How Wide Do All The Possible Computed Digit Sequences Go?
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From: Graham Cooper on 22 Jun 2010 05:43 On Jun 22, 7:39 pm, Rupert <rupertmccal...(a)yahoo.com> wrote: > On Jun 22, 7:33 pm, Graham Cooper <grahamcoop...(a)gmail.com> wrote: > > > > > > > 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 > > I find this one pretty hard to parse. For any ordinal alpha, one may > consider the set of all sequences of decimal digits of length alpha. > However, if you make the requirement that the set be countable, then > the set of alpha for which this is possible is the set of all finite > ordinals. This set has no maximum element. Its least upper bound is > omega but omega is not a member of the set. There is no reason why > this set should have to contain its own least upper bound. You're dismissing the result based on your assumption that the result contradicts. If the length of the set approaches infinity the width of the complete permutations approaches infinity Herc
From: Graham Cooper on 22 Jun 2010 05:48 On Jun 22, 7:40 pm, Sylvia Else <syl...(a)not.here.invalid> wrote: > On 22/06/2010 7:33 PM, Graham Cooper wrote: > > > > > > > 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? > > Why do your questions so often come out garbled? > > However, > > > If you listed digit permutations in an infinite list > > You must mean permutations of an infinite number of digits, otherwise > the list couldn't be infinite, but since there's a requirement to list > them, the listed permutations must be a subset of the set of all the > permutations of the infinite number of digits, since the full set is > uncountable, and therefore incapable of being listed. > > > what is the max digit width that all permutations > > could be calculated? > > God only knows what that means. > > Sylvia. Talk about garbled. You don't parse the sentence because it refutes your beliefs. Try and concentrate on the topic without invoking transfiniteness theory as a refutation. I know they are contradictory. That's the point! Herc Herc
From: Sylvia Else on 22 Jun 2010 05:54 On 22/06/2010 7:48 PM, Graham Cooper wrote: > On Jun 22, 7:40 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: >> On 22/06/2010 7:33 PM, Graham Cooper wrote: >> >> >> >> >> >>> 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? >> >> Why do your questions so often come out garbled? >> >> However, >> >> > If you listed digit permutations in an infinite list >> >> You must mean permutations of an infinite number of digits, otherwise >> the list couldn't be infinite, but since there's a requirement to list >> them, the listed permutations must be a subset of the set of all the >> permutations of the infinite number of digits, since the full set is >> uncountable, and therefore incapable of being listed. >> >> > what is the max digit width that all permutations >> > could be calculated? >> >> God only knows what that means. >> >> Sylvia. > > > Talk about garbled. You don't parse the sentence because it > refutes your beliefs. The sentence was not capable of being parsed. > > Try and concentrate on the topic without invoking transfiniteness > theory as a refutation. I know they are contradictory. That's the > point! You're trying to construct questions that contain the assumption that there are no transfinites, and then use the answers to prove that their aren't. Try framing questions that don't presume the answer. Sylvia.
From: Sylvia Else on 22 Jun 2010 06:02 On 22/06/2010 7:43 PM, Graham Cooper wrote: > On Jun 22, 7:39 pm, Rupert<rupertmccal...(a)yahoo.com> wrote: >> On Jun 22, 7:33 pm, Graham Cooper<grahamcoop...(a)gmail.com> wrote: >> >> >> >> >> >>> 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 >> >> I find this one pretty hard to parse. For any ordinal alpha, one may >> consider the set of all sequences of decimal digits of length alpha. >> However, if you make the requirement that the set be countable, then >> the set of alpha for which this is possible is the set of all finite >> ordinals. This set has no maximum element. Its least upper bound is >> omega but omega is not a member of the set. There is no reason why >> this set should have to contain its own least upper bound. > > > You're dismissing the result based on your assumption > that the result contradicts. > > If the length of the set approaches infinity > the width of the complete permutations approaches infinity That appears to be saying no more than that if you have the five digits abcde and then permute them, each permutation with also have five digits. Ditto for any other number of digits. Alternatively, if by 'width' you meant the number of different permutations, then the statement is still true. Where does it get you? Sylvia.
From: Sylvia Else on 22 Jun 2010 06:04
On 22/06/2010 7:39 PM, Graham Cooper wrote: > On Jun 22, 7:33 pm, Sylvia Else<syl...(a)not.here.invalid> wrote: >> On 22/06/2010 7:21 PM, Graham Cooper wrote: >> >> >> >> >> >>> 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 >> >> False proposition. >> >>> you don't know y ? >> >> Nothing to know - see above. >> >> >> >>> You have 1000 theorems of transfiniteness but can't >>> do sums with infinity? >> >> Sums are not defined with infinity. >> >> Sylvia. > > You are reaching. > > What is false? > > Y = log (x) > > or y = log (x) and x = infinity. That statement is false. Sylvia. |