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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

<t695pj$qhg$1@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=100581&group=sci.math#100581

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Path: i2pn2.org!i2pn.org!eternal-september.org!reader02.eternal-september.org!.POSTED!not-for-mail
From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Fri, 20 May 2022 15:47:12 -0700
Organization: A noiseless patient Spider
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Message-ID: <t695pj$qhg$1@dont-email.me>
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<t68559$1lpg$2@gioia.aioe.org> <t68nvv$hve$1@dont-email.me>
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 by: Chris M. Thomasson - Fri, 20 May 2022 22:47 UTC

On 5/20/2022 3:00 PM, FromTheRafters wrote:
> Jim Burns formulated on Friday :
>> On 5/20/2022 2:51 PM, Chris M. Thomasson wrote:
>>> On 5/20/2022 6:30 AM, sergi o wrote:
>>>> On 5/20/2022 6:02 AM, WM wrote:
>>
>>>>> Regards, WM
>>>>
>>>> you are outside of math, with your black numbers,
>>>> magic math, it is  stupid math.
>>>
>>> dark numbers written on a contrasting color of paper
>>> can be read?  Imaging using black ink to write on a piece
>>> of paper that is black. WM's  dark numbers... ;^)
>>
>> I heard somewhere that black panthers have spots --
>> black-on-black spots.
>>
>> The problem with WM's dark numbers is that
>> he thinks it's impossible to talk about
>> only non-black-panther leopards.
>
> https://www.forbes.com/sites/kionasmith/2017/06/24/alan-turing-described-natures-beauty-with-numbers/?sh=737a7dfc77ae
>
>
> Might be a paywall.
>
> https://www.bbcearth.com/news/the-maths-behind-a-leopards-spots

I saw a recent Nova about the camo of bird eggs trying to evade the
dreaded parasitic cuckoo, that love to "replace" eggs in existing nests...

Re: Natural numbers and vases

<t69oa0$151m$1@gioia.aioe.org>

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From: inva...@invalid.com (sergi o)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Fri, 20 May 2022 23:03:11 -0500
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 by: sergi o - Sat, 21 May 2022 04:03 UTC

On 5/20/2022 5:00 PM, FromTheRafters wrote:
> Jim Burns formulated on Friday :
>> On 5/20/2022 2:51 PM, Chris M. Thomasson wrote:
>>> On 5/20/2022 6:30 AM, sergi o wrote:
>>>> On 5/20/2022 6:02 AM, WM wrote:
>>
>>>>> Regards, WM
>>>>
>>>> you are outside of math, with your black numbers,
>>>> magic math, it is  stupid math.
>>>
>>> dark numbers written on a contrasting color of paper
>>> can be read?  Imaging using black ink to write on a piece
>>> of paper that is black. WM's  dark numbers... ;^)
>>
>> I heard somewhere that black panthers have spots --
>> black-on-black spots.
>>
>> The problem with WM's dark numbers is that
>> he thinks it's impossible to talk about
>> only non-black-panther leopards.
>
> https://www.forbes.com/sites/kionasmith/2017/06/24/alan-turing-described-natures-beauty-with-numbers/?sh=737a7dfc77ae

Numbers and math have many great beautiful areas,
Im currently working on a problem that has easy solutions for simple 2d patterns (that can extend to infinity), but degrades into complexity fast for
more complex 2d patterns, primarly using permutation, combinatioral math very interesting and quite hard too.

>
> Might be a paywall.
>
> https://www.bbcearth.com/news/the-maths-behind-a-leopards-spots

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 - Sat, 21 May 2022 07:22 UTC

On Friday, May 20, 2022 at 8:07:53 AM UTC-3, WM wrote:
> ... not any has less means all together have not less.

Nope. Trivial counterexample Consider a Peano set S. Every element of S has a successor in S. S does not have a successor in S.
So not any has less than 1 but "all together" has less than 1.

--
William Hughes

Re: Natural numbers and vases

<t6ab81$ast$1@dont-email.me>

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sat, 21 May 2022 02:26:19 -0700
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 by: FromTheRafters - Sat, 21 May 2022 09:26 UTC

Chris M. Thomasson explained :
> On 5/20/2022 3:00 PM, FromTheRafters wrote:
>> Jim Burns formulated on Friday :
>>> On 5/20/2022 2:51 PM, Chris M. Thomasson wrote:
>>>> On 5/20/2022 6:30 AM, sergi o wrote:
>>>>> On 5/20/2022 6:02 AM, WM wrote:
>>>
>>>>>> Regards, WM
>>>>>
>>>>> you are outside of math, with your black numbers,
>>>>> magic math, it is  stupid math.
>>>>
>>>> dark numbers written on a contrasting color of paper
>>>> can be read?  Imaging using black ink to write on a piece
>>>> of paper that is black. WM's  dark numbers... ;^)
>>>
>>> I heard somewhere that black panthers have spots --
>>> black-on-black spots.
>>>
>>> The problem with WM's dark numbers is that
>>> he thinks it's impossible to talk about
>>> only non-black-panther leopards.
>>
>> https://www.forbes.com/sites/kionasmith/2017/06/24/alan-turing-described-natures-beauty-with-numbers/?sh=737a7dfc77ae
>>
>>
>> Might be a paywall.
>>
>> https://www.bbcearth.com/news/the-maths-behind-a-leopards-spots
>
> I saw a recent Nova about the camo of bird eggs trying to evade the dreaded
> parasitic cuckoo, that love to "replace" eggs in existing nests...

Yes, I recall another treatment that went into the 'arms race' of
egg-spot patterns for other nest parasites like Brown-headed Cowbirds.

Fascinating stuff.

Re: Natural numbers and vases

<t6ah01$12rd$3@gioia.aioe.org>

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From: oaa...@imadasam.ao (Darin Okimasa)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Followup-To: sci.physics.relativity
Date: Sat, 21 May 2022 11:04:34 -0000 (UTC)
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 by: Darin Okimasa - Sat, 21 May 2022 11:04 UTC

Chris M. Thomasson wrote:

>> So it is not dark now, as I am looking at it occasionally, but it is
>> lights out for that dude when I send this out.
>
> Interesting. Humm... Well, shit. All numbers are dark to a baby? Humm...
> Almost all?

cetarle teeleevizia

Khakhole nazi scumbags jumping up and down in Austria
https://www.bitchute.com/video/h4k8Jcohl1X7/

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 - Sat, 21 May 2022 15:40 UTC

FromTheRafters schrieb am Freitag, 20. Mai 2022 um 13:23:46 UTC+2:
> WM was thinking very hard :

> > You are outside of logic. The set is nothing else but all its elements.
> You have said this before, do you have a citation for that?

Unter einer "Menge" verstehen wir jede Zusammenfassung M von bestimmten wohlunterschiedenen Objekten m unsrer Anschauung oder unseres Denkens (welche die "Elemente" von M genannt werden) zu einem Ganzen.

"every collection of definite well-distinguished objects of our visualization or thinking". [Cantor]

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 - Sat, 21 May 2022 15:46 UTC

Jim Burns schrieb am Freitag, 20. Mai 2022 um 21:25:16 UTC+2:

> The problem with WM's dark numbers is that
> he thinks it's impossible to talk about
> only non-black-panther leopards.

No, that is possible, but there is no actual infinity of them.

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 - Sat, 21 May 2022 15:53 UTC

Fritz Feldhase schrieb am Freitag, 20. Mai 2022 um 23:34:19 UTC+2:
> On Friday, May 20, 2022 at 1:07:53 PM UTC+2, WM wrote:

> > The set is nothing else but all its elements.
> Nonsense. Hint: The set {} is empty. Which of its elements is empty too?

The set does not exist, strictly speaking.

"If, according to our previous use of the word, a class consists of things, is a collection, a collective union of them, then it must disappear when these things disappear. If we burn down all the trees of a forest, then we burn down the forest. Thus an empty class cannot exist." [G. Frege: "Kleine Schriften", I. Agelelli (ed.), 2nd ed., Olms, Hildesheim (1990) p. 195]

"P == O means that the set P does not contain any single point. So it is, strictly speaking, not existing as such." [Cantor, p. 146]

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
Injection-Date: Sat, 21 May 2022 16:00:32 +0000
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 by: WM - Sat, 21 May 2022 16:00 UTC

William schrieb am Samstag, 21. Mai 2022 um 09:22:27 UTC+2:
> On Friday, May 20, 2022 at 8:07:53 AM UTC-3, WM wrote:
> > ... not any has less means all together have not less.
>
> Nope. Trivial counterexample Consider a Peano set S. Every element of S has a successor in S. S does not have a successor in S.

There is no set S but only a pot. inf. collection S. Irrespective of how man elements you have accumulated, you can find or construct one more element.

> So not any has less than 1 but "all together" has less than 1.

In order to have all together "all" must have a meaning. That requires actual infinity.

Regards, WM

Re: Natural numbers and vases

<t6b2jc$kg5$2@gioia.aioe.org>

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sat, 21 May 2022 11:04:59 -0500
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 by: sergi o - Sat, 21 May 2022 16:04 UTC

On 5/21/2022 10:40 AM, WM wrote:
> FromTheRafters schrieb am Freitag, 20. Mai 2022 um 13:23:46 UTC+2:
>> WM was thinking very hard :
>
>>> You are outside of logic. The set is nothing else but all its elements.
>> You have said this before, do you have a citation for that?
>
> Unter einer "Menge" verstehen wir jede Zusammenfassung M von bestimmten wohlunterschiedenen Objekten m unsrer Anschauung oder unseres Denkens (welche die "Elemente" von M genannt werden) zu einem Ganzen.
>
> "every collection of definite well-distinguished objects of our visualization or thinking". [Cantor]
>
> Regards, WM

wrong quote.

what you snipped "again "the set, "all elements", can have a property that "each element" does not have."

you confuse sets with their elements, most all the time. Fail.

Re: Natural numbers and vases

<t6b2oq$or5$1@gioia.aioe.org>

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Subject: Re: Natural numbers and vases
Date: Sat, 21 May 2022 11:07:52 -0500
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 by: sergi o - Sat, 21 May 2022 16:07 UTC

On 5/21/2022 10:53 AM, WM wrote:
> Fritz Feldhase schrieb am Freitag, 20. Mai 2022 um 23:34:19 UTC+2:
>> On Friday, May 20, 2022 at 1:07:53 PM UTC+2, WM wrote:
>
>>> The set is nothing else but all its elements.
>> Nonsense. Hint: The set {} is empty. Which of its elements is empty too?
>
> The set does not exist, strictly speaking.

wrong. it is called the empty set. You ARE new to this aren't you?

>
> "If, according to our previous use of the word, a class consists of things, is a collection, a collective union of them, then it must disappear when these things disappear. If we burn down all the trees of a forest, then we burn down the forest. Thus an empty class cannot exist." [G. Frege: "Kleine Schriften", I. Agelelli (ed.), 2nd ed., Olms, Hildesheim (1990) p. 195]

wrong quote, that refers to class, not sets.

>
> "P == O means that the set P does not contain any single point. So it is, strictly speaking, not existing as such." [Cantor, p. 146]

wrong quote. P exists because Cantor identifies it in his statement.

>
> Regards, WM

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 - Sat, 21 May 2022 16:08 UTC

On Saturday, May 21, 2022 at 1:00:38 PM UTC-3, WM wrote:
> William schrieb am Samstag, 21. Mai 2022 um 09:22:27 UTC+2:
> > On Friday, May 20, 2022 at 8:07:53 AM UTC-3, WM wrote:
> > > ... not any has less means all together have not less.
> >
> > Nope. Trivial counterexample Consider a Peano set S. Every element of S has a successor in S. S does not have a successor in S.
> There is no set S

Piffle. S exists by the Axiom of infinity, It is well known that you do not like the results of taking this axiom, but results that you do no like are not contradictions.

--
William Hughes

Re: Natural numbers and vases

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 by: sergi o - Sat, 21 May 2022 16:09 UTC

On 5/21/2022 10:46 AM, WM wrote:
> Jim Burns schrieb am Freitag, 20. Mai 2022 um 21:25:16 UTC+2:
>
>> The problem with WM's dark numbers is that
>> he thinks it's impossible to talk about
>> only non-black-panther leopards.
>
> No, that is possible, but there is no actual infinity of them.

wrong, your dark numbers have no properties, you cannot conclude anything about them.

>
> Regards, WM

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 - Sat, 21 May 2022 16:45 UTC

On Saturday, May 21, 2022 at 6:08:03 PM UTC+2, sergi o wrote:
> On 5/21/2022 10:53 AM, WM wrote:
> >
> > "If, according to our previous use of the word, a class consists of things, is a collection, a collective union of them, then it must disappear when these things disappear. If we burn down all the trees of a forest, then we burn down the forest. Thus an empty class cannot exist." [G. Frege: "Kleine Schriften", I. Agelelli (ed.), 2nd ed., Olms, Hildesheim (1990) p. 195]
> >
> wrong quote, that refers to class, not sets.

Indeed. That's the the very point of this short paper by Frege: He tried to point out the difference between (his) "sets" and "entities" he called "classes" (referring to some statements by Schröder). Of course there was an empty "set" in Frege's system.

WM is dumb like shit.

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 - Sat, 21 May 2022 17:58 UTC

Fritz Feldhase schrieb am Samstag, 21. Mai 2022 um 18:45:19 UTC+2:
> On Saturday, May 21, 2022 at 6:08:03 PM UTC+2, sergi o wrote:
> > On 5/21/2022 10:53 AM, WM wrote:
> > >
> > > "If, according to our previous use of the word, a class consists of things, is a collection, a collective union of them, then it must disappear when these things disappear. If we burn down all the trees of a forest, then we burn down the forest. Thus an empty class cannot exist." [G. Frege: "Kleine Schriften", I. Agelelli (ed.), 2nd ed., Olms, Hildesheim (1990) p. 195]
> > >
> > wrong quote, that refers to class, not sets.
> Indeed. That's the the very point of this short paper by Frege: He tried to point out the difference between (his) "sets" and "entities" he called "classes" (referring to some statements by Schröder). Of course there was an empty "set" in Frege's system.

Where does he state it?

This statement refers to sets: "P == O means that the set P does not contain any single point. So it is, strictly speaking, not existing as such." [Cantor, p. 146]

This one too: "It is not a genuine set and was introduced by me only for formal reasons." [E. Zermelo, letter to A. Fraenkel (1 Mar 1921)] "I increasingly doubt the justifiability of the 'null set'. Perhaps one can dispense with it by restricting the axiom of separation in a suitable way. Indeed, it serves only the purpose of formal simplification." [E. Zermelo, letter to A. Fraenkel (9 May 1921)]

Regards, WM

Re: Natural numbers and vases

<t6bbe1$682$1@dont-email.me>

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Subject: Re: Natural numbers and vases
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 by: FromTheRafters - Sat, 21 May 2022 18:35 UTC

WM explained on 5/21/2022 :
> FromTheRafters schrieb am Freitag, 20. Mai 2022 um 13:23:46 UTC+2:
>> WM was thinking very hard :
>
>>> You are outside of logic. The set is nothing else but all its elements.
>> You have said this before, do you have a citation for that?
>
> Unter einer "Menge" verstehen wir jede Zusammenfassung M von bestimmten
> wohlunterschiedenen Objekten m unsrer Anschauung oder unseres Denkens (welche
> die "Elemente" von M genannt werden) zu einem Ganzen.
>
> "every collection of definite well-distinguished objects of our visualization
> or thinking". [Cantor]
>
Book cover
==============================================
Mathematics for Physicists pp 13–99 Cite as
basics

Helmut Fischer & Helmut Kaul

Chapters

8296 accesses

summary

"By a set we understand every combination M of certain
well-distinguished objects m our intuition or our thinking (which are
called the elements of M ) into a whole". This is how Georg Cantor 's
contributions to the establishment of set theory , published in 1895,
begin . This “naive” definition should suffice as a starting point.

[...]
===================================================================

Nothing about 'nothing else'.

A bunch of 'would be' elements are not a set.

Re: Natural numbers and vases

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 by: sergi o - Sat, 21 May 2022 18:50 UTC

On 5/21/2022 12:58 PM, WM wrote:
> Fritz Feldhase schrieb am Samstag, 21. Mai 2022 um 18:45:19 UTC+2:
>> On Saturday, May 21, 2022 at 6:08:03 PM UTC+2, sergi o wrote:
>>> On 5/21/2022 10:53 AM, WM wrote:
>>>>
>>>> "If, according to our previous use of the word, a class consists of things, is a collection, a collective union of them, then it must disappear when these things disappear. If we burn down all the trees of a forest, then we burn down the forest. Thus an empty class cannot exist." [G. Frege: "Kleine Schriften", I. Agelelli (ed.), 2nd ed., Olms, Hildesheim (1990) p. 195]
>>>>
>>> wrong quote, that refers to class, not sets.
>> Indeed. That's the the very point of this short paper by Frege: He tried to point out the difference between (his) "sets" and "entities" he called "classes" (referring to some statements by Schröder). Of course there was an empty "set" in Frege's system.
>
> Where does he state it?
>
> This statement refers to sets: "P == O means that the set P does not contain any single point. So it is, strictly speaking, not existing as such." [Cantor, p. 146]

wrong quote. P exists because Cantor identifies it in his statement.

>
> This one too: "It is not a genuine set and was introduced by me only for formal reasons." [E. Zermelo, letter to A. Fraenkel (1 Mar 1921)] "I increasingly doubt the justifiability of the 'null set'. Perhaps one can dispense with it by restricting the axiom of separation in a suitable way. Indeed, it serves only the purpose of formal simplification." [E. Zermelo, letter to A. Fraenkel (9 May 1921)]

from quote above: Zermelo confirms there exists the null set, and it is formally used.

>
> Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
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 by: Chris M. Thomasson - Sat, 21 May 2022 19:28 UTC

On 5/20/2022 9:03 PM, sergi o wrote:
> On 5/20/2022 5:00 PM, FromTheRafters wrote:
>> Jim Burns formulated on Friday :
>>> On 5/20/2022 2:51 PM, Chris M. Thomasson wrote:
>>>> On 5/20/2022 6:30 AM, sergi o wrote:
>>>>> On 5/20/2022 6:02 AM, WM wrote:
>>>
>>>>>> Regards, WM
>>>>>
>>>>> you are outside of math, with your black numbers,
>>>>> magic math, it is  stupid math.
>>>>
>>>> dark numbers written on a contrasting color of paper
>>>> can be read?  Imaging using black ink to write on a piece
>>>> of paper that is black. WM's  dark numbers... ;^)
>>>
>>> I heard somewhere that black panthers have spots --
>>> black-on-black spots.
>>>
>>> The problem with WM's dark numbers is that
>>> he thinks it's impossible to talk about
>>> only non-black-panther leopards.
>>
>> https://www.forbes.com/sites/kionasmith/2017/06/24/alan-turing-described-natures-beauty-with-numbers/?sh=737a7dfc77ae
>>
>
> Numbers and math have many great beautiful areas,
> Im currently working on a problem that has easy solutions for simple 2d
> patterns (that can extend to infinity), but degrades into complexity
> fast for more complex 2d patterns, primarly using permutation,
> combinatioral math very interesting and quite hard too.

Here is an example:

https://www.shadertoy.com/view/3tlcz4

https://www.shadertoy.com/view/4lffzM

>
>>
>> Might be a paywall.
>>
>> https://www.bbcearth.com/news/the-maths-behind-a-leopards-spots
>

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From: chris.m....@gmail.com (Chris M. Thomasson)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sat, 21 May 2022 12:38:56 -0700
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 by: Chris M. Thomasson - Sat, 21 May 2022 19:38 UTC

On 5/21/2022 8:46 AM, WM wrote:
> Jim Burns schrieb am Freitag, 20. Mai 2022 um 21:25:16 UTC+2:
>
>> The problem with WM's dark numbers is that
>> he thinks it's impossible to talk about
>> only non-black-panther leopards.
>
> No, that is possible, but there is no actual infinity of them.

Think of them as fingerprints, or snowflakes. The word unique comes to
mind. Keep in mind that this is in the physical world. I am not sure if
the physical world is infinite. Can we zoom in forever? Also, can we
zoom out forever?

I think you are confusing math the physics again... ;^)

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sat, 21 May 2022 12:41:38 -0700
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 by: Chris M. Thomasson - Sat, 21 May 2022 19:41 UTC

On 5/21/2022 9:00 AM, WM wrote:
> William schrieb am Samstag, 21. Mai 2022 um 09:22:27 UTC+2:
>> On Friday, May 20, 2022 at 8:07:53 AM UTC-3, WM wrote:
>>> ... not any has less means all together have not less.
>>
>> Nope. Trivial counterexample Consider a Peano set S. Every element of S has a successor in S. S does not have a successor in S.
>
> There is no set S but only a pot. inf. collection S. Irrespective of how man elements you have accumulated, you can find or construct one more element.
>
>> So not any has less than 1 but "all together" has less than 1.
>
> In order to have all together "all" must have a meaning. That requires actual infinity.

The whole numbers are actually infinite. Get over it.

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Sat, 21 May 2022 20:32 UTC

FromTheRafters schrieb am Samstag, 21. Mai 2022 um 20:35:55 UTC+2:
> WM explained on 5/21/2022 :
> > FromTheRafters schrieb am Freitag, 20. Mai 2022 um 13:23:46 UTC+2:
> >> WM was thinking very hard :
> >
> >>> You are outside of logic. The set is nothing else but all its elements.
> >> You have said this before, do you have a citation for that?
> >
> > Unter einer "Menge" verstehen wir jede Zusammenfassung M von bestimmten
> > wohlunterschiedenen Objekten m unsrer Anschauung oder unseres Denkens (welche
> > die "Elemente" von M genannt werden) zu einem Ganzen.
> >
> > "every collection of definite well-distinguished objects of our visualization
> > or thinking". [Cantor]

> "By a set we understand every combination M of certain
> well-distinguished objects m our intuition or our thinking (which are
> called the elements of M ) into a whole". This is how Georg Cantor 's
> contributions to the establishment of set theory , published in 1895,
> begin . This “naive” definition should suffice as a starting point.
>
> [...]
> ===================================================================
>
> Nothing about 'nothing else'.

Of course not, since there is nothing else.

> A bunch of 'would be' elements are not a set.

Which bunch of finitely many elements would not be a set?

Regards, WM

Re: Natural numbers and vases

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sat, 21 May 2022 16:34:38 -0400
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 by: Jim Burns - Sat, 21 May 2022 20:34 UTC

On 5/21/2022 3:38 PM, Chris M. Thomasson wrote:

> I am not sure if the physical world is infinite.
> Can we zoom in forever?
> Also, can we zoom out forever?

As far as zooming out is concerned...

We have pretty firm observations for the age/size of
the _observable_ universe.
For that, the answer is "not forever".

Suppose we very reasonably assume that, of all the
universe that exists, observable or not, that part which
we observe is nothing special.

What we observe has a curvature very close to zero,
with a 50/50 chance of being positive or negative.

If the curvature is positive, the answer for the
_whole_ universe is "not forever".

If the curvature is negative,
the _whole_ universe is literally infinite,
and the answer is "forever".

I think that some theorists are suspicious of
how close the observed curvature is to zero
(which is: reallyreallyreally damn close), and they're
thinking about possible underlying principles that
would force the curvature to be exactly zero.
In that case, the answer would be "forever".

As far as zooming in is concerned...

There is a strong consensus that the answer
is "not forever".

The details are being worked out As We Speak,
but everyone seems to agree that some further
theory is needed to explain time, space, and gravity
at the Very Small, and that, when we have it,
time, space, and gravity won't look much like
time, space, and gravity, so it is very likely
that there is some zoom-in which won't make sense
to call a "zoom-in". Thus "not forever".

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 by: sergi o - Sat, 21 May 2022 20:36 UTC

On 5/21/2022 11:00 AM, WM wrote:
> William schrieb am Samstag, 21. Mai 2022 um 09:22:27 UTC+2:
>> On Friday, May 20, 2022 at 8:07:53 AM UTC-3, WM wrote:
>>> ... not any has less means all together have not less.
>>
>> Nope. Trivial counterexample Consider a Peano set S. Every element of S has a successor in S. S does not have a successor in S.
>
> There is no set S

Wrong. you do not even know math protocol! He defined a set S. so you deal with it, what is WRONG with you ?

> but only a pot. inf. collection S.

Wrong. "Every element of S has a successor in S"

> Irrespective of how man elements you have accumulated, you can find or construct one more element.

now you have a different set, it is not the same set.

>
>> So not any has less than 1 but "all together" has less than 1.
>
> In order to have all together "all" must have a meaning. That requires actual infinity.

your thinking is undisciplined.

>
> Regards, WM

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Sat, 21 May 2022 20:37 UTC

William schrieb am Samstag, 21. Mai 2022 um 18:08:14 UTC+2:
> On Saturday, May 21, 2022 at 1:00:38 PM UTC-3, WM wrote:
> > William schrieb am Samstag, 21. Mai 2022 um 09:22:27 UTC+2:
> > > On Friday, May 20, 2022 at 8:07:53 AM UTC-3, WM wrote:
> > > > ... not any has less means all together have not less.
> > >
> > > Nope. Trivial counterexample Consider a Peano set S. Every element of S has a successor in S. S does not have a successor in S.
> > There is no set S
> Piffle. S exists by the Axiom of infinity, It is well known that you do not like the results of taking this axiom, but results that you do no like are not contradictions.

The square circle exists by a similarly invalid axiom. Here are some more:
 Axiom of two even primes: There are two even prime numbers.
 Axiom of prime number triples: There is a second triple of prime numbers, besides (3, 5, 7).
 Axiom of meagre sum: There is a set of n different positive natural numbers with sum n2/2.
How obvious a contradiction has to result from an additional axiom in order to reject it?

Regards, WM

Re: Natural numbers and vases

<t6bj0q$1ie1$1@gioia.aioe.org>

 copy mid

https://www.novabbs.com/tech/article-flat.php?id=100657&group=sci.math#100657

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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: Sat, 21 May 2022 15:45:13 -0500
Organization: Aioe.org NNTP Server
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 by: sergi o - Sat, 21 May 2022 20:45 UTC

On 5/21/2022 3:32 PM, WM wrote:
> FromTheRafters schrieb am Samstag, 21. Mai 2022 um 20:35:55 UTC+2:
>> WM explained on 5/21/2022 :
>>> FromTheRafters schrieb am Freitag, 20. Mai 2022 um 13:23:46 UTC+2:
>>>> WM was thinking very hard :
>>>
>>>>> You are outside of logic. The set is nothing else but all its elements.
>>>> You have said this before, do you have a citation for that?
>>>
>>> Unter einer "Menge" verstehen wir jede Zusammenfassung M von bestimmten
>>> wohlunterschiedenen Objekten m unsrer Anschauung oder unseres Denkens (welche
>>> die "Elemente" von M genannt werden) zu einem Ganzen.
>>>
>>> "every collection of definite well-distinguished objects of our visualization
>>> or thinking". [Cantor]
>
>> "By a set we understand every combination M of certain
>> well-distinguished objects m our intuition or our thinking (which are
>> called the elements of M ) into a whole". This is how Georg Cantor 's
>> contributions to the establishment of set theory , published in 1895,
>> begin . This “naive” definition should suffice as a starting point.
>>
>> [...]
>> ===================================================================
>>
>> Nothing about 'nothing else'.
>
> Of course not, since there is nothing else.
>
>> A bunch of 'would be' elements are not a set.
>
> Which bunch of finitely many elements would not be a set?

why would it ?

your elements are all over the floor!
(yes I realize that could make up a set of elements on the floor, but I haven't declared it as being a set yet (HINT))

Extra Credit : how many different sets would a "bunch" of elements make ?

[(HINT:"bunch"!)]

If I assemble a set of elements, then it would be a set.

finite or infinite is irrelevant.

>
> Regards, WM

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