How Wide Do All The Possible Computed Digit Sequences Go?
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From: Rupert on 22 Jun 2010 02:33 On 6¿ù22ÀÏ, ¿ÀÈÄ4½Ã28ºÐ, 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- ¿øº» ÅؽºÆ® ¼û±â±â - > > - ¿øº» ÅؽºÆ® º¸±â - There does not exist an ordinal number x, such that the set of all sequences of decimal digits of length x has cardinality aleph-null. However, the set of all *computable* sequences of decimal digits of length aleph-null does have cardinality aleph-null. But it is not equal to the set of *all* sequences of decimal digits of length aleph- null.
From: Graham Cooper on 22 Jun 2010 03:06 On Jun 22, 4:33 pm, Rupert <rupertmccal...(a)yahoo.com> wrote: > On 6¿ù22ÀÏ, ¿ÀÈÄ4½Ã28ºÐ, 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- ¿øº» ÅؽºÆ® ¼û±â±â - > > > - ¿øº» ÅؽºÆ® º¸±â - > > There does not exist an ordinal number x, such that the set of all > sequences of decimal digits of length x has cardinality aleph-null. > However, the set of all *computable* sequences of decimal digits of > length aleph-null does have cardinality aleph-null. But it is not > equal to the set of *all* sequences of decimal digits of length aleph- > null. So you are disputing the formula 10^x reals can list all digit permutations x digits wide? I told you all this fairy logic made him fcked in the head! Herc
From: Sylvia Else on 22 Jun 2010 03:48 On 22/06/2010 5:06 PM, Graham Cooper wrote: > On Jun 22, 4:33 pm, Rupert<rupertmccal...(a)yahoo.com> wrote: >> There does not exist an ordinal number x, such that the set of all >> sequences of decimal digits of length x has cardinality aleph-null. >> However, the set of all *computable* sequences of decimal digits of >> length aleph-null does have cardinality aleph-null. But it is not >> equal to the set of *all* sequences of decimal digits of length aleph- >> null. > > > So you are disputing the formula 10^x reals can list > all digit permutations x digits wide? He didn't say that at all. How on Earth did you get there? Sylvia.
From: Graham Cooper on 22 Jun 2010 03:52 On Jun 22, 5:48 pm, Sylvia Else <syl...(a)not.here.invalid> wrote: > On 22/06/2010 5:06 PM, Graham Cooper wrote: > > > On Jun 22, 4:33 pm, Rupert<rupertmccal...(a)yahoo.com> wrote: > >> There does not exist an ordinal number x, such that the set of all > >> sequences of decimal digits of length x has cardinality aleph-null. > >> However, the set of all *computable* sequences of decimal digits of > >> length aleph-null does have cardinality aleph-null. But it is not > >> equal to the set of *all* sequences of decimal digits of length aleph- > >> null. > > > So you are disputing the formula 10^x reals can list > > all digit permutations x digits wide? > > He didn't say that at all. How on Earth did you get there? > > Sylvia. The question I gave him was an application of that formula his answer was not. There is no use explaining this obvious fact to you as your ignorance is only the first step of obfuscation. Herc
From: Sylvia Else on 22 Jun 2010 04:05
On 22/06/2010 5:52 PM, Graham Cooper wrote: > On Jun 22, 5:48 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: >> On 22/06/2010 5:06 PM, Graham Cooper wrote: >> >>> On Jun 22, 4:33 pm, Rupert<rupertmccal...(a)yahoo.com> wrote: >>>> There does not exist an ordinal number x, such that the set of all >>>> sequences of decimal digits of length x has cardinality aleph-null. >>>> However, the set of all *computable* sequences of decimal digits of >>>> length aleph-null does have cardinality aleph-null. But it is not >>>> equal to the set of *all* sequences of decimal digits of length aleph- >>>> null. >> >>> So you are disputing the formula 10^x reals can list >>> all digit permutations x digits wide? >> >> He didn't say that at all. How on Earth did you get there? >> >> Sylvia. > > The question I gave him was an application of that formula > his answer was not. I dare say, but your suggested inference was still not valid. His answer said nothing about what 10^x reals can do. Sylvia. |