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But you'll notice Perl has a goto. -- Larry Wall in <199710211624.JAA17833@wall.org>


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

SubjectAuthor
* Natural numbers and vasesWilliam
+- Re: Natural numbers and vasesRoss A. Finlayson
+* Re: Natural numbers and vasesWM
|+* Re: Natural numbers and vasesWilliam
||`* Re: Natural numbers and vasesWM
|| +- Re: Natural numbers and vasessergio
|| `* Re: Natural numbers and vasesWilliam
||  `* Re: Natural numbers and vasesWM
||   +- Re: Natural numbers and vasessergio
||   `* Re: Natural numbers and vasesWilliam
||    `* Re: Natural numbers and vasesWM
||     +- Re: Natural numbers and vasessergio
||     `* Re: Natural numbers and vasesWilliam
||      +- Re: Natural numbers and vasesFritz Feldhase
||      `* Re: Natural numbers and vasesWM
||       +* Re: Natural numbers and vasesWilliam
||       |+* Re: Natural numbers and vasesGus Gassmann
||       ||`* Re: Natural numbers and vasesFritz Feldhase
||       || `- Re: Natural numbers and vasesGus Gassmann
||       |`* Re: Natural numbers and vasesWM
||       | +- Re: Natural numbers and vasesGus Gassmann
||       | +* Re: Natural numbers and vasesWilliam
||       | |+* Re: Natural numbers and vasesWM
||       | ||+* Re: Natural numbers and vasesWilliam
||       | |||`* Re: Natural numbers and vasesWM
||       | ||| `* Re: Natural numbers and vasesWilliam
||       | |||  +* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |`- Re: Natural numbers and vasessergio
||       | |||  +* Re: Natural numbers and vasesGus Gassmann
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||+- Re: Natural numbers and vasesFromTheRafters
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesGus Gassmann
||       | |||  ||`- Re: Natural numbers and vasesChris M. Thomasson
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||+* Re: Natural numbers and vasesJim Burns
||       | |||  |||`* Re: Natural numbers and vasesWM
||       | |||  ||| +* Re: Natural numbers and vasesJim Burns
||       | |||  ||| |`* Re: Natural numbers and vasesWM
||       | |||  ||| | +* Re: Natural numbers and vasesJim Burns
||       | |||  ||| | |`* Re: Natural numbers and vasesWM
||       | |||  ||| | | +* Re: Natural numbers and vasesJim Burns
||       | |||  ||| | | |`* Re: Natural numbers and vasesWM
||       | |||  ||| | | | `- Re: Natural numbers and vasessergio
||       | |||  ||| | | `- Re: Natural numbers and vasessergio
||       | |||  ||| | `- Re: Natural numbers and vasessergio
||       | |||  ||| `- Re: Natural numbers and vasessergio
||       | |||  ||`* Re: Natural numbers and vasessergio
||       | |||  || `- Re: Natural numbers and vasesChet Hirasi
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+* Re: Natural numbers and vasesGus Gassmann
||       | |||  ||`- Re: Natural numbers and vasesChet Hirasi
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`* Re: Natural numbers and vasessergio
||       | |||  || `* Re: Natural numbers and vasesWM
||       | |||  ||  `* Re: Natural numbers and vasessergio
||       | |||  ||   +* Re: Natural numbers and vasessergio
||       | |||  ||   |`* Re: Natural numbers and vasesFredJeffries
||       | |||  ||   | `- Re: Natural numbers and vasessergio
||       | |||  ||   `* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||    `* Re: Natural numbers and vasessergio
||       | |||  ||     +* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||     |`- Re: Natural numbers and vasessergio
||       | |||  ||     `* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||      `* Re: Natural numbers and vasessergio
||       | |||  ||       `* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||        +* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||        |`- Re: Natural numbers and vasessergio
||       | |||  ||        `- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||+- Re: Natural numbers and vasessergio
||       | |||  ||`* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  || +* Re: Natural numbers and vasesFromTheRafters
||       | |||  || `* Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesGus Gassmann
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |`* Re: Natural numbers and vasesWM
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  `- Re: Natural numbers and vaseszelos...@gmail.com
||       | ||`- Re: Natural numbers and vasessergio
||       | |`* Re: Natural numbers and vasesWM
||       | +- Re: Natural numbers and vasessergio
||       | `* Re: Natural numbers and vasesJim Burns
||       `- Re: Natural numbers and vasessergio
|+- Re: Natural numbers and vasesRoss A. Finlayson
|`- Re: Natural numbers and vasesFritz Feldhase
+* Re: Natural numbers and vasesChris M. Thomasson
+* Re: Natural numbers and vasesMostowski Collapse
`- Re: Natural numbers and vasesSocratis T.n.p.

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Re: Natural numbers and vases

<t7r02o$14tb$1@gioia.aioe.org>

  copy mid

https://www.novabbs.com/tech/article-flat.php?id=102388&group=sci.math#102388

  copy link   Newsgroups: sci.math
Path: i2pn2.org!i2pn.org!aioe.org!jq9Zon5wYWPEc6MdU7JpBw.user.46.165.242.75.POSTED!not-for-mail
From: inva...@invalid.com (sergi o)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Wed, 8 Jun 2022 15:16:24 -0500
Organization: Aioe.org NNTP Server
Message-ID: <t7r02o$14tb$1@gioia.aioe.org>
References: <06d0f903-3235-4be2-8653-85563102704fn@googlegroups.com>
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<fd833c8d-922e-468f-881c-a33e721e22a2n@googlegroups.com>
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 by: sergi o - Wed, 8 Jun 2022 20:16 UTC

On 6/8/2022 2:17 PM, WM wrote:
>
> William schrieb am Mittwoch, 8. Juni 2022 um 17:10:38 UTC+2:
>> On Wednesday, June 8, 2022 at 11:20:08 AM UTC-3, WM wrote:
>>> William schrieb am Mittwoch, 8. Juni 2022 um 16:06:45 UTC+2:
>>
>>>> The set can be represented by a Matrix with no O's.
>>> Only if the O's, which provably cannot disappear,
>> The matrix does not have any O's to appear or disappear.
>
> Look, in the beginning we have this matrix:
>
> XOOO...
> XOOO...
> XOOO...
> XOOO...
> ...

Well, you are wrong. In the beginning you have the matrix of rationals.

your "kisses and hugs" is you channeling hillary clinton's math abilities.

>
> If it is possible to enumerate all fractions, then the X can be distributed over the whole matrix. This is impossible.

because, *your way of doing this is wrong and always will be*, As Cantor Proved there is a one to one mapping of all the rationals to the natural
numbers. Using a very simple proof too.

> Your spell "all fractions are enumerated" is lie.

That is a lie.

> If it was true, then this could in fact be done.

Liar, it is because you do it wrong, and always will.

>
> Regards, WM

Accept the FACT, that Cantor Proved it, and you cannot un-prove it.

No matter how you swaparoofest, Frame Achillies, etc You will never un-prove Cantor.

Re: Natural numbers and vases

<457af65d-ab36-4860-8712-31d016a0cbben@googlegroups.com>

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Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
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 by: William - Wed, 8 Jun 2022 20:36 UTC

On Wednesday, June 8, 2022 at 4:17:44 PM UTC-3, WM wrote:
> William schrieb am Mittwoch, 8. Juni 2022 um 17:10:38 UTC+2:
> > On Wednesday, June 8, 2022 at 11:20:08 AM UTC-3, WM wrote:
> > > William schrieb am Mittwoch, 8. Juni 2022 um 16:06:45 UTC+2:
> >
> > > > The set can be represented by a Matrix with no O's.
> > > Only if the O's, which provably cannot disappear,
> > The matrix does not have any O's to appear or disappear.
> Look, in the beginning we have this matrix:
>
> XOOO...
> XOOO...
> XOOO...
> XOOO...
> ...

You cannot get rid of the O's by applying exchanges. So what? You cannot get the bijection by applying exchanges.

--
William Hughes

Re: Natural numbers and vases

<t7r6qj$fq5$1@dont-email.me>

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Wed, 08 Jun 2022 18:11:26 -0400
Organization: Peripheral Visions
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 by: FromTheRafters - Wed, 8 Jun 2022 22:11 UTC

WM explained on 6/8/2022 :
> William schrieb am Mittwoch, 8. Juni 2022 um 17:10:38 UTC+2:
>> On Wednesday, June 8, 2022 at 11:20:08 AM UTC-3, WM wrote:
>>> William schrieb am Mittwoch, 8. Juni 2022 um 16:06:45 UTC+2:
>>>> The set can be represented by a Matrix with no O's.
>>> Only if the O's, which provably cannot disappear,
>> The matrix does not have any O's to appear or disappear.
>
> Look, in the beginning we have this matrix:
>
> XOOO...
> XOOO...
> XOOO...
> XOOO...
> ...
>
> If it is possible to enumerate all fractions, then the X can be distributed
> over the whole matrix. This is impossible.

By the Muckymath Axiom of Because I Said So, so powerful, that one.

For the rest of us, a countably infinite set can be visualized in the
mind's eye as either an N sequence or and N by N cartesian plane of
sequences without causing any brain strain.

Re: Natural numbers and vases

<t7std2$1q4g$1@gioia.aioe.org>

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases
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 by: sergi o - Thu, 9 Jun 2022 13:42 UTC

On 6/8/2022 5:11 PM, FromTheRafters wrote:
> WM explained on 6/8/2022 :
>> William schrieb am Mittwoch, 8. Juni 2022 um 17:10:38 UTC+2:
>>> On Wednesday, June 8, 2022 at 11:20:08 AM UTC-3, WM wrote:
>>>> William schrieb am Mittwoch, 8. Juni 2022 um 16:06:45 UTC+2:
>>>>> The set can be represented by a Matrix with no O's.
>>>> Only if the O's, which provably cannot disappear,
>>> The matrix does not have any O's to appear or disappear.
>>
>> Look, in the beginning we have this matrix:
>>
>> XOOO...
>> XOOO...
>> XOOO...
>> XOOO...
>> ...
>>
>> If it is possible to enumerate all fractions, then the X can be distributed over the whole matrix. This is impossible.
>
> By the Muckymath Axiom of Because I Said So, so powerful, that one.
>
> For the rest of us, a countably infinite set can be visualized in the mind's eye as either an N sequence or and N by N cartesian plane of sequences
> without causing any brain strain.

it can be extended to N by N by N as well,
consider adding 3 new 2D sides to a cube and growing it that way.

a similar index change equation, x,y,z => k ( like m,n => k for 2D to 1D )

Re: Natural numbers and vases

<f8b5a2cf-0f92-42aa-9eb5-475579717c16n@googlegroups.com>

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Thu, 9 Jun 2022 14:52 UTC

William schrieb am Mittwoch, 8. Juni 2022 um 22:36:41 UTC+2:
> On Wednesday, June 8, 2022 at 4:17:44 PM UTC-3, WM wrote:

> > Look, in the beginning we have this matrix:
> >
> > XOOO...
> > XOOO...
> > XOOO...
> > XOOO...
> > ...
> You cannot get rid of the O's by applying exchanges. So what?

You cannot enumerate fractions without applying natural indexes and, in my language, without applying exchanges.

> You cannot get the bijection by applying exchanges.

That means you cannot get the bijection.

By the way, dark numbers are also evident in this example:

∀n∈N:|N \ {1,2,3,...,n}| = ℵo.

Almost all natural numbers remain. According to the universal quantifier this is valid for all natural numbers. Apply one after the other. Nothing will change. Always ℵo natural numbers will be left.

But if it is done too fast, simultaneously say, then nothing remains

N− \ {1,2,3,...}=∅.

This indicates either dark numbers or a time dependence of ZF. What do you prefer?

Regards, WM

Re: Natural numbers and vases

<fa30923e-8f6a-4a79-8998-474c055df7efn@googlegroups.com>

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Thu, 9 Jun 2022 14:55 UTC

FromTheRafters schrieb am Donnerstag, 9. Juni 2022 um 00:11:41 UTC+2:

> For the rest of us, a countably infinite set can be visualized in the
> mind's eye as either an N sequence

Instead of your mind's eye apply logic.

∀n∈N:|N \ {1,2,3,...,n}|=ℵo.

Almost all natural numbers remain. According to the universal quantifier this is valid for all natural numbers. Apply one after the other. Nothing will change. Always ℵo natural numbers will be left.

But here nothing remains:

N\{1,2,3,...}=∅.

This indicates either dark numbers or a time dependence of ZF. What do you prefer?

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
Injection-Date: Thu, 09 Jun 2022 15:00:01 +0000
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 by: William - Thu, 9 Jun 2022 14:59 UTC

On Thursday, June 9, 2022 at 11:52:55 AM UTC-3, WM wrote:

> > You cannot get the bijection by applying exchanges.
> That means you cannot get the bijection.

Piffle, The bijection exists.

--
William Hughes

Re: Natural numbers and vases

<8a29ffed-280d-4b8e-86a0-16a4116dd573n@googlegroups.com>

  copy mid

https://www.novabbs.com/tech/article-flat.php?id=102488&group=sci.math#102488

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Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
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 by: William - Thu, 9 Jun 2022 15:09 UTC

On Thursday, June 9, 2022 at 11:52:55 AM UTC-3, WM wrote:
> ∀n∈N:|N \ {1,2,3,...,n}| = ℵo.

Each element of |N is finite.

|N\{1,2,3,...} = {}

|N = {1,2,3,...} is infinite

--
William Hughes

Re: Natural numbers and vases

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Thu, 09 Jun 2022 12:06:18 -0400
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 by: FromTheRafters - Thu, 9 Jun 2022 16:06 UTC

sergi o presented the following explanation :
> On 6/8/2022 5:11 PM, FromTheRafters wrote:
>> WM explained on 6/8/2022 :
>>> William schrieb am Mittwoch, 8. Juni 2022 um 17:10:38 UTC+2:
>>>> On Wednesday, June 8, 2022 at 11:20:08 AM UTC-3, WM wrote:
>>>>> William schrieb am Mittwoch, 8. Juni 2022 um 16:06:45 UTC+2:
>>>>>> The set can be represented by a Matrix with no O's.
>>>>> Only if the O's, which provably cannot disappear,
>>>> The matrix does not have any O's to appear or disappear.
>>>
>>> Look, in the beginning we have this matrix:
>>>
>>> XOOO...
>>> XOOO...
>>> XOOO...
>>> XOOO...
>>> ...
>>>
>>> If it is possible to enumerate all fractions, then the X can be
>>> distributed over the whole matrix. This is impossible.
>>
>> By the Muckymath Axiom of Because I Said So, so powerful, that one.
>>
>> For the rest of us, a countably infinite set can be visualized in the
>> mind's eye as either an N sequence or and N by N cartesian plane of
>> sequences without causing any brain strain.
>
> it can be extended to N by N by N as well,
> consider adding 3 new 2D sides to a cube and growing it that way.
>
> a similar index change equation, x,y,z => k ( like m,n => k for 2D to 1D )

Yes, Aleph-null raised to power remains the same very big size, but two
raised to the Aleph-null is very very big.

Re: Natural numbers and vases

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Thu, 09 Jun 2022 12:08:02 -0400
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 by: FromTheRafters - Thu, 9 Jun 2022 16:08 UTC

WM brought next idea :
> FromTheRafters schrieb am Donnerstag, 9. Juni 2022 um 00:11:41 UTC+2:
>
>> For the rest of us, a countably infinite set can be visualized in the
>> mind's eye as either an N sequence
>
> Instead of your mind's eye apply logic.
>
> ∀n∈N:|N \ {1,2,3,...,n}|=ℵo.

I told you already, set difference is not subtraction.

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 - Thu, 9 Jun 2022 16:57 UTC

FromTheRafters schrieb am Donnerstag, 9. Juni 2022 um 18:08:17 UTC+2:
> WM brought next idea :
> > FromTheRafters schrieb am Donnerstag, 9. Juni 2022 um 00:11:41 UTC+2:
> >
> >> For the rest of us, a countably infinite set can be visualized in the
> >> mind's eye as either an N sequence
> >
> > Instead of your mind's eye apply logic.
> >
> > ∀n∈N:|N \ {1,2,3,...,n}|=ℵo.
> I told you already, set difference is not subtraction.

Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. (Wikipedia and also common sense)

Regards, WM

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 - Thu, 9 Jun 2022 17:00 UTC

William schrieb am Donnerstag, 9. Juni 2022 um 17:09:48 UTC+2:
> On Thursday, June 9, 2022 at 11:52:55 AM UTC-3, WM wrote:
> > ∀n∈N:|N \ {1,2,3,...,n}| = ℵo.
> Each element of |N is finite.

All together are infinite. If all are subtracted, then an infinite set is subtracted.

Regards, WM

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 - Thu, 9 Jun 2022 17:01 UTC

William schrieb am Donnerstag, 9. Juni 2022 um 17:00:09 UTC+2:
> On Thursday, June 9, 2022 at 11:52:55 AM UTC-3, WM wrote:
>
> > > You cannot get the bijection by applying exchanges.
> > That means you cannot get the bijection.
> Piffle, The bijection exists.

Not by doing it, and not in a way that could be checked.

William Hughes

Re: Natural numbers and vases

<c1ae8180-b005-f776-7530-9d153720c802@att.net>

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Thu, 9 Jun 2022 13:44:04 -0400
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 by: Jim Burns - Thu, 9 Jun 2022 17:44 UTC

On 6/9/2022 1:01 PM, WM wrote:
> William schrieb
> am Donnerstag, 9. Juni 2022 um 17:00:09 UTC+2:
>> On Thursday, June 9, 2022 at 11:52:55 AM UTC-3,
>> WM wrote:

>>>> You cannot get the bijection by
>>>> applying exchanges.
>>>
>>> That means you cannot get the bijection.
>>
>> Piffle, The bijection exists.
>
> Not by doing it,
> and not in a way that could be checked.

The bijection,
the collection of pairs ⟨m/n,k/1⟩,
is known to exist.

We can know a fact about each one of infinitely-many
without performing infinitely-many checks.

It does not take a miracle to describe the things
which we are discussing. That description is true
of each one, even if there are infinitely-many.

It does not take a miracle to NOT advance to
further claims that are NOT always,always,always
true of whatever the earlier claims are true of.

We start without checking each one.
We advance without checking each one.
We know,
after advancing to finitely-many further claims,
that this last claim is true of the same
infinitely-many that the first claim was true of.
No checks.

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
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 by: William - Thu, 9 Jun 2022 18:05 UTC

On Thursday, June 9, 2022 at 2:00:19 PM UTC-3, WM wrote:

> If all are subtracted, then an infinite set is subtracted.

Correct. ∀n∈N:|N \ {1,2,3,...,n}| = ℵo is an infinite number of statements. Each statement is about subtracting a finite set. You cannot combine these statements to a statement about subtracting an infinite set.

--
William Hughes

Re: Natural numbers and vases

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Thu, 09 Jun 2022 14:24:25 -0400
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 by: FromTheRafters - Thu, 9 Jun 2022 18:24 UTC

WM formulated on Thursday :
> FromTheRafters schrieb am Donnerstag, 9. Juni 2022 um 18:08:17 UTC+2:
>> WM brought next idea :
>>> FromTheRafters schrieb am Donnerstag, 9. Juni 2022 um 00:11:41 UTC+2:
>>>
>>>> For the rest of us, a countably infinite set can be visualized in the
>>>> mind's eye as either an N sequence
>>>
>>> Instead of your mind's eye apply logic.
>>>
>>> ∀n∈N:|N \ {1,2,3,...,n}|=ℵo.
>> I told you already, set difference is not subtraction.
>
> Subtraction is an arithmetic operation that represents the operation of
> removing objects from a collection. (Wikipedia and also common sense)

But that is not what your notation means.

Re: Natural numbers and vases

<2dba79e2-eb36-48fe-a0f5-0166f2fc565dn@googlegroups.com>

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Subject: Re: Natural numbers and vases
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Thu, 9 Jun 2022 20:40 UTC

On Thursday, June 9, 2022 at 6:57:51 PM UTC+2, WM wrote:
> FromTheRafters schrieb am Donnerstag, 9. Juni 2022 um 18:08:17 UTC+2:
> >
> > I told you already, /set difference/ is not /subtraction/.
> >
> Subtraction is an arithmetic operation that <bla> (Wikipedia

You do understand that there's a DIFFERENCE between an __arithmetic operation__ and a __set-theoretic__ operation, idiot?

> and also common sense)

Holy shit!!!

We are talking about a __mathematical theory__ here, you silly idiot! A mathematical theory is ruled by /primitive notions/ and /defined notions/, /axioms/ and /(derived) theorems/.

You can't decide TECHNICAL questions (in the context of set theory) by reference to "common sense", you silly crank.

Learn some logic, learn some math, Mückenheim!

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 - Thu, 9 Jun 2022 20:45 UTC

On Thursday, June 9, 2022 at 7:00:19 PM UTC+2, WM wrote:
> William schrieb am Donnerstag, 9. Juni 2022 um 17:09:48 UTC+2:
> > On Thursday, June 9, 2022 at 11:52:55 AM UTC-3, WM wrote:
> > >
> > > ∀n ∈ N: | N \ {1, 2, 3, ..., n} | = ℵo.

So what?

> > Each element of IN is finite.

right. Moreover for each and every n e IN, the set

{1, 2, 3, ..., n}

is finite.

> All [natural numbers] together [form an] infinite [set].

Indeed. IN = {n : n e IN} and card(IN) = ℵo.

So what's your point, you silly crank?

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 - Fri, 10 Jun 2022 13:34 UTC


Jim Burns schrieb am Donnerstag, 9. Juni 2022 um 19:44:16 UTC+2:
> On 6/9/2022 1:01 PM, WM wrote:

> > Not by doing it,
> > and not in a way that could be checked.
> The bijection,
> the collection of pairs ⟨m/n,k/1⟩,
> is known to exist.

It is believed so, but it cannot be constructed.

On the contrary when constructing it, we see that construction fails.
>
> We can know a fact about each one of infinitely-many
> without performing infinitely-many checks.

Potential infinity is right so, but that is not what Cantor claimed.
>
> It does not take a miracle to describe the things
> which we are discussing. That description is true
> of each one, even if there are infinitely-many.

It does! For instance you cannot exhaust ℕ by counting it:
∀n ∈ ℕ: |ℕ \ {1, 2, 3, ..., n}| = ℵo.

How should the fractions be counted exhaustively by individuals?

> We start without checking each one.
> We advance without checking each one.
> We know,
> after advancing to finitely-many further claims,
> that this last claim is true of the same
> infinitely-many that the first claim was true of.
> No checks.

That's why hitherto no-one has recognized the failure.

Regards, WM

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 - Fri, 10 Jun 2022 13:40 UTC

William schrieb am Donnerstag, 9. Juni 2022 um 20:05:56 UTC+2:
> On Thursday, June 9, 2022 at 2:00:19 PM UTC-3, WM wrote:
>
> > If all are subtracted, then an infinite set is subtracted.
> Correct. ∀n∈N:|N \ {1,2,3,...,n}| = ℵo is an infinite number of statements. Each statement is about subtracting a finite set. You cannot combine these statements to a statement about subtracting an infinite set.

Why not? ∀n∈N says "for all n without exception".

Look ∀n∈N: N \ {1,2,3,...,n} means counting the natural numbers by individuals n. That cannot be done exhaustively.

How should the larger set of fractions be exhaustively counted by those very n which fail to exhaustively count N? A miracle.

Regards, WM

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 - Fri, 10 Jun 2022 13:44 UTC

FromTheRafters schrieb am Donnerstag, 9. Juni 2022 um 20:24:39 UTC+2:
> WM formulated on Thursday :
> > FromTheRafters schrieb am Donnerstag, 9. Juni 2022 um 18:08:17 UTC+2:
> >> WM brought next idea :
> >>> FromTheRafters schrieb am Donnerstag, 9. Juni 2022 um 00:11:41 UTC+2:
> >>>
> >>>> For the rest of us, a countably infinite set can be visualized in the
> >>>> mind's eye as either an N sequence
> >>>
> >>> Instead of your mind's eye apply logic.
> >>>
> >>> ∀n∈N:|N \ {1,2,3,...,n}|=ℵo.
> >> I told you already, set difference is not subtraction.
> >
> > Subtraction is an arithmetic operation that represents the operation of
> > removing objects from a collection. (Wikipedia and also common sense)
> But that is not what your notation means.

It is. But you can also understand it as counting N. As the attempt to count N, to be precise. As an attempt which fails. The elements n of N cannot exhaustively count N. How should they exhaustively count all fractions?

Regards, WM

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 - Fri, 10 Jun 2022 13:49 UTC

Fritz Feldhase schrieb am Donnerstag, 9. Juni 2022 um 22:41:01 UTC+2:

> You can't decide TECHNICAL questions (in the context of set theory) by reference to "common sense",

I know. No-one with common sense can accept set theory.

> What's your point?

The elements n of ℕ cannot exhaustively count ℕ as is shown by the attempted counting
∀n ∈ ℕ: |ℕ \ {1, 2, 3, ..., n}| = ℵo .
How should they exhaustively count all fractions?

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
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 by: FromTheRafters - Fri, 10 Jun 2022 13:55 UTC

WM formulated on Friday :
> William schrieb am Donnerstag, 9. Juni 2022 um 20:05:56 UTC+2:
>> On Thursday, June 9, 2022 at 2:00:19 PM UTC-3, WM wrote:
>>
>>> If all are subtracted, then an infinite set is subtracted.
>> Correct. ∀n∈N:|N \ {1,2,3,...,n}| = ℵo is an infinite number of statements.
>> Each statement is about subtracting a finite set. You cannot combine these
>> statements to a statement about subtracting an infinite set.
>
> Why not? ∀n∈N says "for all n without exception".
>
> Look ∀n∈N: N \ {1,2,3,...,n} means counting the natural numbers by
> individuals n.

Does it? It looks to me like the special symbol for the 'set' of
natural numbers is being compared (set difference) to the 'set' of
'elements' in a FISON ending at n -- not necessarily to any order those
elements are in.

Re: Natural numbers and vases

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From: askaske...@gmail.com (WM)
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 by: WM - Fri, 10 Jun 2022 13:58 UTC

FromTheRafters schrieb am Freitag, 10. Juni 2022 um 15:55:25 UTC+2:
> WM formulated on Friday :
> > William schrieb am Donnerstag, 9. Juni 2022 um 20:05:56 UTC+2:
> >> On Thursday, June 9, 2022 at 2:00:19 PM UTC-3, WM wrote:
> >>
> >>> If all are subtracted, then an infinite set is subtracted.
> >> Correct. ∀n∈N:|N \ {1,2,3,...,n}| = ℵo is an infinite number of statements.
> >> Each statement is about subtracting a finite set. You cannot combine these
> >> statements to a statement about subtracting an infinite set.
> >
> > Why not? ∀n∈N says "for all n without exception".
> >
> > Look ∀n∈N: N \ {1,2,3,...,n} means counting the natural numbers by
> > individuals n.
> Does it? It looks to me like the special symbol for the 'set' of
> natural numbers is being compared (set difference) to the 'set' of
> 'elements' in a FISON ending at n

You overlooked the universal quantifier. All n are applied.

Regards, WM

Re: Natural numbers and vases

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 by: sergi o - Fri, 10 Jun 2022 14:00 UTC

On 6/10/2022 8:34 AM, WM wrote:
>
> Jim Burns schrieb am Donnerstag, 9. Juni 2022 um 19:44:16 UTC+2:
>> On 6/9/2022 1:01 PM, WM wrote:
>
>>> Not by doing it,
>>> and not in a way that could be checked.
>> The bijection,
>> the collection of pairs ⟨m/n,k/1⟩,
>> is known to exist.
>
> It is believed so, but it cannot be constructed.

Liar.

>
> On the contrary when constructing it, we see that construction fails.

Liar.

>>
>> We can know a fact about each one of infinitely-many
>> without performing infinitely-many checks.
>
> Potential infinity is right so, but that is not what Cantor claimed.

Potential infinity = finite

>>
>> It does not take a miracle to describe the things
>> which we are discussing. That description is true
>> of each one, even if there are infinitely-many.
>
> It does! For instance you cannot exhaust ℕ by counting it:
> ∀n ∈ ℕ: |ℕ \ {1, 2, 3, ..., n}| = ℵo.

that is not a "counting" equation, dummy.

>
> How should the fractions be counted exhaustively by individuals?
>
>> We start without checking each one.
>> We advance without checking each one.
>> We know,
>> after advancing to finitely-many further claims,
>> that this last claim is true of the same
>> infinitely-many that the first claim was true of.
>> No checks.
>
> That's why hitherto no-one has recognized the failure.

there is no failure.

>
> Regards, WM

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