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"When people are least sure, they are often most dogmatic." -- John Kenneth Galbraith

Re: Natural numbers and vases III

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

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Re: Natural numbers and vases III

<tf0kct$30eio$1@dont-email.me>

copy mid

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sat, 03 Sep 2022 18:27:33 -0400
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by: FromTheRafters - Sat, 3 Sep 2022 22:27 UTC

WM wrote on 9/3/2022 :
> Jim Burns schrieb am Freitag, 2. September 2022 um 23:21:14 UTC+2:
>
>> Consider some set ? of dark numbers
>
> Consider a bathtub.

An infinite bathtub?

Re: Natural numbers and vases III

<tf0m8a$n9o$1@gioia.aioe.org>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=111309&group=sci.math#111309

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From: Tom...@bolamail.etc (Tom Bola)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 4 Sep 2022 00:59:21 +0200
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by: Tom Bola - Sat, 3 Sep 2022 22:59 UTC

FromTheRafters schrieb:
> WM wrote on 9/3/2022 :
>> Jim Burns schrieb am Freitag, 2. September 2022 um 23:21:14 UTC+2:
>>
>>> Consider some set ? of dark numbers
>>
>> Consider a bathtub.
>
> An infinite bathtub?

A "potential" infinite rather than an "actually" infinite one, ROTFL.

Idiot WM feels his destiny is to teach this the dumb mankind...

Re: Natural numbers and vases III

<tf0nl1$30o7t$1@dont-email.me>

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sat, 03 Sep 2022 19:23:05 -0400
Organization: Peripheral Visions
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by: FromTheRafters - Sat, 3 Sep 2022 23:23 UTC

Tom Bola explained :
> FromTheRafters schrieb:
>> WM wrote on 9/3/2022 :
>>> Jim Burns schrieb am Freitag, 2. September 2022 um 23:21:14 UTC+2:
>>>
>>>> Consider some set ? of dark numbers
>>>
>>> Consider a bathtub.
>>
>> An infinite bathtub?
>
> A "potential" infinite rather than an "actually" infinite one, ROTFL.
>
> Idiot WM feels his destiny is to teach this the dumb mankind...

His arguments never hold water.

Re: Natural numbers and vases III

<f1d214a0-afd0-757e-42ca-fbe667edfc4f@att.net>

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 4 Sep 2022 00:59:26 -0400
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by: Jim Burns - Sun, 4 Sep 2022 04:59 UTC

On 9/3/2022 4:15 PM, WM wrote:
> Jim Burns schrieb am Freitag,
> 2. September 2022 um 19:22:17 UTC+2:
>> On 9/2/2022 9:32 AM, WM wrote:
>>> Jim Burns schrieb am Donnerstag,
>>> 1. September 2022 um 20:52:33 UTC+2:

>>>> If it arises from our description that
>>>> all the end segments are infinite and
>>>> the intersection of all the end segments
>>>> is empty,
>>>
>>> This is a contradiction,
>>> because endsegments are decreasing.
>>
>> Each non-∅ end segment of ⋃𝓕 is infinite.
>
> Wrong.

Infinity is not
a reallyreallyreallyreallyreallyreally
large number.

> As soon as there is no longer an infinite
> common set, the next state of affairs is
> a finite set

As soon as there is no longer an infinite
common set
of infinite end segments of ⋃𝓕,
the next[2] state of affairs is ∅

It's also true that
the next[1] state of affairs after E(2)
is E(3).

However, "next[1]" and "next[2]" are different
senses of "next".

"next[1]"
No set 𝐵 exists between E(2) and E(3)
~∃𝐵, E(2) ⊃ 𝐵 ⊃ E(3)

Let 𝓔 be
the set of all infinite end segments of ⋃𝓕,

"next[2]"
No set 𝐵 exists between all of 𝓔 and ∅
~∃𝐵, ∀𝐸 ∈ 𝓔, 𝐸 ⊃ 𝐵 ⊃ ∅

"next[1]"
No set 𝐵 exists between E(2) and E(3)

E(2) and E(3) differ by one element, 2
thus
either 2 is in 𝐵 and 𝐵 = E(2)
or 2 is not in 𝐵 and 𝐵 = E(3).

"next[2]"
No set 𝐵 exists between all of 𝓔 and ∅

| Assume otherwise.
| Assume ∀𝐸 ∈ 𝓔, 𝐸 ⊃ 𝐵ₖ ⊃ ∅
| k ∈ 𝐵ₖ
| | Define
| E(k+1) = { m ∈ ⋃𝓕 : k < m }
| | 𝐵ₖ ⊃ E(k+1) ⊃ ∅
| | However,
| E(k+1) = { m ∈ ⋃𝓕 : k < m }
| is an infinite end segment of ⋃𝓕.
| E(k+1) ∈ 𝓔
| E(k+1) ⊃ 𝐵ₖ ⊃ ∅
| 𝐵ₖ ⊅ E(k+1)
| Contradiction.

Therefore,
no set 𝐵 exists between all of 𝓔 and ∅

Re: Natural numbers and vases III

<5b28d0a8-e2fb-06a6-9e71-3e32365e8092@att.net>

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 4 Sep 2022 03:07:33 -0400
Organization: A noiseless patient Spider
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by: Jim Burns - Sun, 4 Sep 2022 07:07 UTC

On 9/4/2022 12:59 AM, Jim Burns wrote:
> On 9/3/2022 4:15 PM, WM wrote:
>> Jim Burns schrieb am Freitag,
>> 2. September 2022 um 19:22:17 UTC+2:
>>> On 9/2/2022 9:32 AM, WM wrote:
>>>> Jim Burns schrieb am Donnerstag,
>>>> 1. September 2022 um 20:52:33 UTC+2:
>
>>>>> If it arises from our description that
>>>>> all the end segments are infinite and
>>>>> the intersection of all the end segments
>>>>> is empty,
>>>>
>>>> This is a contradiction,
>>>> because endsegments are decreasing.
>>>
>>> Each non-∅ end segment of ⋃𝓕 is infinite.
>>
>> Wrong.
>
> Infinity is not
> a reallyreallyreallyreallyreallyreally
> large number.
>
>> As soon as there is no longer an infinite
>> common set, the next state of affairs is
>> a finite set
>
> As soon as there is no longer an infinite
> common set
> of infinite end segments of ⋃𝓕,
> the next[2] state of affairs is ∅
>
> It's also true that
> the next[1] state of affairs after E(2)
> is E(3).
>
> However, "next[1]" and "next[2]" are different
> senses of "next".
>
> "next[1]"
> No set 𝐵 exists between E(2) and E(3)
> ~∃𝐵, E(2) ⊃ 𝐵 ⊃ E(3)
>
> Let 𝓔 be
> the set of all infinite end segments of ⋃𝓕,
>
> "next[2]"
> No set 𝐵 exists between all of 𝓔 and ∅
> ~∃𝐵, ∀𝐸 ∈ 𝓔, 𝐸 ⊃ 𝐵 ⊃ ∅
>
>
> "next[1]"
> No set 𝐵 exists between E(2) and E(3)
>
> E(2) and E(3) differ by one element, 2
> thus
> either 2 is in 𝐵 and 𝐵 = E(2)
> or 2 is not in 𝐵 and 𝐵 = E(3).
>

"next[2]"
No set 𝐵 exists between all of 𝓔 and ∅

| Assume otherwise.
| Assume ∀𝐸 ∈ 𝓔, 𝐸 ⊃ 𝐵ₖ ⊃ ∅
| k ∈ 𝐵ₖ
| | Define
| E(k+1) = { m ∈ ⋃𝓕 : k < m }
| | k ∉ E(k+1)
| k ∈ 𝐵ₖ
| E(k+1) ⊅ 𝐵ₖ
| | However,
| E(k+1) = { m ∈ ⋃𝓕 : k < m }
| is an infinite end segment of ⋃𝓕.
| E(k+1) ∈ 𝓔
| E(k+1) ⊃ 𝐵ₖ ⊃ ∅
| Contradiction.

Therefore,
no set 𝐵 exists between all of 𝓔 and ∅

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Sun, 4 Sep 2022 14:02 UTC

FromTheRafters schrieb am Sonntag, 4. September 2022 um 00:27:50 UTC+2:
> WM wrote on 9/3/2022 :
> > Jim Burns schrieb am Freitag, 2. September 2022 um 23:21:14 UTC+2:
> >
> >> Consider some set ? of dark numbers
> >
> > Consider a bathtub.
>
> An infinite bathtub?

That does not matter. Any bathtub that is not empty will do.
And possibly some logic: As long as it is not empty, it is not empty and was not empty before. Therefore the intersection of its states is not empty.

Regards, WM

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 4 Sep 2022 09:07:25 -0500
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by: Sergio - Sun, 4 Sep 2022 14:07 UTC

On 9/4/2022 9:02 AM, WM wrote:
> FromTheRafters schrieb am Sonntag, 4. September 2022 um 00:27:50 UTC+2:
>> WM wrote on 9/3/2022 :
>>> Jim Burns schrieb am Freitag, 2. September 2022 um 23:21:14 UTC+2:
>>>
>>>> Consider some set ? of dark numbers
>>>
>>> Consider a bathtub.
>>
>> An infinite bathtub?
>
> That does not matter.

*Of Course it matters*!!

you are using defective leaky FINITE bathtubs, no wonder !

> Any bathtub that is not empty will do.

so you get a FINITE bathtub and put a cup of water in, then what ?

> And possibly some logic: As long as it is not empty, it is not empty and was not empty before. Therefore the intersection of its states is not empty.

so you stare at it ?

IS THIS WHAT YOUR MATH IS ?

>
> Regards, WM

Did Framed Achilles and his defective race turtle put you up to this ??

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Sun, 4 Sep 2022 14:16 UTC

On Sunday, September 4, 2022 at 4:02:17 PM UTC+2, WM wrote:

> Therefore the intersection of its states is not empty.

If the states only consider the water in your idiotic "leaking (finite) bathtube" the "intersection of its states" is certainly "empty", since there is a state which is "empty" (especially if your bathtube is leaking at a constant rate).

You are a complete idiot.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Sun, 4 Sep 2022 14:24 UTC

Jim Burns schrieb am Sonntag, 4. September 2022 um 06:59:39 UTC+2:
> On 9/3/2022 4:15 PM, WM wrote:

> > As soon as there is no longer an infinite
> > common set, the next state of affairs is
> > a finite set
>
> As soon as there is no longer an infinite
> common set
> of infinite end segments of ⋃𝓕,
> the next[2] state of affairs is ∅

Then the basics of endsegments would be violated:
∀k ∈ ℕ : ∩{E(1), E(2), ..., E(k+1)} = ∩{E(1), E(2), ..., E(k)} \ {k} .
Note "all k", that means all natural numbers. And there is no junmp because of
∀k ∈ ℕ: E(k+1) = E(k) \ {k} .
Only one by one.
>
> It's also true that
> the next[1] state of affairs after E(2)
> is E(3).
>
> However, "next[1]" and "next[2]" are different
> senses of "next".

Nonsense. This is the only sense: ∀k ∈ ℕ: E(k+1) = E(k) \ {k} .
>
> "next[1]"
> No set 𝐵 exists between E(2) and E(3)

> "next[2]"
> No set 𝐵 exists between all of 𝓔 and ∅

Nonsense.

∀k ∈ ℕ: E(k+1) = E(k) \ {k} .

But nice that you have thrown off your mask.
>
> | Assume otherwise.

No assumption required. ∀k ∈ ℕ: E(k+1) = E(k) \ {k} stands firmly.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Sun, 4 Sep 2022 14:26 UTC

Jim Burns schrieb am Sonntag, 4. September 2022 um 09:07:45 UTC+2:

> No set 𝐵 exists between all of 𝓔 and ∅
>
> | Assume otherwise.
> | Assume ∀𝐸 ∈ 𝓔, 𝐸 ⊃ 𝐵ₖ ⊃ ∅
> | k ∈ 𝐵ₖ

That is your mistake. Dark numbers cannot be individualized. But they are existing because
∀k ∈ ℕ: E(k+1) = E(k) \ {k} .
You violate it.

Regards, WM

Re: Natural numbers and vases III

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From: horand.g...@gmail.com (Gus Gassmann)
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by: Gus Gassmann - Sun, 4 Sep 2022 14:27 UTC

On Sunday, 4 September 2022 at 11:02:17 UTC-3, WM wrote:
[...]
> That does not matter. Any bathtub that is not empty will do.
> And possibly some logic: As long as it is not empty, it is not empty and was not empty before.

Correct.

> Therefore the intersection of its states is not empty.

Nope. I thought your entire point was that the bathtub _can_ empty. Unlike the intersection of an infinite number of end segments, however, the bathtub is guaranteed to empty in finite time (unless you add more water to it). The intersection of end segments is not empty for any finite collection of end segments, and is empty for any infinite collection.

It would be nice if you could either put your remaining synapsis in gear before you post, or else *FUCK OFF*.

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by: Sergio - Sun, 4 Sep 2022 14:28 UTC

On 9/4/2022 9:16 AM, Fritz Feldhase wrote:
> On Sunday, September 4, 2022 at 4:02:17 PM UTC+2, WM wrote:
>
>> Therefore the intersection of its states is not empty.
>
> If the states only consider the water in your idiotic "leaking (finite) bathtube" the "intersection of its states" is certainly "empty", since there is a state which is "empty" (especially if your bathtube is leaking at a constant rate).
>
> You are a complete idiot.

agree,

WM does not think in equations, but in visions of objects

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 4 Sep 2022 09:36:20 -0500
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by: Sergio - Sun, 4 Sep 2022 14:36 UTC

On 9/4/2022 9:26 AM, WM wrote:
> Jim Burns schrieb am Sonntag, 4. September 2022 um 09:07:45 UTC+2:
>
>> No set 𝐵 exists between all of 𝓔 and ∅
>>
>> | Assume otherwise.
>> | Assume ∀𝐸 ∈ 𝓔, 𝐸 ⊃ 𝐵ₖ ⊃ ∅
>> | k ∈ 𝐵ₖ
>
> That is your mistake. Dark numbers cannot be individualized. But they are existing because
> ∀k ∈ ℕ: E(k+1) = E(k) \ {k} .

Wrong.

>
> Regards, WM

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 4 Sep 2022 09:40:54 -0500
Organization: Aioe.org NNTP Server
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by: Sergio - Sun, 4 Sep 2022 14:40 UTC

On 9/4/2022 9:24 AM, WM wrote:
> Jim Burns schrieb am Sonntag, 4. September 2022 um 06:59:39 UTC+2:
>> On 9/3/2022 4:15 PM, WM wrote:
>
>>> As soon as there is no longer an infinite
>>> common set, the next state of affairs is
>>> a finite set
>>
>> As soon as there is no longer an infinite
>> common set
>> of infinite end segments of ⋃𝓕,
>> the next[2] state of affairs is ∅
>
> Then the basics of endsegments would be violated:
> ∀k ∈ ℕ : ∩{E(1), E(2), ..., E(k+1)} = ∩{E(1), E(2), ..., E(k)} \ {k} .
> Note "all k", that means all natural numbers. And there is no junmp because of
> ∀k ∈ ℕ: E(k+1) = E(k) \ {k} .
> Only one by one.
>>
>> It's also true that
>> the next[1] state of affairs after E(2)
>> is E(3).
>>
>> However, "next[1]" and "next[2]" are different
>> senses of "next".
>
> Nonsense. This is the only sense: ∀k ∈ ℕ: E(k+1) = E(k) \ {k} .
>>
>> "next[1]"
>> No set 𝐵 exists between E(2) and E(3)
>
>> "next[2]"
>> No set 𝐵 exists between all of 𝓔 and ∅
>
> Nonsense.
>
> ∀k ∈ ℕ: E(k+1) = E(k) \ {k} .
>
> But nice that you have thrown off your mask.
>>
>> | Assume otherwise.
>
> No assumption required. ∀k ∈ ℕ: E(k+1) = E(k) \ {k} stands firmly.
>
> Regards, WM

∀k ∈ ℕ: E(k+1) = E(k) \ {k} is only the relationship between two adjacent endsegments, that is all.

It does not create dark numbers, it is not a step by step process.

Jim Burns showed there are no dark numbers between any endsegments, so there are no dark numbers.

the only one with a mask on around here is WM, as a Pretend Mathematician.

Re: Natural numbers and vases III

<tf2hd4$38u26$1@dont-email.me>

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 04 Sep 2022 11:48:50 -0400
Organization: Peripheral Visions
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by: FromTheRafters - Sun, 4 Sep 2022 15:48 UTC

Sergio used his keyboard to write :
> On 9/4/2022 9:24 AM, WM wrote:
>> Jim Burns schrieb am Sonntag, 4. September 2022 um 06:59:39 UTC+2:
>>> On 9/3/2022 4:15 PM, WM wrote:
>>
>>>> As soon as there is no longer an infinite
>>>> common set, the next state of affairs is
>>>> a finite set
>>>
>>> As soon as there is no longer an infinite
>>> common set
>>> of infinite end segments of ⋃?,
>>> the next[2] state of affairs is ∅
>>
>> Then the basics of endsegments would be violated:
>> ∀k ∈ ℕ : ∩{E(1), E(2), ..., E(k+1)} = ∩{E(1), E(2), ..., E(k)} \ {k} .
>> Note "all k", that means all natural numbers. And there is no junmp because
>> of
>> ∀k ∈ ℕ: E(k+1) = E(k) \ {k} .
>> Only one by one.
>>>
>>> It's also true that
>>> the next[1] state of affairs after E(2)
>>> is E(3).
>>>
>>> However, "next[1]" and "next[2]" are different
>>> senses of "next".
>>
>> Nonsense. This is the only sense: ∀k ∈ ℕ: E(k+1) = E(k) \ {k} .
>>>
>>> "next[1]"
>>> No set ? exists between E(2) and E(3)
>>
>>> "next[2]"
>>> No set ? exists between all of ? and ∅
>>
>> Nonsense.
>>
>> ∀k ∈ ℕ: E(k+1) = E(k) \ {k} .
>>
>> But nice that you have thrown off your mask.
>>>
>>> | Assume otherwise.
>>
>> No assumption required. ∀k ∈ ℕ: E(k+1) = E(k) \ {k} stands firmly.
>>
>> Regards, WM
>
> ∀k ∈ ℕ: E(k+1) = E(k) \ {k} is only the relationship between two adjacent
> endsegments, that is all.
>
> It does not create dark numbers, it is not a step by step process.

As Fritz Feldhase alluded to, WM only uses induction when it fits his
purpose. He doesn't realize that he gets hoisted by his own petard. Jim
Burns has consistently shown this by taking WM's babbling and giving it
as 'logical' a foundation as he could and drawing an opposite
conclusion.

Re: Natural numbers and vases III

<tf2hmt$38v1b$1@dont-email.me>

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 04 Sep 2022 11:54:03 -0400
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by: FromTheRafters - Sun, 4 Sep 2022 15:54 UTC

WM explained :
> FromTheRafters schrieb am Sonntag, 4. September 2022 um 00:27:50 UTC+2:
>> WM wrote on 9/3/2022 :
>>> Jim Burns schrieb am Freitag, 2. September 2022 um 23:21:14 UTC+2:
>>>
>>>> Consider some set ? of dark numbers
>>>
>>> Consider a bathtub.
>>
>> An infinite bathtub?
>
> That does not matter. Any bathtub that is not empty will do.

Is that why you use the naturals without zero? Does the emptyset cause
problems in your theory?

> And possibly some logic: As long as it is not empty, it is not empty and was
> not empty before. Therefore the intersection of its states is not empty.

What? It doesn't become a new bathtub when its contents change? You're
gonna need a bigger bathtub.

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 4 Sep 2022 11:38:05 -0500
Organization: Aioe.org NNTP Server
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by: Sergio - Sun, 4 Sep 2022 16:38 UTC

On 9/4/2022 10:54 AM, FromTheRafters wrote:
> WM explained :
>> FromTheRafters schrieb am Sonntag, 4. September 2022 um 00:27:50 UTC+2:
>>> WM wrote on 9/3/2022 :
>>>> Jim Burns schrieb am Freitag, 2. September 2022 um 23:21:14 UTC+2:
>>>>> Consider some set ? of dark numbers
>>>>
>>>> Consider a bathtub.
>>>
>>> An infinite bathtub?
>>
>> That does not matter. Any bathtub that is not empty will do.
>
> Is that why you use the naturals without zero? Does the emptyset cause problems in your theory?
>
>> And possibly some logic: As long as it is not empty, it is not empty and was not empty before. Therefore the intersection of its states is not empty.
>
> What? It doesn't become a new bathtub when its contents change? You're gonna need a bigger bathtub.

WM could lower gravity to 0, then his bathtubs would not leak, the water would ahere to the tub as a glob.
Then the intersection would not be empty.
Just change the laws of physics and that solves his defective bathtub problem

Re: Natural numbers and vases III

<938fc508-a8c4-ff51-bb68-6a2b63ccf6d9@att.net>

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 4 Sep 2022 13:26:15 -0400
Organization: A noiseless patient Spider
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by: Jim Burns - Sun, 4 Sep 2022 17:26 UTC

On 9/4/2022 10:26 AM, WM wrote:
> Jim Burns schrieb am Sonntag,
> 4. September 2022 um 09:07:45 UTC+2:

>> No set 𝐵 exists between all of 𝓔 and ∅
>>
>> | Assume otherwise.
>> | Assume ∀𝐸 ∈ 𝓔, 𝐸 ⊃ 𝐵ₖ ⊃ ∅
>> | k ∈ 𝐵ₖ
>
> That is your mistake.
> Dark numbers cannot be individualized.

<unsnip/>
>> Let 𝓔 be
>> the set of all infinite end segments of ⋃𝓕,

⋃𝓕 is an end segment of ⋃𝓕
⋃𝓕 ∈ 𝓔
| _Assuming 𝐵ₖ exists_
| ⋃𝓕 ⊃ 𝐵ₖ ⊃ ∅

We immediately see
no 𝐵 ⊄ ⋃𝓕 exists between all of 𝓔 and ∅
since ⋃𝓕 ⊅ 𝐵 ⊃ ∅

Furthermore, for 𝐵ₖ ⊂ ⋃𝓕, k ∈ 𝐵ₖ
k ∈ ⋃𝓕
E(k+1) ∈ 𝓔
E(k+1) ⊅ 𝐵ₖ ⊃ ∅

Either 𝐵 ⊄ ⋃𝓕 or 𝐵 ⊂ ⋃𝓕

If 𝐵 ⊄ ⋃𝓕 then
~∀𝐸 ∈ 𝓔, 𝐸 ⊃ 𝐵 ⊃ ∅

If 𝐵 ⊂ ⋃𝓕 then
~∀𝐸 ∈ 𝓔, 𝐸 ⊃ 𝐵 ⊃ ∅

Therefore,
~∀𝐸 ∈ 𝓔, 𝐸 ⊃ 𝐵 ⊃ ∅

No set 𝐵 exists between all of 𝓔 and ∅
~∃𝐵, ∀𝐸 ∈ 𝓔, 𝐸 ⊃ 𝐵 ⊃ ∅

> But they are existing because
> ∀k ∈ ℕ: E(k+1) = E(k) \ {k} .
> You violate it.

No, I use it:
E(k+1) = E(k)\{k}
k ∉ E(k+1)
k ∈ 𝐵ₖ
E(k+1) ⊅ 𝐵ₖ ⊃ ∅
𝐵ₖ is NOT between all of 𝓔 and ∅

Re: Natural numbers and vases III

<5fcad0d6-d246-ae8e-68f1-0fcbac241d9f@att.net>

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 4 Sep 2022 14:16:54 -0400
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by: Jim Burns - Sun, 4 Sep 2022 18:16 UTC

On 9/4/2022 10:24 AM, WM wrote:
> Jim Burns schrieb am Sonntag,
> 4. September 2022 um 06:59:39 UTC+2:
>> On 9/3/2022 4:15 PM, WM wrote:

>>> As soon as there is no longer an infinite
>>> common set, the next state of affairs is
>>> a finite set
>>
>> As soon as there is no longer an infinite
>> common set
>> of infinite end segments of ⋃𝓕,
>> the next[2] state of affairs is ∅

>> It's also true that
>> the next[1] state of affairs after E(2)
>> is E(3).
>>
>> However, "next[1]" and "next[2]" are different
>> senses of "next".
>
> Nonsense.
> This is the only sense:
> ∀k ∈ ℕ: E(k+1) = E(k) \ {k} .

E(k+1) is next[1] after E(k)
No set exists which is after (⊂) E(k) and
before (⊃) E(k+1)

∅ is next[2] after all of 𝓔
No set exists which is after (⊂) each 𝐸 ∈ 𝓔
and before (⊃) ∅

.... no set which is NOT subset ⋃𝓕
because
⋃𝓕 is an end segment of ⋃𝓕
⋃𝓕 ⊅ 𝐵 ⊃ ∅
and 𝐵 is not such a set.

.... no set which IS subset ⋃𝓕
because
𝐵ₖ ⊃ ∅
k ∈ 𝐵ₖ
⋃𝓕 ⊃ 𝐵ₖ
k ∈ ⋃𝓕
k ∉ E(k+1)
E(k+1) ⊅ 𝐵ₖ ⊃ ∅
and 𝐵ₖ is not such a set.

.... no set.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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by: zelos...@gmail.com - Mon, 5 Sep 2022 05:32 UTC

fredag 2 september 2022 kl. 15:33:01 UTC+2 skrev WM:
> Jim Burns schrieb am Donnerstag, 1. September 2022 um 20:52:33 UTC+2:
> > On 9/1/2022 9:16 AM, WM wrote:
> > > Jim Burns schrieb am Mittwoch,
> > > 31. August 2022 um 18:12:28 UTC+2:
> > >> No end segment is last (⊇) of all
> > >> end segments.
> > >
> > > True.
> > > The reason is this:
> > > The infinite, definable endsegments are
> > > potentially infinite.
> > Your use of "potentially infinite" is a
> > _virtus dormitiva_
> No, it has come down from ancient mathematics, Cantor, and modern mathematics.
> > If it arises from our description that
> > all the end segments are infinite and
> > the intersection of all the end segments
> > is empty,
> This is a contradiction, because endsegments are decreasing. But before they have decreaed to the empty set, they contain what all predecessors contain.
> > This description does immediately not rule out
> > your dark numbers and dark end segments.
> > Dark numbers could conceivably be in 𝐸
> > which are > each i in ⋃𝓕\𝐸
> >
> > However,
> > this description requires 𝐸 subset ⋃𝓕
> That is a wrong desription.
>
> Regards, WM
There is no contradiction, it follows logically from the definitions. Even my students understand this and they are in their early 20s

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: fredjeff...@gmail.com (FredJeffries)
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by: FredJeffries - Mon, 5 Sep 2022 19:41 UTC

On Thursday, September 1, 2022 at 6:05:42 AM UTC-7, WM wrote:
> Gus Gassmann schrieb am Mittwoch, 31. August 2022 um 17:04:08 UTC+2:
> > On Wednesday, 31 August 2022 at 10:15:07 UTC-3, WM wrote:
> > [...]
> > > So the infinite loss does not concern every natnumber in the endsegments. Why should it concern every natnumber of the intersection?
> > Because the card() function is not continuous,
>
> Why is it not continuous?

Here we have a prime example of our esteemed Professor's inability to grasp the respective roles of proof and counterexample in logic and mathematics.

For over two decades he has been shown a counterexample to a universal generalization. But, instead, he demands a 'proof' that the generalization does not hold.

Elsewhere, he 'demonstrates' the truth of his version on 'inclusion monotony' by giving a single example, the sequence real number segments
(0, 1 + 1/n) where it holds.

Perhaps this reversal of roles in his mind is related to his cluelessness concerning quantifiers and the reversals thereof?

https://en.wikipedia.org/wiki/Counterexample

Re: Natural numbers and vases III

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Date: Mon, 5 Sep 2022 18:23:59 -0400
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by: Jim Burns - Mon, 5 Sep 2022 22:23 UTC

On 9/3/2022 4:21 PM, WM wrote:
> Jim Burns schrieb am Freitag,
> 2. September 2022 um 23:21:14 UTC+2:

>> Consider some set 𝔻 of dark numbers
>
> Consider a bathtub.

Consider a bathtub (⋃𝓕)⊕𝔻

Of all the water in the tub,
some water leaks ⋃𝓕
and some water does not leak 𝔻

For each state 𝐹 of the leaked water,
((⋃𝓕)⊕𝔻)\𝐹 is in the bathtub.

For each state 𝐹 of the leaked water,
more water to be leaked is in the bathtub.
((⋃𝓕)⊕𝔻)\𝐹 ≠ 𝔻

| Because 𝐹 ≠ ⋃𝓕
| Because 𝐹ₙ∪⟨n+1⟩ is also a FISON.

Any water that, in any state, is leaked
is not in the intersection of all bathtub-states.

The intersection of all bathtub-states
must be a subset of 𝔻 the water that
does not leak.

If there is no water that does not leak,
𝔻 = ∅, then the intersection of
all the bathtub-states is a subset of ∅
which has one subset, itself: ∅

Remember that, for each 𝐹,
((⋃𝓕)⊕𝔻)\𝐹 ≠ 𝔻

If 𝔻 = ∅,
((⋃𝓕)⊕∅)\𝐹 ≠ ∅

The bathtub is never empty.
And the intersection of bathtub-states
is empty.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Tue, 6 Sep 2022 09:56 UTC

FredJeffries schrieb am Montag, 5. September 2022 um 21:41:45 UTC+2:

> Elsewhere, he 'demonstrates' the truth of his version on 'inclusion monotony' by giving a single example, the sequence real number segments
> (0, 1 + 1/n) where it holds.

That was only an answer to the argument that inclusion monotony never holds in the infinite case.
>
Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: WM - Tue, 6 Sep 2022 10:01 UTC

Gus Gassmann schrieb am Sonntag, 4. September 2022 um 16:27:38 UTC+2:
> On Sunday, 4 September 2022 at 11:02:17 UTC-3, WM wrote:
> [...]
> > That does not matter. Any bathtub that is not empty will do.
> > And possibly some logic: As long as it is not empty, it is not empty and was not empty before.
> Correct.
> > Therefore the intersection of its states is not empty.
> Nope. I thought your entire point was that the bathtub _can_ empty. Unlike the intersection of an infinite number of end segments, however, the bathtub is guaranteed to empty in finite time

No, it may happen that at every time only half of its contents is lost.

> The intersection of end segments is not empty for any finite collection of end segments, and is empty for any infinite collection.

Wrong.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: WM - Tue, 6 Sep 2022 10:07 UTC

Jim Burns schrieb am Dienstag, 6. September 2022 um 00:24:09 UTC+2:

> Remember that, for each 𝐹,
> ((⋃𝓕)⊕𝔻)\𝐹 ≠ 𝔻

It is larger.
>
> If 𝔻 = ∅,
> ((⋃𝓕)⊕∅)\𝐹 ≠ ∅

𝔻 =/= ∅
>
> The bathtub is never empty.
> And the intersection of bathtub-states
> is empty.

Wrong. Much ado before an unjustified conclusion.

Regards WM

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

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