novaBBS - sci.math - Re: Natural numbers and vases III

Re: Natural numbers and vases III

<te3rgg$1c6p$1@gioia.aioe.org>

https://www.novabbs.com/tech/article-flat.php?id=110082&group=sci.math#110082

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 23 Aug 2022 19:31:11 -0500
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by: Sergio - Wed, 24 Aug 2022 00:31 UTC

Re: Natural numbers and vases III

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https://www.novabbs.com/tech/article-flat.php?id=110098&group=sci.math#110098

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Subject: Re: Natural numbers and vases III
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by: zelos...@gmail.com - Wed, 24 Aug 2022 05:40 UTC

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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by: zelos...@gmail.com - Wed, 24 Aug 2022 05:43 UTC

onsdag 24 augusti 2022 kl. 00:43:02 UTC+2 skrev Retard Eram semper recta:
> On Tuesday, 23 August 2022 at 08:28:41 UTC-4, zelos malum wrote:
> > tisdag 23 augusti 2022 kl. 13:52:11 UTC+2 skrev Eram semper recta:
> > > On Monday, 22 August 2022 at 12:53:05 UTC-4, WM wrote:
> > > > William schrieb am Montag, 22. August 2022 um 17:47:08 UTC+2:
> > > > > On Monday, August 22, 2022 at 10:30:55 AM UTC-3, WM wrote:
> > > > > > William schrieb am Samstag, 20. August 2022 um 16:30:41 UTC+2:
> > > > > > > On Saturday, August 20, 2022 at 10:48:54 AM UTC-3, WM wrote:
> > > > > > >
> > > > > > > > I am not interested in the set but only in all its elements..
> > > > > > > Piffle "all its elements" is the set.
> > > > > > How man natural numbers can be used without using the set |N?
> > > > > Irrelevant Piffle that has no bearing on the fact that "all its elements" is the set
> > > > But how many elements are not the set?
> > > They want to claim [A] The set N has no largest element and [B] N contains ALL of its elements. They refuse to accept that these statements are mutually exclusive.
> > Because they aren't.
>
> Anyone with a modicum of intelligence knows those two statements are mutually exclusive. You have none.

Anyone with even baseline intelligence knows they are not mutually exclusive. You are a complete fucking moron.

>
> > >
> > > One of the first properties of "sets" is that their elements are **distinct**. As you say, if they are mostly not there, then one can't even begin to talk about distinctness (definable or dark numbers as you call them). Just saying n ∈ N means n is a **distinct** element of N given the property that n is a fraction with denominator the unit. The statement says nothing about "ALL". To have ALL, it is required that ALL elements can be listed. This is not the case with the junk concept called "infinite set".
> > If your complain is that we cannot write it down on a piece of paper you are truly a fucking moron.
>
> Strawman argument and not even relevant whether they can be written down or not. It's obvious you understood exactly nothing from the above paragraph. You can't claim all the members are distinct if you don't know what they are, you retard!

We can claim they are distinct as long as we can prove that any two element, they are not equal :) I don't need to know what those two are, I just need to prove it one way or another.

>
> Don't project your feeble thoughts onto others.

Comes from the idiot.

>
>
> > >
> > > Whichever way one looks at it, they are basically screwed because ∈ implies membership meaning a set whose members are ALL known.
> > >
> > > Set theory is not mathematics.
> > It very much is.
>
> You can keep dreaming. Set theory will in the not-too-distant future be excluded from all mathematics courses.

There is no dreaming, it is part of mathematics and has been for over a century, get over it already.

And no, it will remain part of mathematics long after you're dead :) A forgotten crank.

>
> >
> > >
> > > >
> > > > Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: thenewca...@gmail.com (Eram semper recta)
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by: Eram semper recta - Wed, 24 Aug 2022 11:56 UTC

On Tuesday, 23 August 2022 at 12:28:41 UTC-4, WM wrote:
> FredJeffries schrieb am Dienstag, 23. August 2022 um 17:59:40 UTC+2:
> > On Tuesday, August 23, 2022 at 6:51:55 AM UTC-7, WM wrote:
> > > FredJeffries schrieb am Montag, 22. August 2022 um 19:48:08 UTC+2:
> > > > > On Monday, August 22, 2022 at 3:36:34 PM UTC+2, WM wrote:
> > > >
> > > > > > there are ℵo natural numbers but most of them cannot be counted.
> > > > How do you know that there are ℵo of them if they cannot be counted?
> > > I use ℵo as expressing actual infinity (i.e. more than every finite number).
> > Who cares what you 'use'?
> You.
> >
> > I'll rephrase the question: How do you know that there are 'more than every finite number' of them if they cannot be counted?
> I know it because they cannot be counted. Every finite number of numbers can be counted.

Yes, because counting them is akin to *identifying* them which is possible only if they are *distinct*. So, in this sense, countability is again exposed for the meaningless and useless concept that it is. Installing ℵo by decree as a "cardinal number" (*) of some sort is not only anti-mathematical nonsense, but also cultish in every sense of the word. First, Cantor's set theory delusions and then Druidry injected into mathematics. Ironically, this wasn't even done in secret. To wit, the fool David Hilbert openly stated absurd nonsense "No one shall remove us from the paradise Cantor created for us". Hilbert was not even a mathematician's arse. This is what happens when stupid and inept people like Jim Burns, William, etc in this newsgroup get to be called math academics. Such individuals have zero mathematical aptitude.

(*) This practice escaped scrutiny when the high priests of mainstream math academia introduced elaborate symbols for constants such as π and √2 into the club called numbers. To wit, π and √2 are just symbols for (rational - redundant since to be a number implies rationality) numbers from which the constants are themselves realised.

>
> Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Wed, 24 Aug 2022 12:22 UTC

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Wed, 24 Aug 2022 12:32 UTC

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: WM - Wed, 24 Aug 2022 12:40 UTC

Re: Natural numbers and vases III

<te5aa8$19pu$1@gioia.aioe.org>

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by: Sergio - Wed, 24 Aug 2022 13:49 UTC

Re: Natural numbers and vases III

<te5acq$19pu$2@gioia.aioe.org>

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by: Sergio - Wed, 24 Aug 2022 13:51 UTC

Re: Natural numbers and vases III

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From: thenewca...@gmail.com (Eram semper recta)
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by: Eram semper recta - Wed, 24 Aug 2022 14:29 UTC

Re: Natural numbers and vases III

<te5eat$16gv$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 24 Aug 2022 09:58:36 -0500
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by: Sergio - Wed, 24 Aug 2022 14:58 UTC

Re: Natural numbers and vases III

<te5fta$3bn74$1@dont-email.me>

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 24 Aug 2022 11:25:25 -0400
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by: FromTheRafters - Wed, 24 Aug 2022 15:25 UTC

Re: Natural numbers and vases III

<te5h1f$3br3l$1@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=110140&group=sci.math#110140

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 24 Aug 2022 11:44:42 -0400
Organization: Peripheral Visions
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by: FromTheRafters - Wed, 24 Aug 2022 15:44 UTC

Re: Natural numbers and vases III

<b8c5cca6-a0eb-d15a-9cb6-35952b9961a8@att.net>

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 24 Aug 2022 13:35:36 -0400
Organization: A noiseless patient Spider
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by: Jim Burns - Wed, 24 Aug 2022 17:35 UTC

Re: Natural numbers and vases III

<te5pvp$sqo$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
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Subject: Re: Natural numbers and vases III
Date: Wed, 24 Aug 2022 13:17:27 -0500
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by: Sergio - Wed, 24 Aug 2022 18:17 UTC

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Wed, 24 Aug 2022 18:31 UTC

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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by: William - Wed, 24 Aug 2022 19:49 UTC

Re: Natural numbers and vases III

<281d00e2-599b-4f04-9466-05730aed8ac7n@googlegroups.com>

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Wed, 24 Aug 2022 20:16 UTC

Re: Natural numbers and vases III

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by: Gus Gassmann - Wed, 24 Aug 2022 20:26 UTC

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: Sergio - Wed, 24 Aug 2022 20:32 UTC

On 8/24/2022 3:16 PM, Fritz Feldhase wrote:
> On Wednesday, August 24, 2022 at 9:49:34 PM UTC+2, William wrote:
>> On Wednesday, August 24, 2022 at 9:22:06 AM UTC-3, WM wrote:
>>>
>>> All definable elements have ℵ₀ successors
>>> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
>
> Actually, each and every natural number has ℵ₀ successors:
>
> ∀n ∈ ℕ: | ℕ \ {1, 2, 3, ..., n} | = ℵo
>
>> So what? They are not the same successors. So you cannot combine all these statements to form
>>
>> |ℕ_ def\ {1, 2, 3, ...}| = ℵo
>
> or to
>
> | ℕ \ {1, 2, 3, ...} | = ℵo .
>
> But MÜCKENHEIM can. By an application of "Mückenheim's law":
>
> | If An e IN: PHI[{1, ..., n}], then PHI[{1, 2, 3, ...}].
>
> So it's easy to derive
>
> | ℕ \ {1, 2, 3, ...} | = ℵo
>
> from
>
> ∀n ∈ ℕ: | ℕ \ {1, 2, 3, ..., n} | = ℵo .
>
> Just a simple application of Mückenheim's law.
>
>
>

I focus in on the area of concern;

, ..., n}

, ...}

see? one has a pesky n, the other does not. the second, it's n has been "emitted", or has "ascended", or "pried out with a n-prying crowbar"...
or perhaps is it actually a "different mathematical statement" , hmmm could be...

"emitted","ascended", "pried out with a n-prying crowbar", "removed", "etc" are all part of "Mückenheim's (f)law" [silent f]

Conclusion;
keep the n, you got infinity.
pry it out and ascend it outta here, then you get nothing.

[to file: file under misunderstanding common Math Nomenclature]

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: WM - Wed, 24 Aug 2022 20:52 UTC

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: WM - Wed, 24 Aug 2022 20:58 UTC

Re: Natural numbers and vases III

<te64ns$3dtl2$1@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=110167&group=sci.math#110167

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 24 Aug 2022 17:20:55 -0400
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by: FromTheRafters - Wed, 24 Aug 2022 21:20 UTC

Re: Natural numbers and vases III

<te64ps$3dtrt$1@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=110168&group=sci.math#110168

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by: FromTheRafters - Wed, 24 Aug 2022 21:21 UTC

Re: Natural numbers and vases III

<te6599$1k23$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 24 Aug 2022 16:30:16 -0500
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by: Sergio - Wed, 24 Aug 2022 21:30 UTC

Sex is like air. It's only a big deal if you can't get any.

tech / sci.math / Re: Natural numbers and vases III

tech / sci.math / Re: Natural numbers and vases III

Subject	Author
Natural numbers and vases III	WM
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	sergi o
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	Surgio
Re: Natural numbers and vases III	Jim Burns
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	Jim Burns
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Surgio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Surgio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	Jim Africani
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	Sergio
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	FredJeffries
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FredJeffries
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	FredJeffries
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Eduardo Faqtardo
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Archimedes Plutonium
Re: Natural numbers and vases III	Archimedes Plutonium