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

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Mon, 13 Jun 2022 18:33 UTC

On Monday, June 13, 2022 at 4:16:38 PM UTC+2, WM wrote:
> FromTheRafters schrieb am Sonntag, 12. Juni 2022 um 20:38:06 UTC+2:
> > After serious thinking WM wrote :
> > >
> > > Fritz Feldhase schrieb am Sonntag, 12. Juni 2022 um 16:32:30 UTC+2:
> > >> On Sunday, June 12, 2022 at 2:43:30 PM UTC+2, WM wrote:
> > >>> FromTheRafters schrieb am Sonntag, 12. Juni 2022 um 02:09:28 UTC+2:
> > >>>> WM was thinking very hard:
> > >>>>>
> > >>>>> Note that well-order is the basis for bijection.
> > >>>>>
> > >>>> Is there a bijection between sets {elephant, donkey, walrus} and
> > >>>> {monkey, garden hoe, geode}?
> > >>>>
> > >>>> Are these 'well ordered' sets?
> > >>>>
> > >>> Every extensionally given set is well-ordered by the order of writing.
> > >>>
> > >> No, it isn't
>
> It is a list!

So what?The list is just a convenient way for specifying the elements in the set.

When specifying s e t s using an expression of the form {<list>} the order of <list> is not not relevant.

Hence:

> > >> M = {elephant, donkey, walrus} = {donkey, elephant, walrus} = {walrus, donkey,
> > >> elephant} = ...
> > >
> > > This yields three well-orderings. One is sufficient.

So M _is_ well-ordered in three different ways "at the same time"?

Which is "the chosen one". And how would we know?

> > Because changing the listed order (permutation) of the elements does
> > not affect bijection. Now you say well-order is the basis for it?
> >
> Yes, but one is enough.

Consider the sets M with @ in M and % in M and Ax(x =/= % v x =/= @ -> x !e M) [where @ =/= %]
and M' with @' in M' and %' in M' and Ax(x =/= %' v x =/= @' -> x !e M') [where @' =/= %'].

Then f: M = M' defined with f(x) = x' for all x e M is a bijection.

Which well-order of M "is the basis for this bijection"?

> > Is a donkey less than a walrus but greater than an elephant?
> >
> Well-order has nothing to do with largeness.

Oh really?

> 3, 2, 1 is also well-ordered.

Oh, really? But this isn't a set, you know!

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Mon, 13 Jun 2022 19:04 UTC

Re: Natural numbers and vases

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by: sergi o - Mon, 13 Jun 2022 19:05 UTC

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Mon, 13 Jun 2022 19:22 UTC

Re: Natural numbers and vases

<t884jr$8n0$1@dont-email.me>

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Mon, 13 Jun 2022 15:53:28 -0400
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by: FromTheRafters - Mon, 13 Jun 2022 19:53 UTC

Re: Natural numbers and vases

<06613343-7c85-4a87-ab22-3a194d183354n@googlegroups.com>

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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by: WM - Mon, 13 Jun 2022 20:01 UTC

Re: Natural numbers and vases

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by: WM - Mon, 13 Jun 2022 20:03 UTC

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
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by: WM - Mon, 13 Jun 2022 20:08 UTC

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Mon, 13 Jun 2022 21:04 UTC

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
Date: Mon, 13 Jun 2022 17:06:06 -0500
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by: sergi o - Mon, 13 Jun 2022 22:06 UTC

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
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by: sergi o - Mon, 13 Jun 2022 22:07 UTC

Re: Natural numbers and vases

<t88civ$121e$3@gioia.aioe.org>

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Subject: Re: Natural numbers and vases
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by: sergi o - Mon, 13 Jun 2022 22:09 UTC

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Mon, 13 Jun 2022 22:32 UTC

Re: Natural numbers and vases

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by: Fritz Feldhase - Mon, 13 Jun 2022 22:35 UTC

Re: Natural numbers and vases

<87zgigkmog.fsf@bsb.me.uk>

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Subject: Re: Natural numbers and vases
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by: Ben Bacarisse - Tue, 14 Jun 2022 02:23 UTC

Re: Natural numbers and vases

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by: Fritz Feldhase - Tue, 14 Jun 2022 04:11 UTC

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
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by: zelos...@gmail.com - Tue, 14 Jun 2022 05:21 UTC

Re: Natural numbers and vases

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https://www.novabbs.com/tech/article-flat.php?id=103166&group=sci.math#103166

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Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
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by: William - Tue, 14 Jun 2022 12:15 UTC

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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by: WM - Tue, 14 Jun 2022 14:25 UTC

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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by: WM - Tue, 14 Jun 2022 14:26 UTC

Re: Natural numbers and vases

<142ab0d8-774e-4f58-8f2f-684b67f0d2een@googlegroups.com>

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https://www.novabbs.com/tech/article-flat.php?id=103173&group=sci.math#103173

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Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
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by: William - Tue, 14 Jun 2022 14:56 UTC

Re: Natural numbers and vases

<t8aaha$89p$1@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=103178&group=sci.math#103178

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Tue, 14 Jun 2022 11:46:47 -0400
Organization: Peripheral Visions
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by: FromTheRafters - Tue, 14 Jun 2022 15:46 UTC

Re: Natural numbers and vases

<70c2c420-f785-4c49-8089-41aab227a6c6n@googlegroups.com>

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Subject: Re: Natural numbers and vases
From: franz.fr...@gmail.com (Fritz Feldhase)
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Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
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Re: Natural numbers and vases

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User-Agent: G2/1.0
MIME-Version: 1.0
Message-ID: <d3cc9a46-ecf2-4d39-a7bc-eb7a4f32aa92n@googlegroups.com>
Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
Injection-Date: Tue, 14 Jun 2022 18:08:51 +0000
Content-Type: text/plain; charset="UTF-8"
X-Received-Bytes: 9786

by: WM - Tue, 14 Jun 2022 18:08 UTC

Subject	Author
Natural numbers and vases	William
Re: Natural numbers and vases	Ross A. Finlayson
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	William
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	Gus Gassmann
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	Gus Gassmann
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	Gus Gassmann
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	Gus Gassmann
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	FromTheRafters
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	Gus Gassmann
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	Gus Gassmann
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	Gus Gassmann
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	William
Re: Natural numbers and vases	Gus Gassmann
Re: Natural numbers and vases	Chris M. Thomasson
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	Gus Gassmann
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	Jim Burns
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	Jim Burns
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	Jim Burns
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	Jim Burns
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	Chet Hirasi
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	Gus Gassmann
Re: Natural numbers and vases	Chet Hirasi
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	FredJeffries
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	Chris M. Thomasson
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	Chris M. Thomasson
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	Chris M. Thomasson
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	Chris M. Thomasson
Re: Natural numbers and vases	Chris M. Thomasson
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	Chris M. Thomasson
Re: Natural numbers and vases	FromTheRafters
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	Gus Gassmann
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	Gus Gassmann
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	Gus Gassmann
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	William
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	zelos...@gmail.com
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	zelos...@gmail.com
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	zelos...@gmail.com
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	zelos...@gmail.com
Re: Natural numbers and vases	zelos...@gmail.com
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	zelos...@gmail.com
Re: Natural numbers and vases	zelos...@gmail.com
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	WM
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	Jim Burns
Re: Natural numbers and vases	sergio
Re: Natural numbers and vases	Ross A. Finlayson
Re: Natural numbers and vases	Fritz Feldhase
Re: Natural numbers and vases	Chris M. Thomasson
Re: Natural numbers and vases	Mostowski Collapse
Re: Natural numbers and vases	Socratis T.n.p.