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tech / sci.math / Re: The Matheological Explosion

SubjectAuthor
* The Matheological ExplosionWM
+- Re: The Matheological Explosionsergio
+* Re: The Matheological ExplosionWilliam
|`* Re: The Matheological ExplosionWM
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| | +* Re: The Matheological ExplosionJim Burns
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| | | `* Re: The Matheological ExplosionJim Burns
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| | |   `* Re: The Matheological ExplosionJim Burns
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| | |     `* Re: The Matheological ExplosionJim Burns
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| | |       +* Re: The Matheological ExplosionGus Gassmann
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| | |       | +- Re: The Matheological ExplosionFritz Feldhase
| | |       | +- Re: The Matheological ExplosionFritz Feldhase
| | |       | +- Re: The Matheological Explosionsergio
| | |       | `- Re: The Matheological ExplosionGus Gassmann
| | |       +- Re: The Matheological Explosionsergio
| | |       +* Re: The Matheological ExplosionJim Burns
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| | |       | `* Re: The Matheological ExplosionJim Burns
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| | |       |   `* Re: The Matheological ExplosionJim Burns
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| | |       |     +- Re: The Matheological Explosionzelos...@gmail.com
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| | |       |     |    `- Re: The Matheological ExplosionGus Gassmann
| | |       |     +* Re: The Matheological ExplosionJim Burns
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| | |       |     |   |||    +* Re: The Matheological Explosionzelos...@gmail.com
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| | |       |     |   `* Re: The Matheological ExplosionJim Burns
| | |       |     |    `* Re: The Matheological ExplosionWM
| | |       |     |     `* Re: The Matheological ExplosionJim Burns
| | |       |     |      `* Re: The Matheological ExplosionWM
| | |       |     |       +- Re: The Matheological Explosionsergio
| | |       |     |       `* Re: The Matheological ExplosionJim Burns
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| | |       |     |         +- Re: The Matheological Explosionsergio
| | |       |     |         `* Re: The Matheological ExplosionJim Burns
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| | |       |     |           |`* Re: The Matheological ExplosionWM
| | |       |     |           | +* Re: The Matheological ExplosionFromTheRafters
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| | |       |     |           | |  | `- Re: The Matheological ExplosionGus Gassmann
| | |       |     |           | |  +- Re: The Matheological ExplosionFritz Feldhase
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| | |       |     |           | `- Re: The Matheological Explosionsergio
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| | |       |     +- Re: The Matheological ExplosionGus Gassmann
| | |       |     +* Re: The Matheological ExplosionWM
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| | |       |     +- Re: The Matheological ExplosionGus Gassmann
| | |       |     +- Re: The Matheological Explosionzelos...@gmail.com
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| | |       |     +- Re: The Matheological ExplosionGus Gassmann
| | |       |     +- Re: The Matheological Explosionzelos...@gmail.com
| | |       |     +* Re: The Matheological ExplosionWM
| | |       |     +* Re: The Matheological ExplosionWM
| | |       |     +- Re: The Matheological ExplosionGus Gassmann
| | |       |     +- Re: The Matheological Explosionzelos...@gmail.com
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| | |       |     +- Re: The Matheological ExplosionGus Gassmann
| | |       |     +- Re: The Matheological Explosionzelos...@gmail.com
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| | |       |     +- Re: The Matheological ExplosionGus Gassmann
| | |       |     +- Re: The Matheological ExplosionWM
| | |       |     +* Re: The Matheological ExplosionWM
| | |       |     +- Re: The Matheological ExplosionGus Gassmann
| | |       |     +* Re: The Matheological ExplosionWM
| | |       |     +- Re: The Matheological Explosionzelos...@gmail.com
| | |       |     +* Re: The Matheological ExplosionWM
| | |       |     +- Re: The Matheological ExplosionGus Gassmann
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| | |       |     +- Re: The Matheological Explosionzelos...@gmail.com
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| | |       `- Re: The Matheological Explosionzelos...@gmail.com
| | +* Re: The Matheological ExplosionWilliam
| | +- Re: The Matheological Explosionsergio
| | `- Re: The Matheological ExplosionGus Gassmann
| `* Re: The Matheological Explosionsergio
`* Re: The Matheological Explosionsergio

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Re: The Matheological Explosion

<sufans$1b2j$1@gioia.aioe.org>

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https://www.novabbs.com/tech/article-flat.php?id=91035&group=sci.math#91035

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: The Matheological Explosion
Date: Mon, 14 Feb 2022 22:38:19 -0600
Organization: Aioe.org NNTP Server
Message-ID: <sufans$1b2j$1@gioia.aioe.org>
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<suepar$spo$1@dont-email.me> <87czjphtjs.fsf@bsb.me.uk>
<suetni$ei9$1@dont-email.me> <877d9wizxi.fsf@bsb.me.uk>
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 by: sergio - Tue, 15 Feb 2022 04:38 UTC

On 2/14/2022 9:14 PM, Ben Bacarisse wrote:
> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>
>> On 2/14/2022 4:17 PM, Ben Bacarisse wrote:
>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>
>>>> I don't think that you understand that any 2-ary infinite tree can be
>>>> stored in a 1-ary infinite tree.
>>> Well I, for one, don't! What does "can be stored in" mean?
>>>
>>
>> Think of storing a 2-ary balanced infinite tree in a 1-ary infinite
>> array.
>
> Adding another undefined concept is not the best way to define something
> else. I now don't know what two kinds of "storing" are rather than just
> one.
>
>> It can be done.
>
> So you say, but since I don't know what "it" is, I asked for an
> explanation.
>
>> Storing a 3d tree in a 1d array is possible as
>> well.
>
> I think some words may have got mixed up. 3d tree?
>
>> Think of index, offset type of methods to find the nodes, parent
>> children, say a 2-ary tree in a 1-ary array...
>
> Do you just mean that there is a one-to-one mapping between the nodes?
> That's not a very interesting claim, but I would not call that "storing"
> one tree "in" another. A tree has edges and therefore paths. The
> complete infinite binary tree has more paths then the complete infinite
> unary tree, so the word "storing" must be covering something up.
>
> Maybe something more concrete wold help. If the set of nodes (for both
> trees) is N (the natural numbers), the binary tree has edge set {(n,
> 2n), (n, 2n+1)} and the unary tree has edge set {(n, n+1)} (with n in N
> in both cases). What does it mean to store the first in the second?
>

3D array (think cube) can be mapped into 1D array, start in a corner and go on the diagonals, stay near the corner and expand out, no infinity
problems, all by simple indexing.

tree is wrong wrod.

Re: The Matheological Explosion

<sufapg$1b2j$2@gioia.aioe.org>

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: The Matheological Explosion
Date: Mon, 14 Feb 2022 22:39:10 -0600
Organization: Aioe.org NNTP Server
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<suepar$spo$1@dont-email.me> <87czjphtjs.fsf@bsb.me.uk>
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 by: sergio - Tue, 15 Feb 2022 04:39 UTC

On 2/14/2022 6:17 PM, Ben Bacarisse wrote:
> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>
>> I don't think that you understand that any 2-ary infinite tree can be
>> stored in a 1-ary infinite tree.
>
> Well I, for one, don't! What does "can be stored in" mean?
>
rather "converted into" and arrays, not trees

Re: The Matheological Explosion

<sufqbd$t3p$1@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=91051&group=sci.math#91051

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From: erra...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: The Matheological Explosion
Date: Tue, 15 Feb 2022 04:03:28 -0500
Organization: Peripheral Visions
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 by: FromTheRafters - Tue, 15 Feb 2022 09:03 UTC

Chris M. Thomasson submitted this idea :
> On 2/13/2022 3:15 AM, WM wrote:
>> Chris M. Thomasson schrieb am Samstag, 12. Februar 2022 um 10:15:42 UTC+1:
>>
>>> think of Cantor Pairing creating an infinite number of single numbers
>>> from two numbers, and vise versa.
>>
>> All positive fractions m/n are contained in the matrix
>>
>> 1/1, 1/2, 1/3, 1/4, ...
>> 2/1, 2/2, 2/3, 2/4, ...
>> 3/1, 3/2, 3/3, 3/4, ...
>> 4/1, 4/2, 4/3, 4/4, ...
>> 5/1, 5/2, 5/3, 5/4, ...
>> ...
>>
>> Cantor claims that all can be indexed by natural numbers, i.e., written in
>> a sequence, when he uses the sequence
> [...]
>
> The set of natural numbers is infinite. Therefore, it can be used to index
> any other infinite set. Period.

Countably infinite.

Re: The Matheological Explosion

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Subject: Re: The Matheological Explosion
From: askaske...@gmail.com (WM)
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 by: WM - Tue, 15 Feb 2022 10:11 UTC

Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 01:18:00 UTC+1:
> What does "can be stored in" mean?

Let me answer this question:

Cantor claims that all fractions of

1/1, 1/2, 1/3, 1/4, ...
2/1, 2/2, 2/3, 2/4, ...
3/1, 3/2, 3/3, 3/4, ...
4/1, 4/2, 4/3, 4/4, ...
5/1, 5/2, 5/3, 5/4, ...
....

can be accomodated in the first column such that you can find each fraction there

1/1, __, __, __, ...
1/2, __, __, __, ...
2/1, __, __, __, ...
1/3, __, __, __, ...
2/2, __, __, __, ...
....

That means they are stored there.

However this claim is wrong because only then *all* fractions will be accomodated there, when those who are initially sitting at those places will be removed intermediately until their turn has come to enter their final place in the first column. Here are the first configurations based on exchanges of fractions

1/1, 2/1, 1/3, 1/4, ... 1/1, 3/1, 1/3, 1/4, ... 1/1, 3/1, 4/1, 1/4, ... 1/1, 3/1, 4/1, 1/4, ...
1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 5/1, 2/3, 2/4, ...
3/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ...
4/1, 4/2, 4/3, 4/4, ... 4/1, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ...
5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 2/2, 5/2, 5/3, 5/4, ...
.... ... ... ...

It should be clear that never any place of the matrix will become empty, let alone infinitely many.

Regards, WM

Re: The Matheological Explosion

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Subject: Re: The Matheological Explosion
From: askaske...@gmail.com (WM)
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 by: WM - Tue, 15 Feb 2022 10:20 UTC

FromTheRafters schrieb am Dienstag, 15. Februar 2022 um 10:05:07 UTC+1:
> Chris M. Thomasson submitted this idea :

> > The set of natural numbers is infinite. Therefore, it can be used to index
> > any other infinite set. Period.

Disproved claim.

> Countably infinite.

Not even that. Indexing all fractions of

1/1, 1/2, 1/3, 1/4, ...
2/1, 2/2, 2/3, 2/4, ...
3/1, 3/2, 3/3, 3/4, ...
4/1, 4/2, 4/3, 4/4, ...
5/1, 5/2, 5/3, 5/4, ...
....

is tantamount to accomodating them in the first column such that the rest is empty

1/1, __, __, __, ...
1/2, __, __, __, ...
2/1, __, __, __, ...
1/3, __, __, __, ...
2/2, __, __, __, ...
....

However this claim is wrong because only then *all* fractions will be accomodated there, when those which are initially sitting at those places will be removed intermediately until their turn has come to enter their final place in the first column. Here are the first configurations based on exchanges of native and indexed fractions

1/1, 2/1, 1/3, 1/4, ... 1/1, 3/1, 1/3, 1/4, ... 1/1, 3/1, 4/1, 1/4, ... 1/1, 3/1, 4/1, 1/4, ...
1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 5/1, 2/3, 2/4, ...
3/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ...
4/1, 4/2, 4/3, 4/4, ... 4/1, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ...
5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 2/2, 5/2, 5/3, 5/4, ...
.... ... ... ...

It should be clear that never any place of the matrix will become empty, let alone infinitely many. Therefore never all fractions are indexed.

Regards, WM

Re: The Matheological Explosion

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Subject: Re: The Matheological Explosion
From: askaske...@gmail.com (WM)
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 by: WM - Tue, 15 Feb 2022 10:51 UTC

zelos...@gmail.com schrieb am Dienstag, 15. Februar 2022 um 11:21:12 UTC+1:
> tisdag 15 februari 2022 kl. 11:12:06 UTC+1 skrev WM:
> > Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 01:18:00 UTC+1:
> > > What does "can be stored in" mean?
> > Let me answer this question:
> >
> > Cantor claims that all fractions of
> > 1/1, 1/2, 1/3, 1/4, ...
> > 2/1, 2/2, 2/3, 2/4, ...
> > 3/1, 3/2, 3/3, 3/4, ...
> > 4/1, 4/2, 4/3, 4/4, ...
> > 5/1, 5/2, 5/3, 5/4, ...
> > ...
> > can be accomodated in the first column such that you can find each fraction there
> > 1/1, __, __, __, ...
> > 1/2, __, __, __, ...
> > 2/1, __, __, __, ...
> > 1/3, __, __, __, ...
> > 2/2, __, __, __, ...
> > ...
> > That means they are stored there.
> >
> > However this claim is wrong because only then *all* fractions will be accomodated there, when those who are initially sitting at those places will be removed intermediately until their turn has come to enter their final place in the first column. Here are the first configurations based on exchanges of fractions
> > 1/1, 2/1, 1/3, 1/4, ... 1/1, 3/1, 1/3, 1/4, ... 1/1, 3/1, 4/1, 1/4, ... 1/1, 3/1, 4/1, 1/4, ...
> > 1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 5/1, 2/3, 2/4, ...
> > 3/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ...
> > 4/1, 4/2, 4/3, 4/4, ... 4/1, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ...
> > 5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 2/2, 5/2, 5/3, 5/4, ...
> > ... ... ... ...
> >
> > It should be clear that never any place of the matrix will become empty, let alone infinitely many.
> >
> He claims nothing of the sort

No? Is the first column not an infinite sequence ?
>
> He claim there is a function from N to Q+

Yes, obviously that is nonsense.
>
> You then claim that through any FINITE amount of transpositions it cannot be "emptied"

It cannot be emptied by any infinite amount of transpositions, because never a place will be cleared. You know? Never means never.

> But it is WHOLY IRRELEVANT! The fact transpositions fail is of NO relevance to the existence of the function and has no implication the existence

There is a function, created by myself, an infinite sequence of configurations of the contents of the matrix. It shows that never more than a vanishing part of all fractions will have entered the first column.

But here is another argument, perhaps even simple enough for you to understand: In the following matrix Cantor can cover all X by cookies O

OXXX...
OXXX...
OXXX...
OXXX...
....

when exchanging O by X until all all X have disappeared. Based on this claim I have created a new strategy game. Cover the first three columns by NATO-blue B, Russian-red R, and Sino-yellow Y cookies:

BRYXXX...
BRYXXX...
BRYXXX...
BRYXXX...
BRYXXX...
BRYXXX...
....

Then each of three global players B, R, Y, tries to get the world power by occupying all matrix places by placing there cookies of his colour. If Cantor was right, then all three should have a winning startegy and all should have won finally in full peace (because no-one can get more than all). A nice application of set theory --- if it works.

Regards, WM

Re: The Matheological Explosion

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Subject: Re: The Matheological Explosion
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 by: Ben Bacarisse - Tue, 15 Feb 2022 10:56 UTC

"Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:

> On 2/14/2022 7:14 PM, Ben Bacarisse wrote:
>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
> [...]
>> in both cases). What does it mean to store the first in the second?
>
> From one node we can find its parent nodes. Also, we can find its
> child nodes. n-ary.

Of course. Can you explain what the phrase in question means? Saying
other, rather obvious things, does not help know what you meant.

And the link you posted sheds no light on it.

--
Ben.

Re: The Matheological Explosion

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: sci.math
Subject: Re: The Matheological Explosion
Date: Tue, 15 Feb 2022 11:02:14 +0000
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 by: Ben Bacarisse - Tue, 15 Feb 2022 11:02 UTC

WM <askasker48@gmail.com> writes:

> Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 01:18:00 UTC+1:
>> What does "can be stored in" mean?
>
> Let me answer this question:
>
> Cantor claims that all fractions of
>
> 1/1, 1/2, 1/3, 1/4, ...
> 2/1, 2/2, 2/3, 2/4, ...
> 3/1, 3/2, 3/3, 3/4, ...
> 4/1, 4/2, 4/3, 4/4, ...
> 5/1, 5/2, 5/3, 5/4, ...
> ...

No trees.

> can be accomodated in the first column such that you can find each
> fraction there
>
> 1/1, __, __, __, ...
> 1/2, __, __, __, ...
> 2/1, __, __, __, ...
> 1/3, __, __, __, ...
> 2/2, __, __, __, ...
> ...
>
> That means they are stored there.
>
> However this claim is wrong because only then *all* fractions will be
> accomodated there, when those who are initially sitting at those
> places will be removed intermediately until their turn has come to
> enter their final place in the first column. Here are the first
> configurations based on exchanges of fractions
>
> 1/1, 2/1, 1/3, 1/4, ... 1/1, 3/1, 1/3, 1/4, ... 1/1, 3/1, 4/1, 1/4, ... 1/1, 3/1, 4/1, 1/4, ...
> 1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 5/1, 2/3, 2/4, ...
> 3/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ...
> 4/1, 4/2, 4/3, 4/4, ... 4/1, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ...
> 5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 2/2, 5/2, 5/3, 5/4, ...
> ... ... ... ...
>
> It should be clear that never any place of the matrix will become
> empty, let alone infinitely many.

I am glad you are retired. Switching one ill-defined phrase for another
whilst switching the topic is not how to explain anything.

I don't think you know what CMT meant. I'm not sure even he does.

--
Ben.

Re: The Matheological Explosion

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: sci.math
Subject: Re: The Matheological Explosion
Date: Tue, 15 Feb 2022 11:09:59 +0000
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 by: Ben Bacarisse - Tue, 15 Feb 2022 11:09 UTC

sergio <invalid@invalid.com> writes:

>>>> "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> writes:
>>>>
>>>>> I don't think that you understand that any 2-ary infinite tree can be
>>>>> stored in a 1-ary infinite tree.

> 3D array (think cube) can be mapped into 1D array, start in a corner
> and go on the diagonals, stay near the corner and expand out, no
> infinity problems, all by simple indexing.

Obviously. If you can explain what CMT meant by the original phrase,
please do.

--
Ben.

Re: The Matheological Explosion

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Subject: Re: The Matheological Explosion
From: askaske...@gmail.com (WM)
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 by: WM - Tue, 15 Feb 2022 11:15 UTC

Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 12:02:33 UTC+1:
> WM <askas...@gmail.com> writes:
> > Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 01:18:00 UTC+1:
> >> What does "can be stored in" mean?

> I am glad you are retired. Switching one ill-defined phrase for another
> whilst switching the topic is not how to explain anything.
>
> I don't think you know what CMT meant. I'm not sure even he does.
>
I have answered your question. That was about cbsi, not CMT.

Regards, WM

Re: The Matheological Explosion

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: The Matheological Explosion
Date: Tue, 15 Feb 2022 06:28:46 -0600
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 by: sergio - Tue, 15 Feb 2022 12:28 UTC

On 2/15/2022 4:20 AM, WM wrote:
> FromTheRafters schrieb am Dienstag, 15. Februar 2022 um 10:05:07 UTC+1:
>> Chris M. Thomasson submitted this idea :
>
>>> The set of natural numbers is infinite. Therefore, it can be used to index
>>> any other infinite set. Period.
>
> Disproved claim.

liar.

>
>> Countably infinite.
>
> Not even that. Indexing all fractions of
>
> 1/1, 1/2, 1/3, 1/4, ...
> 2/1, 2/2, 2/3, 2/4, ...
> 3/1, 3/2, 3/3, 3/4, ...
> 4/1, 4/2, 4/3, 4/4, ...
> 5/1, 5/2, 5/3, 5/4, ...
> ...
>
> is tantamount to accomodating them in the first column such that the rest is empty

liar. you fail to understand the matrix of rational numbers. "Tantamount" is a word used by pretenders, and trolls.

<snip failure>

> Regards, WM
>

Re: The Matheological Explosion

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From: erra...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: The Matheological Explosion
Date: Tue, 15 Feb 2022 08:02:52 -0500
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 by: FromTheRafters - Tue, 15 Feb 2022 13:02 UTC

WM has brought this to us :
> Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 01:18:00 UTC+1:
>> What does "can be stored in" mean?
>
> Let me answer this question:

This subthread has nothing to do with your obsession.

Only Chris can answer this question. I suspect he just means that
information can be converted into numbers and those numbers can be
represented in many different ways. He thinks more in terms of
programming than he does in mathematical terms, so 'storing' probably
just means the information is retrievable.

Re: The Matheological Explosion

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From: erra...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: The Matheological Explosion
Date: Tue, 15 Feb 2022 08:05:26 -0500
Organization: Peripheral Visions
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 by: FromTheRafters - Tue, 15 Feb 2022 13:05 UTC

WM presented the following explanation :
> FromTheRafters schrieb am Dienstag, 15. Februar 2022 um 10:05:07 UTC+1:
>> Chris M. Thomasson submitted this idea :
>
>>> The set of natural numbers is infinite. Therefore, it can be used to index
>>> any other infinite set. Period.
>
> Disproved claim.
>
>> Countably infinite.
>
> Not even that. Indexing all fractions of
>
> 1/1, 1/2, 1/3, 1/4, ...
> 2/1, 2/2, 2/3, 2/4, ...
> 3/1, 3/2, 3/3, 3/4, ...
> 4/1, 4/2, 4/3, 4/4, ...
> 5/1, 5/2, 5/3, 5/4, ...
> ...
>
> is tantamount to accomodating them in the first column such that the rest is
> empty

No it isn't.

Re: The Matheological Explosion

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Subject: Re: The Matheological Explosion
From: askaske...@gmail.com (WM)
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 by: WM - Tue, 15 Feb 2022 14:10 UTC

FromTheRafters schrieb am Dienstag, 15. Februar 2022 um 14:07:07 UTC+1:
> WM presented the following explanation :

> > Not even that. Indexing all fractions of
> >
> > 1/1, 1/2, 1/3, 1/4, ...
> > 2/1, 2/2, 2/3, 2/4, ...
> > 3/1, 3/2, 3/3, 3/4, ...
> > 4/1, 4/2, 4/3, 4/4, ...
> > 5/1, 5/2, 5/3, 5/4, ...
> > ...
> >
> > is tantamount to accomodating them in the first column such that the rest is
> > empty
> No it isn't.

No? Is it not
k = (m + n - 1)(m + n - 2)/2 + m ?

Is it not
1/1, 1/2, 2/1, 1/3, 2/2, ... ?

Is it not
1/1, 1/2, 2/1, 1/3, 2/2, ...
__, __, __, __, __, __, ...
__, __, __, __, __, __, ...
__, __, __, __, __, __, ...
__, __, __, __, __, __, ...
.... ?

Is it not
1/1, __, __, __, ...
1/2, __, __, __, ...
2/1, __, __, __, ...
1/3, __, __, __, ...
2/2, __, __, __, ...
.... ?

Please indicate the first deviation.

Regards, WM

Re: The Matheological Explosion

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Subject: Re: The Matheological Explosion
From: askaske...@gmail.com (WM)
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 by: WM - Tue, 15 Feb 2022 14:10 UTC

FromTheRafters schrieb am Dienstag, 15. Februar 2022 um 14:04:29 UTC+1:
> WM has brought this to us :
> > Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 01:18:00 UTC+1:
> >> What does "can be stored in" mean?
> >
> > Let me answer this question:
> This subthread has nothing to do with your obsession.

Look at the OP to see the topic of this thread.

Regards, WM

Re: The Matheological Explosion

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Subject: Re: The Matheological Explosion
Date: Tue, 15 Feb 2022 14:21:16 +0000
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 by: Ben Bacarisse - Tue, 15 Feb 2022 14:21 UTC

WM <askasker48@gmail.com> writes:

> Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 12:02:33 UTC+1:
>> WM <askas...@gmail.com> writes:
>> > Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 01:18:00 UTC+1:
>> >> What does "can be stored in" mean?
>
>> I am glad you are retired. Switching one ill-defined phrase for another
>> whilst switching the topic is not how to explain anything.
>>
>> I don't think you know what CMT meant. I'm not sure even he does.
>>
> I have answered your question. That was about cbsi, not CMT.

Don't be silly. I know what "can be stored in" means when it's about
tea and jars or about clothes and suitcases. I know what it means in a
hundred contexts, but I was asking about what CMT meant when he wrote
it. He was not talking about tea or clothes. Nor was he talking about
your latest delusion with the rationals.

You don't know what meant, and I still don't.

--
Ben.

Re: The Matheological Explosion

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 by: Ben Bacarisse - Tue, 15 Feb 2022 14:26 UTC

FromTheRafters <erratic@nomail.afraid.org> writes:

> WM has brought this to us :
>> Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 01:18:00 UTC+1:
>>> What does "can be stored in" mean?
>>
>> Let me answer this question:
>
> This subthread has nothing to do with your obsession.
>
> Only Chris can answer this question. I suspect he just means that
> information can be converted into numbers and those numbers can be
> represented in many different ways. He thinks more in terms of
> programming than he does in mathematical terms, so 'storing' probably
> just means the information is retrievable.

That was my best guess, but the information is not "retrievable" in any
way that makes sense.

--
Ben.

Re: The Matheological Explosion

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Date: Tue, 15 Feb 2022 08:45:30 -0600
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 by: sergio - Tue, 15 Feb 2022 14:45 UTC

On 2/15/2022 8:21 AM, Ben Bacarisse wrote:
> WM <askasker48@gmail.com> writes:
>
>> Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 12:02:33 UTC+1:
>>> WM <askas...@gmail.com> writes:
>>>> Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 01:18:00 UTC+1:
>>>>> What does "can be stored in" mean?
>>
>>> I am glad you are retired. Switching one ill-defined phrase for another
>>> whilst switching the topic is not how to explain anything.
>>>
>>> I don't think you know what CMT meant. I'm not sure even he does.
>>>
>> I have answered your question. That was about cbsi, not CMT.
>
> Don't be silly. I know what "can be stored in" means when it's about
> tea and jars or about clothes and suitcases. I know what it means in a
> hundred contexts, but I was asking about what CMT meant when he wrote
> it. He was not talking about tea or clothes. Nor was he talking about
> your latest delusion with the rationals.
>
> You don't know what meant, and I still don't.
>

for WM,

2D => 1D mapping.

did you know that each character on your screen has already been through 3 of those mappings already ?

Re: The Matheological Explosion

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: The Matheological Explosion
Date: Tue, 15 Feb 2022 08:46:31 -0600
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 by: sergio - Tue, 15 Feb 2022 14:46 UTC

On 2/15/2022 7:02 AM, FromTheRafters wrote:
> WM has brought this to us :
>> Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 01:18:00 UTC+1:
>>> What does "can be stored in" mean?
>>
>> Let me answer this question:
>
> This subthread has nothing to do with your obsession.
>
> Only Chris can answer this question. I suspect he just means that information can be converted into numbers and those numbers can be represented in many
> different ways. He thinks more in terms of programming than he does in mathematical terms, so 'storing' probably just means the information is retrievable.

Bet WM's storing is writing it on slips of paper and putting into a jar.

Re: The Matheological Explosion

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: The Matheological Explosion
Date: Tue, 15 Feb 2022 08:47:54 -0600
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 by: sergio - Tue, 15 Feb 2022 14:47 UTC

On 2/15/2022 8:26 AM, Ben Bacarisse wrote:
> FromTheRafters <erratic@nomail.afraid.org> writes:
>
>> WM has brought this to us :
>>> Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 01:18:00 UTC+1:
>>>> What does "can be stored in" mean?
>>>
>>> Let me answer this question:
>>
>> This subthread has nothing to do with your obsession.
>>
>> Only Chris can answer this question. I suspect he just means that
>> information can be converted into numbers and those numbers can be
>> represented in many different ways. He thinks more in terms of
>> programming than he does in mathematical terms, so 'storing' probably
>> just means the information is retrievable.
>
> That was my best guess, but the information is not "retrievable" in any
> way that makes sense.
>

How about using knots on a string ?
(there was a memory storage divice like that, a native tribe somewhere)

Re: The Matheological Explosion

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From: inva...@invalid.com (sergio)
Newsgroups: sci.math
Subject: Re: The Matheological Explosion
Date: Tue, 15 Feb 2022 08:50:12 -0600
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 by: sergio - Tue, 15 Feb 2022 14:50 UTC

On 2/15/2022 8:10 AM, WM wrote:
> FromTheRafters schrieb am Dienstag, 15. Februar 2022 um 14:07:07 UTC+1:
>> WM presented the following explanation :
>
>>> Not even that. Indexing all fractions of
>>>
>>> 1/1, 1/2, 1/3, 1/4, ...
>>> 2/1, 2/2, 2/3, 2/4, ...
>>> 3/1, 3/2, 3/3, 3/4, ...
>>> 4/1, 4/2, 4/3, 4/4, ...
>>> 5/1, 5/2, 5/3, 5/4, ...
>>> ...
>>>
>>> is tantamount to accomodating them in the first column such that the rest is
>>> empty
>> No it isn't.
>
> No? Is it not
> k = (m + n - 1)(m + n - 2)/2 + m ?
>
> Is it not
> 1/1, 1/2, 2/1, 1/3, 2/2, ... ?
>
> Is it not
> 1/1, 1/2, 2/1, 1/3, 2/2, ...
> __, __, __, __, __, __, ...
> __, __, __, __, __, __, ...
> __, __, __, __, __, __, ...
> __, __, __, __, __, __, ...
> ... ?
>
> Is it not
> 1/1, __, __, __, ...
> 1/2, __, __, __, ...
> 2/1, __, __, __, ...
> 1/3, __, __, __, ...
> 2/2, __, __, __, ...
> ... ?
>
> Please indicate the first deviation.
>
> Regards, WM
>

first deviation is here...

> Is it not
> 1/1, 1/2, 2/1, 1/3, 2/2, ...
> __, __, __, __, __, __, ...
> __, __, __, __, __, __, ...
> __, __, __, __, __, __, ...
> __, __, __, __, __, __, ...
> ... ?
>
> Is it not
> 1/1, __, __, __, ...
> 1/2, __, __, __, ...
> 2/1, __, __, __, ...
> 1/3, __, __, __, ...
> 2/2, __, __, __, ...
> ... ?

Re: The Matheological Explosion

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Subject: Re: The Matheological Explosion
From: horand.g...@gmail.com (Gus Gassmann)
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 by: Gus Gassmann - Tue, 15 Feb 2022 15:44 UTC

On Tuesday, 15 February 2022 at 10:48:20 UTC-4, sergio wrote:
> On 2/15/2022 8:26 AM, Ben Bacarisse wrote:
> > FromTheRafters <err...@nomail.afraid.org> writes:
> >
> >> WM has brought this to us :
> >>> Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 01:18:00 UTC+1:
> >>>> What does "can be stored in" mean?
> >>>
> >>> Let me answer this question:
> >>
> >> This subthread has nothing to do with your obsession.
> >>
> >> Only Chris can answer this question. I suspect he just means that
> >> information can be converted into numbers and those numbers can be
> >> represented in many different ways. He thinks more in terms of
> >> programming than he does in mathematical terms, so 'storing' probably
> >> just means the information is retrievable.
> >
> > That was my best guess, but the information is not "retrievable" in any
> > way that makes sense.
> >
> How about using knots on a string ?
> (there was a memory storage divice like that, a native tribe somewhere)

Quipus, Incas, modern day Peru.

Re: The Matheological Explosion

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From: erra...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: The Matheological Explosion
Date: Tue, 15 Feb 2022 16:04:48 -0500
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 by: FromTheRafters - Tue, 15 Feb 2022 21:04 UTC

WM brought next idea :
> FromTheRafters schrieb am Dienstag, 15. Februar 2022 um 14:04:29 UTC+1:
>> WM has brought this to us :
>>> Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 01:18:00 UTC+1:
>>>> What does "can be stored in" mean?
>>>
>>> Let me answer this question:
>> This subthread has nothing to do with your obsession.
>
> Look at the OP to see the topic of this thread.

I said "subthread".

Re: The Matheological Explosion

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Newsgroups: sci.math
Subject: Re: The Matheological Explosion
Date: Tue, 15 Feb 2022 16:12:10 -0500
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 by: FromTheRafters - Tue, 15 Feb 2022 21:12 UTC

sergio formulated the question :
> On 2/15/2022 8:26 AM, Ben Bacarisse wrote:
>> FromTheRafters <erratic@nomail.afraid.org> writes:
>>
>>> WM has brought this to us :
>>>> Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 01:18:00 UTC+1:
>>>>> What does "can be stored in" mean?
>>>>
>>>> Let me answer this question:
>>>
>>> This subthread has nothing to do with your obsession.
>>>
>>> Only Chris can answer this question. I suspect he just means that
>>> information can be converted into numbers and those numbers can be
>>> represented in many different ways. He thinks more in terms of
>>> programming than he does in mathematical terms, so 'storing' probably
>>> just means the information is retrievable.
>>
>> That was my best guess, but the information is not "retrievable" in any
>> way that makes sense.
>>
>
> How about using knots on a string ?
> (there was a memory storage divice like that, a native tribe somewhere)

IIRC looms were used to place code in a cloth's woven pattern. That is,
essentially, knots in string, no?

Re: The Matheological Explosion

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 by: FromTheRafters - Tue, 15 Feb 2022 21:16 UTC

sergio formulated the question :
> On 2/15/2022 7:02 AM, FromTheRafters wrote:
>> WM has brought this to us :
>>> Ben Bacarisse schrieb am Dienstag, 15. Februar 2022 um 01:18:00 UTC+1:
>>>> What does "can be stored in" mean?
>>>
>>> Let me answer this question:
>>
>> This subthread has nothing to do with your obsession.
>>
>> Only Chris can answer this question. I suspect he just means that
>> information can be converted into numbers and those numbers can be
>> represented in many different ways. He thinks more in terms of programming
>> than he does in mathematical terms, so 'storing' probably just means the
>> information is retrievable.
>
> Bet WM's storing is writing it on slips of paper and putting into a jar.

He probably uses discarded Turing Machine tape to write on, a
potentially unlimited supply.


tech / sci.math / Re: The Matheological Explosion

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