 On Jun 24, 1:12 pm, Tim Little <t...(a)little-possums.net> 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". > > - Tim Actually Tim your comments are quite correct. If I used the term "has all digits (in order) (segmented)" it's clear. Herc
From: Graham Cooper on 24 Jun 2010 02:56 On Jun 24, 11:22 am, Rupert <rupertmccal...(a)yahoo.com> wrote: > On Jun 23, 12:17 pm, Graham Cooper <grahamcoop...(a)gmail.com> wrote: > > > > > > > On Jun 23, 11:31 am, Rupert <rupertmccal...(a)yahoo.com> wrote: > > > > On Jun 22, 7:36 pm, Graham Cooper <grahamcoop...(a)gmail.com> wrote: > > > > > On Jun 22, 4:28 pm, Graham Cooper <grahamcoop...(a)gmail.com> wrote: > > > > > > On Jun 22, 3:21 pm, Rupert <rupertmccal...(a)yahoo.com> wrote: > > > > > > > On Jun 22, 6:44 am, Graham Cooper <grahamcoop...(a)gmail.com> wrote: > > > > > > > > On Jun 22, 12:08 am, Graham Cooper <grahamcoop...(a)gmail.com> wrote: > > > > > > > > > On Jun 21, 10:40 pm, Sylvia Else <syl...(a)not.here.invalid> wrote: > > > > > > > > > > On 21/06/2010 5:03 PM, Rupert wrote: > > > > > > > > > > > On Jun 21, 4:28 pm, "|-|ercules"<radgray...(a)yahoo.com> wrote: > > > > > > > > > >> Every possible combination X wide... > > > > > > > > > > >> What is X? > > > > > > > > > > >> Now watch as 100 mathematicians fail to parse a trivial question. > > > > > > > > > > >> Someone MUST know what idea I'm getting at! > > > > > > > > > > >> This ternary set covers all possible digits sequences 2 digits wide! > > > > > > > > > > >> 0.00 > > > > > > > > > >> 0.01 > > > > > > > > > >> 0.02 > > > > > > > > > >> 0.10 > > > > > > > > > >> 0.11 > > > > > > > > > >> 0.12 > > > > > > > > > >> 0.20 > > > > > > > > > >> 0.21 > > > > > > > > > >> 0.22 > > > > > > > > > > >> HOW WIDE ARE ALL_POSSIBLE_SEQUENCES COVERED IN THE SET OF COMPUTABLE REALS? > > > > > > > > > > >> Herc > > > > > > > > > >> -- > > > > > > > > > >> If you ever rob someone, even to get your own stuff back, don't use the phrase > > > > > > > > > >> "Nobody leave the room!" ~ OJ Simpson > > > > > > > > > > > It would probably be a good idea for you to talk instead about the set > > > > > > > > > > of all computable sequences of digits base n, where n is some integer > > > > > > > > > > greater than one. Then the length of each sequence would be aleph- > > > > > > > > > > null. But not every sequence of length aleph-null would be included. > > > > > > > > > > That answer looks correct. > > > > > > > > > > But I guarantee that Herc won't accept it. > > > > > > > > > > Sylvia. > > > > > > > > > It's truly hilarious. It's like using a Santa clause metaphor > > > > > > > > to explain why Santa clause is not real, > > > > > > > > but it will do for now. > > > > > > > > > Herc > > > > > > > > Actually on second reading I think Rupert threw a red herring > > > > > > > > He didn't adress the question at all. How wide are all possible > > > > > > > permutations of digits covered? This is different to all possible > > > > > > > listed sequences he just answered that numbers are inf. long! > > > > > > > > Herc- Hide quoted text - > > > > > > > > - Show quoted text - > > > > > > > I'm afraid I don't understand the question. > > > > > > If it takes 10^x reals to have every permutation x digits wide > > > > > how many digits wide would oo reals make? > > > > > > Herc > > > > > Where is my reference to computable reals here Rupert? > > > > > This is a question with a quantity answer. > > > > > If you can't answer say so. > > > > > Herc- Hide quoted text - > > > > > - Show quoted text - > > > > There does not exist a cardinal number x, such that the set of all > > > sequences of decimal digits of length x has cardinality aleph-null. > > > > If you have some cardinal number x and a set of sequences of decimal > > > digits of length x of cardinality aleph-null, then it must be the case > > > that this set does not contain all the sequences of decimal digits of > > > length x. > > > > That is my answer to your question as best I understand it. But I am > > > not sure I really understand what you are talking about. > > > The topic of the thread is the width of permutations > > Well, that certainly wasn't clear to me before. It seemed to me tha we > were talking about sequences of decimal digits. Permutations of which > set, pray tell? > > > as in every permutation of a certain width > > and it's relation to the size of the list of reals. > > > You are refuting that this width approaches infinity > > as the list of reals approaches infinity > > based on > > > a/. You don't know what I'm referring to > > b/. Reverse engineering that there is no defined width > > because it refutes transfiniteness theory > > > you're avoiding the question plain and simple > > I think my problem is that I don't understand the question. But that > doesn't mean I'm not trying. Here's a simple heuristic to check if you're on the ball or not. The question began HOW WIDE your answer began THERE IS Herc
From: Sylvia Else on 24 Jun 2010 03:00 On 24/06/2010 1:12 PM, Tim Little wrote: > On 2010-06-23, Sylvia Else<sylvia(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.
From: Graham Cooper on 24 Jun 2010 03:09
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? 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! But one of these days one of is going to confirm oo digits of every sequence are ALL THERE Herc |