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: Rupert on 22 Jun 2010 05:09 On Jun 22, 6:14 pm, Graham Cooper <grahamcoop...(a)gmail.com> wrote: > On Jun 22, 6:05 pm, Sylvia Else <syl...(a)not.here.invalid> wrote: > > > > > 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. > > What kind of muddled logic is that? > > LOL > > sorry Rupert for the personal attack. But you ignored > my question last thread that you made a comment > > Herc I think I must have not read your response.
From: Rupert on 22 Jun 2010 05:10 On Jun 22, 6:30 pm, Graham Cooper <grahamcoop...(a)gmail.com> wrote: > On Jun 22, 6:19 pm, Sylvia Else <syl...(a)not.here.invalid> wrote: > > > > > On 22/06/2010 6:14 PM, Graham Cooper wrote: > > > > On Jun 22, 6:05 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: > > >> 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. > > > > What kind of muddled logic is that? > > > Well, did his answer say something about what 10^x reals can do? If so, > > what did it say? Where did it say it? > > > Sylvia. > > Huh? He didn't use the the formula to answer the question > so I said he must be disputing the formula. As the answer is > a simple application of the formula. > No. That's not right. The formula says that, if x is any cardinal, then the set of all sequences of decimal digits of length x has cardinality 10^x. But you were not talking about the set of all sequences of decimal digits of length x, for any cardinal x. You were talking about the set of all *computable* sequences of decimal digits of length aleph-null. The formula does not apply in that situation. > If you're going to disagree with me say opposing statements > this is very confusing where you're going, as predicted > > Herc
From: Sylvia Else on 22 Jun 2010 05:14 On 22/06/2010 6:30 PM, Graham Cooper wrote: > On Jun 22, 6:19 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: >> On 22/06/2010 6:14 PM, Graham Cooper wrote: >> >> >> >> >> >>> On Jun 22, 6:05 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: >>>> 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. >> >>> What kind of muddled logic is that? >> >> Well, did his answer say something about what 10^x reals can do? If so, >> what did it say? Where did it say it? >> >> Sylvia. > > Huh? He didn't use the the formula to answer the question > so I said he must be disputing the formula. As the answer is > a simple application of the formula. It's hardly a simple application. For a start, your question was phrased the other way around, so that a logarithm to base 10 and ceiling function would be required for a finite set of numbers. But you can't just plug infinity into functions that are valid for finite arguments, and expect to get a meaningful answer, and it's not surprising that Rupert didn't try. > > If you're going to disagree with me say opposing statements > this is very confusing where you're going, as predicted What does that mean? Why does your ability to express yourself in English take these turns for the worse? Sylvia.
From: Graham Cooper on 22 Jun 2010 05:21 On Jun 22, 7:14 pm, Sylvia Else <syl...(a)not.here.invalid> wrote: > On 22/06/2010 6:30 PM, Graham Cooper wrote: > > > > > > > On Jun 22, 6:19 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: > >> On 22/06/2010 6:14 PM, Graham Cooper wrote: > > >>> On Jun 22, 6:05 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: > >>>> 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. > > >>> What kind of muddled logic is that? > > >> Well, did his answer say something about what 10^x reals can do? If so, > >> what did it say? Where did it say it? > > >> Sylvia. > > > Huh? He didn't use the the formula to answer the question > > so I said he must be disputing the formula. As the answer is > > a simple application of the formula. > > It's hardly a simple application. For a start, your question was phrased > the other way around, so that a logarithm to base 10 and ceiling > function would be required for a finite set of numbers. But you can't > just plug infinity into functions that are valid for finite arguments, > and expect to get a meaningful answer, and it's not surprising that > Rupert didn't try. > > > > > If you're going to disagree with me say opposing statements > > this is very confusing where you're going, as predicted > > What does that mean? Why does your ability to express yourself in > English take these turns for the worse? > > Sylvia. So if y = log (x) and x = infinity you don't know y ? You have 1000 theorems of transfiniteness but can't do sums with infinity? Herc
From: Graham Cooper on 22 Jun 2010 05:33
On Jun 22, 7:10 pm, Rupert <rupertmccal...(a)yahoo.com> wrote: > On Jun 22, 6:30 pm, Graham Cooper <grahamcoop...(a)gmail.com> wrote: > > > > > > > On Jun 22, 6:19 pm, Sylvia Else <syl...(a)not.here.invalid> wrote: > > > > On 22/06/2010 6:14 PM, Graham Cooper wrote: > > > > > On Jun 22, 6:05 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: > > > >> 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. > > > > > What kind of muddled logic is that? > > > > Well, did his answer say something about what 10^x reals can do? If so, > > > what did it say? Where did it say it? > > > > Sylvia. > > > Huh? He didn't use the the formula to answer the question > > so I said he must be disputing the formula. As the answer is > > a simple application of the formula. > > No. That's not right. The formula says that, if x is any cardinal, > then the set of all sequences of decimal digits of length x has > cardinality 10^x. > > But you were not talking about the set of all sequences of decimal > digits of length x, for any cardinal x. You were talking about the set > of all *computable* sequences of decimal digits of length aleph-null. > The formula does not apply in that situation. > > > > > If you're going to disagree with me say opposing statements > > this is very confusing where you're going, as predicted > > > Herc If you listed digit permutations in an infinite list what is the max digit width that all permutations could be calculated? Herc |