How Wide Do All The Possible Computed Digit Sequences Go? [Math]

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From: Sylvia Else on 22 Jun 2010 20:48

On 23/06/2010 6:17 AM, Graham Cooper wrote:
> On Jun 22, 9:56 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
>> On 22/06/2010 8:13 PM, Graham Cooper wrote:
>>
>>
>>
>>
>>
>>> On Jun 22, 8:04 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
>>>> 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.
>>
>>> Why? Ignoring your other copious bullshit.
>>
>> The function log(x) is not defined for x = infinity, so whatever value y
>> has, it cannot possibly equal the result from the log function.
>>
>> The nearest you can get is that y tends to infinity as x tends to infinity.
>>
>> Sylvia.
>
> So as number of reals in the list of computable reals tends to oo
> the digit width of 'every permutation' tends to infinity.
>
> BUT if the number of computable reals WAS oo the digit width
> of 'every permutation' is NOT infinity.

You're applying the reasoning backwards.

An incorrect line of reasoning can lead to a correct result.

For example, I allege the following to be a theorem:

2 + 2 = 4, therefore sqrt(9) = 3.

You can dismantle the reasoning, and show that it is not a theorem. but
sqrt(9) is still 3.

>
> What abou this
>
> x = oo
> y = x
>
> what is y?

I have no problem with y being oo (provided the = operator is transitive
in the particular set of axioms involved).

Sylvia.

From: Rupert on 22 Jun 2010 21:29

On Jun 22, 7:43 pm, Graham Cooper <grahamcoop...(a)gmail.com> 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.
>

What result?

I said "There is no reason why this set should have to contain its own
least upper bound" because that's true. If you think you can offer a
reason I am happy to listen. (Probably shows that I have too much time
on my hands, but I will gladly listen.)

> If the length of the set approaches infinity
> the width of the complete permutations approaches infinity
>

What ever exactly that means.

I think you just need to be a bit clearer about what your point is.

From: Rupert on 22 Jun 2010 21:31

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.

From: Graham Cooper on 22 Jun 2010 22:17

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
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

Herc

From: Graham Cooper on 22 Jun 2010 22:20

On Jun 23, 10:48 am, Sylvia Else <syl...(a)not.here.invalid> wrote:
> On 23/06/2010 6:17 AM, Graham Cooper wrote:
>
>
>
>
>
> > On Jun 22, 9:56 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
> >> On 22/06/2010 8:13 PM, Graham Cooper wrote:
>
> >>> On Jun 22, 8:04 pm, Sylvia Else<syl...(a)not.here.invalid> wrote:
> >>>> 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.
>
> >>> Why? Ignoring your other copious bullshit.
>
> >> The function log(x) is not defined for x = infinity, so whatever value y
> >> has, it cannot possibly equal the result from the log function.
>
> >> The nearest you can get is that y tends to infinity as x tends to infinity.
>
> >> Sylvia.
>
> > So as number of reals in the list of computable reals tends to oo
> > the digit width of 'every permutation' tends to infinity.
>
> > BUT if the number of computable reals WAS oo the digit width
> > of 'every permutation' is NOT infinity.
>
> You're applying the reasoning backwards.
>
> An incorrect line of reasoning can lead to a correct result.
>
> For example, I allege the following to be a theorem:
>
> 2 + 2 = 4, therefore sqrt(9) = 3.
>
> You can dismantle the reasoning, and show that it is not a theorem. but
> sqrt(9) is still 3.
>
>
>
> > What abou this
>
> > x = oo
> > y = x
>
> > what is y?
>
> I have no problem with y being oo (provided the = operator is transitive
> in the particular set of axioms involved).
>
> Sylvia.

What about

y = 1 * x
x = oo

what is y?

Herc