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

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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

From: Sylvia Else on 24 Jun 2010 09:35

On 24/06/2010 5:09 PM, Graham Cooper wrote:
> 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?

I never said it was an implication *of* hc3. I say it's an implication
*in* hc3.

>
> 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!

You need to prove that they're all in the set, or you have nothing.

> But one of these days
> one of is going to confirm oo digits of every sequence are ALL THERE

Sylvia.
>