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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
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	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
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Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	William
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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	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

<te7veq$6ua$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 25 Aug 2022 09:03:05 -0500
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by: Sergio - Thu, 25 Aug 2022 14:03 UTC

On 8/25/2022 8:56 AM, WM wrote:
> FromTheRafters schrieb am Donnerstag, 25. August 2022 um 15:42:00 UTC+2:
>> WM explained on 8/25/2022 :
>>> FromTheRafters schrieb am Mittwoch, 24. August 2022 um 17:25:40 UTC+2:
>>>> WM formulated the question :
>>>
>>>>> They are mutually exclusive, but only intelligent persons can recognize it.
>>>> But if you understand mathematics, you know that things are defined in
>>>> such a way that we are able to work with them. Sometimes things seem
>>>> counterintuitive, but make sense once you understand them.
>>>>
>>> I understand two basic truths which a serious mathematician cannot deny but
>>> which are denied by matheologians:
>>>
>>> (1) The intersection of inclusion-monotonic infinite sets is infinite.
>> What is 'inclusion monotonic' about your sequence of endsegments? Taken
>> as ordered sets, each 'next' one is not a superset of each 'previous'
>> one
>
> But a subset.

inclusion monotonic = red herring

>
>>> (2) By exchanging X and O the matrix
>>> XOO...
>>> XOO...
>>> XOO...
>>> ...
>>> cannot lose any O.
>> Which has nothing to do with the topic.
>
> So it appears at first glance. But this matrix proves dark numbers

QUACK!! it is not math at all.

>
> Regards, WM

Re: Natural numbers and vases III

<te7vgc$3llvo$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: Thu, 25 Aug 2022 10:03:51 -0400
Organization: Peripheral Visions
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by: FromTheRafters - Thu, 25 Aug 2022 14:03 UTC

WM expressed precisely :
> FromTheRafters schrieb am Mittwoch, 24. August 2022 um 23:22:13 UTC+2:
>> WM used his keyboard to write :
>>> William schrieb am Mittwoch, 24. August 2022 um 21:49:34 UTC+2:
>>>> On Wednesday, August 24, 2022 at 9:22:06 AM UTC-3, WM wrote:
>>>>
>>>>> All definable elements have ℵ₀ successors
>>>>> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
>>>> So what? They are not the same successors.
>>>
>>> ℵo of them are the same.
>>>
>>>> So you cannot combine all these statements to form
>>>>
>>>>> ℕ_ def\ {1, 2, 3, ...}| = ℵo
>>>
>>> Can you find any two sets of successors which have not ℵo numbers in
>>> common? No. All infinite endsegments have ℵo elements in common.
>> Wrong again, or still wrong.
>
> I said "all" and you cannot find any counter example. So "all" is correct.

Is this another example of your matheology's underlying logic? Absence
of evidence is not evidence of absence to the rest of us.

> Why do you claim that nonsense if you have no counter example?

Aleph_zero is not a 'number of elements' it is a size. Look up
"Cardinality" to see the difference between finite set size and
infinite set size and cardinal arithmetic.

Re: Natural numbers and vases III

<53929fd7-ec2b-42b0-a46d-b76ece03b45bn@googlegroups.com>

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Subject: Re: Natural numbers and vases III
From: thenewca...@gmail.com (Eram semper recta)
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by: Eram semper recta - Thu, 25 Aug 2022 14:08 UTC

On Thursday, 25 August 2022 at 09:20:06 UTC-4, WM wrote:
> Eram semper recta schrieb am Mittwoch, 24. August 2022 um 16:29:36 UTC+2:
> > On Wednesday, 24 August 2022 at 08:32:35 UTC-4, WM wrote:
> > > zelos schrieb am Mittwoch, 24. August 2022 um 07:43:40 UTC+2:
> > > > onsdag 24 augusti 2022 kl. 00:43:02 UTC+2 skrev Retard Eram semper recta:
> > > > > On Tuesday, 23 August 2022 at 08:28:41 UTC-4, zelos malum wrote:
> > >
> > > > > > > They want to claim [A] The set N has no largest element and [B] N contains ALL of its elements. They refuse to accept that these statements are mutually exclusive.
> > > > > > Because they aren't.
> > > > >
> > > > > Anyone with a modicum of intelligence knows those two statements are mutually exclusive. You have none.
> > > > Anyone with even baseline intelligence knows they are not mutually exclusive. You are a complete fucking moron.
> > > They are mutually exclusive, but only intelligent persons can recognize it.
> >
> > > The only way to reconcile them is to accept that most elements are not in a linear order or cannot be recognized to be in a linear order.
> > And we can dismiss your last concern about linear order because we know |N is ordered.
>
> Then it is no complete.

It is never complete to begin with.

>
> Regards, WM

Re: Natural numbers and vases III

<te7vol$3lmqd$1@dont-email.me>

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https://www.novabbs.com/tech/article-flat.php?id=110243&group=sci.math#110243

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Path: i2pn2.org!i2pn.org!eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail
From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 25 Aug 2022 10:08:16 -0400
Organization: Peripheral Visions
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by: FromTheRafters - Thu, 25 Aug 2022 14:08 UTC

Sergio brought next idea :
> On 8/25/2022 8:31 AM, WM wrote:
>> FromTheRafters schrieb am Mittwoch, 24. August 2022 um 23:22:13 UTC+2:
>>> WM used his keyboard to write :
>>>> William schrieb am Mittwoch, 24. August 2022 um 21:49:34 UTC+2:
>>>>> On Wednesday, August 24, 2022 at 9:22:06 AM UTC-3, WM wrote:
>>>>>
>>>>>> All definable elements have ℵ₀ successors
>>>>>> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
>>>>> So what? They are not the same successors.
>>>>
>>>> ℵo of them are the same.
>>>>
>>>>> So you cannot combine all these statements to form
>>>>>
>>>>>> ℕ_ def\ {1, 2, 3, ...}| = ℵo
>>>>
>>>> Can you find any two sets of successors which have not ℵo numbers in
>>>> common?
>>>> No. All infinite endsegments have ℵo elements in common.
>>> Wrong again, or still wrong.
>>
>> I said "all" and you cannot find any counter example. So "all" is correct.
>> Why do you claim that nonsense if you have no counter example?
>>
>> Regards, WM
>
>
> Name the natural number that is in common with all endsegments. Fail. Which
> means you are wrong again.

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

He's still wrong though. :)

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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 - Thu, 25 Aug 2022 14:12 UTC

On Thursday, August 25, 2022 at 3:42:00 PM UTC+2, FromTheRafters wrote:
> WM explained on 8/25/2022 :
> >
> > (1) The intersection of inclusion-monotonic infinite sets is infinite.
> >
> What is 'inclusion monotonic' about your sequence of endsegments? Taken
> as ordered sets, each 'next' one is not a superset of each 'previous'
> one as is the case with their associated FISONs.

Huh?! But each 'next' one is a subset of each 'previous'.

Mückenheim uses non-standard terminology, but he's not wrong about the fact as such.

SEE: https://proofwiki.org/wiki/Definition:Monotone_Sequence_of_Sets !!!

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Subject: Re: Natural numbers and vases III
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by: FromTheRafters - Thu, 25 Aug 2022 14:13 UTC

on 8/25/2022, WM supposed :
> zelos...@gmail.com schrieb am Donnerstag, 25. August 2022 um 07:29:56 UTC+2:
>> onsdag 24 augusti 2022 kl. 14:22:06 UTC+2 skrev WM:
>
>>> All definable elements have ℵ₀ successors
>>> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
>> That is again all of N, so N_def=N
>>
>>> All elements have no succesors
>>
>> False, all elements have infinitely many successors
>>
>>> ℕ \ {1, 2, 3, ...} = { }
>>
>> It is true for any set.
>
> What makes the difference between all elements and the set?

The set.

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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 - Thu, 25 Aug 2022 14:15 UTC

On Thursday, August 25, 2022 at 4:04:06 PM UTC+2, FromTheRafters wrote:

> Aleph_0 is not a 'number of elements' it is a size. Look up "Cardinality" to see

this: "In mathematics, the cardinality of a set is a measure of the "number of elements" of the set." (Wikipedia, Cardinality)

:-)

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Thu, 25 Aug 2022 14:19 UTC

FromTheRafters schrieb am Donnerstag, 25. August 2022 um 16:04:06 UTC+2:
> WM expressed precisely :

> >>> Can you find any two sets of successors which have not ℵo numbers in
> >>> common? No. All infinite endsegments have ℵo elements in common.
> >> Wrong again, or still wrong.
> >
> > I said "all" and you cannot find any counter example. So "all" is correct.
> > Why do you claim that nonsense if you have no counter example?
> Aleph_zero is not a 'number of elements' it is a size.

The intersection is produced by endsegments E(n) with finite index n only. It does not matter what aleph_0 is. Either endsegments with finite indices produce the empty intersection or there is none. Note there is no endsegment with index aleph_0.

Regards, WM

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Subject: Re: Natural numbers and vases III
From: thenewca...@gmail.com (Eram semper recta)
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by: Eram semper recta - Thu, 25 Aug 2022 14:22 UTC

On Monday, 18 July 2022 at 17:29:37 UTC-4, WM wrote:
> William schrieb am Montag, 18. Juli 2022 um 20:17:17 UTC+2:
> > On Monday, July 18, 2022 at 2:47:34 PM UTC-3, WM wrote:
>
> > Let |N_b be the subset of |N of elements that are in the bijection,
> > Let |N_s be the subset of |N of elements that have a successor
> > > > Simple induction shows that 1. each element (without exception) is in the bijection
>
> By the way, this is wrong. Simple induction shows that every element in the bijection has infinitely many successors.
>
> > So 1. is |N_b = |N
> >
> > > Removing them leaves nothing.
> >
> > |N\|N_b = {}
> > > > and 2. each element (without exception) has a successor.
> > So 2. is |N_s = |N
> > > Removing them leaves infinitely many succesors
> > Nope |N\|N_s={}. Correct is to say "removing any element of |N_s leaves infinitely many successors". However "them", |N_s, is not an element of |N_s ,
>
> All elements of |N_s are elements of |N_s.
>
> > so the fact that "removing them" leave nothing is not a contradiction.
>
> We don't remove the set but all its elements. If this is not the same, then something is wrong in Cantor-land.
> >
> > From "removing any element of |N_s leaves infinitely many successors" we can conclude that "removing any finite subset of |N_s leaves infinitely many successors". However, "them", |N_s, is not a finite subset of |N_s , so the fact that "removing them" leave nothing is not a contradiction.
>
> It is a contradiction that the elements cannot be handled as elements. The reason is of course that set theory fails otherwise.
>
> Regards, WM

Quick question: In the following document (5 pages long) I prove that ∞ - ∞ = 0. Cantor cranks still persist in their delusions after they read it. What makes you hopeful that they will concede aleph0 is nonsense?

https://www.academia.edu/78740399/Georg_Cantor_the_father_of_all_mainstream_mathematical_cranks

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Subject: Re: Natural numbers and vases III
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by: FromTheRafters - Thu, 25 Aug 2022 14:23 UTC

WM laid this down on his screen :
> FromTheRafters schrieb am Donnerstag, 25. August 2022 um 15:42:00 UTC+2:
>> WM explained on 8/25/2022 :
>>> FromTheRafters schrieb am Mittwoch, 24. August 2022 um 17:25:40 UTC+2:
>>>> WM formulated the question :
>>>
>>>>> They are mutually exclusive, but only intelligent persons can recognize
>>>>> it.
>>>> But if you understand mathematics, you know that things are defined in
>>>> such a way that we are able to work with them. Sometimes things seem
>>>> counterintuitive, but make sense once you understand them.
>>>>
>>> I understand two basic truths which a serious mathematician cannot deny but
>>> which are denied by matheologians:
>>>
>>> (1) The intersection of inclusion-monotonic infinite sets is infinite.
>> What is 'inclusion monotonic' about your sequence of endsegments? Taken
>> as ordered sets, each 'next' one is not a superset of each 'previous'
>> one
>
> But a subset.

A "Proper Subset" with induction so it is still of size Aleph_zero.

>>> cannot lose any O.
>> Which has nothing to do with the topic.
>
> So it appears at first glance. But this matrix proves dark numbers. The X's
> can be exchanged with the O's such that every definable position of the
> matrix is covered by an X. Nevertheless no O has been deleted. Where are
> they? At dark positions.

Pure fantasy!

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: Thu, 25 Aug 2022 09:30:39 -0500
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by: Sergio - Thu, 25 Aug 2022 14:30 UTC

On 8/25/2022 9:12 AM, Fritz Feldhase wrote:
> On Thursday, August 25, 2022 at 3:42:00 PM UTC+2, FromTheRafters wrote:
>> WM explained on 8/25/2022 :
>>>
>>> (1) The intersection of inclusion-monotonic infinite sets is infinite.
>>>
>> What is 'inclusion monotonic' about your sequence of endsegments? Taken
>> as ordered sets, each 'next' one is not a superset of each 'previous'
>> one as is the case with their associated FISONs.
>
> Huh?! But each 'next' one is a subset of each 'previous'.
>
> Mückenheim uses non-standard terminology, but he's not wrong about the fact as such.

WM is a rock or sheeps counting kind of guy, so perhaps he is thinking of those Russian Nesting Dolls...

>
> SEE: https://proofwiki.org/wiki/Definition:Monotone_Sequence_of_Sets !!!

Re: Natural numbers and vases III

<te81nl$1cf5$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 25 Aug 2022 09:41:56 -0500
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by: Sergio - Thu, 25 Aug 2022 14:41 UTC

On 8/25/2022 9:19 AM, WM wrote:
> FromTheRafters schrieb am Donnerstag, 25. August 2022 um 16:04:06 UTC+2:
>> WM expressed precisely :
>
>>>>> Can you find any two sets of successors which have not ℵo numbers in
>>>>> common? No. All infinite endsegments have ℵo elements in common.
>>>> Wrong again, or still wrong.
>>>
>>> I said "all" and you cannot find any counter example. So "all" is correct.
>>> Why do you claim that nonsense if you have no counter example?
>> Aleph_zero is not a 'number of elements' it is a size.
>
> The intersection is produced by endsegments E(n) with finite index n only.

try to state it more clearly. do you mean the intersection of E(1), E(2),...,E(n) ? it is infinite.

> It does not matter what aleph_0 is.

yes it does, aleph_0 = aleph_0 - k

> Either endsegments with finite indices produce the empty intersection or there is none.

try to state what you mean more clearly, that is sloppy nonsense.

> Note there is no endsegment with index aleph_0.

why dont you use EQUATIONS instead ?

>
> Regards, WM

Re: Natural numbers and vases III

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 25 Aug 2022 11:15:02 -0400
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by: FromTheRafters - Thu, 25 Aug 2022 15:15 UTC

Fritz Feldhase pretended :
> On Thursday, August 25, 2022 at 3:42:00 PM UTC+2, FromTheRafters wrote:
>> WM explained on 8/25/2022 :
>>>
>>> (1) The intersection of inclusion-monotonic infinite sets is infinite.
>>>
>> What is 'inclusion monotonic' about your sequence of endsegments? Taken
>> as ordered sets, each 'next' one is not a superset of each 'previous'
>> one as is the case with their associated FISONs.
>
> Huh?! But each 'next' one is a subset of each 'previous'.

Yes, and again I was asking him to explain himself.

How is his sequence *inclusion* monotone when each successive set is an
inductive *proper* subset of the immediately previous inductive set in
the sequence?

He is counting infinity as a number, a last element, which all
endsegments tail off into and saying that stepping backward from
infinity (as in backward from Aleph_zero Chuck Norris style) aleph_zero
is included in each set.

Sure, the sequence of set *sizes* in this sequence of sets is
(aleph_zero, aleph_zero, aleph_zero, aleph_zero, aleph_zero,
aleph_zero, aleph_zero,...) and is inclusion monotonic, but he says he
is not talking about cardinality. What then?

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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by: William - Thu, 25 Aug 2022 15:17 UTC

On Thursday, August 25, 2022 at 10:37:04 AM UTC-3, WM wrote:
> William schrieb am Donnerstag, 25. August 2022 um 03:05:30 UTC+2:
> > On Wednesday, August 24, 2022 at 5:52:10 PM UTC-3, WM wrote:
> >
> > > Can you find any two sets of successors which have not ℵo numbers in common? No
> > So what? The statement.
> > > All infinite endsegments have ℵo elements in common
> > (i.e. there is a single unchanging set S of cardinality ℵo, such that S is contained in each endsegment) does not follow.
> But if only ℵo elements are required, then my statement is true.

Piffle.

> And that is only what is relevant. Moreover each nonempty endsegment has at least one natnumber in common with all non-empty endsegments. Assume not..

This assumption is true (and does not lead to a contradiction).

>Assume for simplicity that every endsegment has only one element.

This assumption may be simple but it is false. Unsurprisingly it leads to a contradiction.

--
William Hughes

Re: Natural numbers and vases III

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 25 Aug 2022 11:20:33 -0400
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by: FromTheRafters - Thu, 25 Aug 2022 15:20 UTC

Fritz Feldhase was thinking very hard :
> On Thursday, August 25, 2022 at 4:04:06 PM UTC+2, FromTheRafters wrote:
>
>> Aleph_0 is not a 'number of elements' it is a size. Look up "Cardinality" to
>> see
>
> this: "In mathematics, the cardinality of a set is a measure of the "number
> of elements" of the set." (Wikipedia, Cardinality)
>
> :-)

Yeah, funny guy. :-D

Same source:

"Our intuition gained from finite sets breaks down when dealing with
infinite sets."

https://en.wikipedia.org/wiki/Cardinality#Infinite_sets

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 - Thu, 25 Aug 2022 15:25 UTC

On Thursday, August 25, 2022 at 5:15:27 PM UTC+2, FromTheRafters wrote:
> Fritz Feldhase pretended :
> > On Thursday, August 25, 2022 at 3:42:00 PM UTC+2, FromTheRafters wrote:
> >> WM explained on 8/25/2022 :
> >>>
> >>> (1) The intersection of inclusion-monotonic infinite sets is infinite..
> >>>
> >> What is 'inclusion monotonic' about your sequence of endsegments? Taken
> >> as ordered sets, each 'next' one is not a superset of each 'previous'
> >> one as is the case with their associated FISONs.
> >
> > Huh?! But each 'next' one is a subset of each 'previous'.
> >
> Yes, and again I was asking him to explain himself.

1. Don't ask silly questions, dumbo.

2. You are not in a booth with Mückenheim, you know, idiot.

3. He just gave you the very same answer, asshole.

> How is his sequence *inclusion* monotone when each successive set is a
> [...] *proper* subset of the immediately previous [...] set in the sequence?

???

Holy shit!

We just have E(n+1) c E(n for all n e IN.

CAN'T YOU READ???!!!

>>>> https://proofwiki.org/wiki/Definition:Monotone_Sequence_of_Sets

READ IT, YOU FUCKING ASSHOLE!

> but he says he is not talking about cardinality. What then?

THE SUBSET-RELATION!!!

HINT:

> > What is 'inclusion monotonic' about your sequence of endsegments? Taken
> > as ordered sets, each 'next' one is not a superset of each 'previous' one
>
> But a subset. [WM]

Re: Natural numbers and vases III

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 25 Aug 2022 11:35:33 -0400
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by: FromTheRafters - Thu, 25 Aug 2022 15:35 UTC

WM brought next idea :
> FromTheRafters schrieb am Donnerstag, 25. August 2022 um 16:04:06 UTC+2:
>> WM expressed precisely :
>
>>>>> Can you find any two sets of successors which have not ℵo numbers in
>>>>> common? No. All infinite endsegments have ℵo elements in common.
>>>> Wrong again, or still wrong.
>>>
>>> I said "all" and you cannot find any counter example. So "all" is correct.
>>> Why do you claim that nonsense if you have no counter example?
>> Aleph_zero is not a 'number of elements' it is a size.
>
> The intersection is produced by endsegments E(n) with finite index n only.

Each segment has to start somewhere.

> It does not matter what aleph_0 is.

It is the size of each of the endsegments when they are taken as sets,
they are inductive subsets of the natural numbers.

> Either endsegments with finite indices

What other kinds are there?

> produce the empty intersection or there is none.

By the axiom of BISS

> Note there is no endsegment with index aleph_0.

Good, because it is not a natural number.

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 25 Aug 2022 11:41:57 -0400
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by: FromTheRafters - Thu, 25 Aug 2022 15:41 UTC

Fritz Feldhase was thinking very hard :
> On Thursday, August 25, 2022 at 5:15:27 PM UTC+2, FromTheRafters wrote:
>> Fritz Feldhase pretended :
>>> On Thursday, August 25, 2022 at 3:42:00 PM UTC+2, FromTheRafters wrote:
>>>> WM explained on 8/25/2022 :
>>>>>
>>>>> (1) The intersection of inclusion-monotonic infinite sets is infinite.
>>>>>
>>>> What is 'inclusion monotonic' about your sequence of endsegments? Taken
>>>> as ordered sets, each 'next' one is not a superset of each 'previous'
>>>> one as is the case with their associated FISONs.
>>>
>>> Huh?! But each 'next' one is a subset of each 'previous'.
>>>
>> Yes, and again I was asking him to explain himself.
>
> 1. Don't ask silly questions, dumbo.

Why not?

> 2. You are not in a booth with Mückenheim, you know, idiot.

I'm also not an adolescent.

> 3. He just gave you the very same answer, asshole.

So that puts you and he on equal footing.

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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 - Thu, 25 Aug 2022 15:58 UTC

On Thursday, August 25, 2022 at 5:42:14 PM UTC+2, FromTheRafters wrote:
> Fritz Feldhase was thinking very hard :

> > 3. He just gave you the very same answer
> >
> So that puts you and he on equal footing.

Concerning this "question", yes.

It seems to me that this is one of the one or two things in math he really knows.

If you weren't an ignorant asshole you might learn it too. :-)

Some sources:
https://proofwiki.org/wiki/Definition:Monotone_Sequence_of_Sets
https://en.wikipedia.org/wiki/Set-theoretic_limit#Monotone_sequences

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Subject: Re: Natural numbers and vases III
From: thenewca...@gmail.com (Eram semper recta)
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by: Eram semper recta - Thu, 25 Aug 2022 17:07 UTC

On Thursday, 25 August 2022 at 11:59:02 UTC-4, Fritz Feldhase wrote:

> https://proofwiki.org/wiki/Definition:Monotone_Sequence_of_Sets

Remove the following from your Wiki logo!

όπερ έδει δείξαι

It has nothing to do with your anti-mathematical garbage!

Re: Natural numbers and vases III

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From: james.g....@att.net (Jim Burns)
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Subject: Re: Natural numbers and vases III
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by: Jim Burns - Thu, 25 Aug 2022 18:00 UTC

On 8/25/2022 11:20 AM, FromTheRafters wrote:

> "Our intuition gained from finite sets
> breaks down when dealing with infinite sets."
> https://en.wikipedia.org/wiki/Cardinality#Infinite_sets

One way to proceed despite broken down
intuitions is to depend only upon such
facts as hold in both the finite and the
infinite realms.

If x refers to one of infinitely-many,
and we already know P(x) and P(x) -> Q(x),
then we should allow ourselves to claim
we also know Q(x). And so on.

This is tedious.
We would like our intuition returned,
thank you very much.

Returning our intuition (improved)
is the purpose of mathematical exercises,
it seems to me.

Where do intuitions come from, in general?

It seems to me one's intuition that
throwing the dart _this way_ will stick it
in the center of that round thing comes
from _practice_ throwing the dart, mostly
unsuccessfully, at first. But one builds up
a mental library of dart-throwing experiences.

It seems to me that one is not finished,
even if one can repeat word-for-word the whole
text, if one has not corrected one's intuition.
I hope doing the exercises does that.
I don't know what else would.

Re: Natural numbers and vases III

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From: FTR...@nomail.afraid.org (FromTheRafters)
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Subject: Re: Natural numbers and vases III
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by: FromTheRafters - Thu, 25 Aug 2022 18:17 UTC

Fritz Feldhase explained on 8/25/2022 :
> On Thursday, August 25, 2022 at 5:42:14 PM UTC+2, FromTheRafters wrote:
>> Fritz Feldhase was thinking very hard :
>
>>> 3. He just gave you the very same answer
>>>
>> So that puts you and he on equal footing.
>
> Concerning this "question", yes.
>
> It seems to me that this is one of the one or two things in math he really
> knows.
>
> If you weren't an ignorant asshole you might learn it too. :-)
>
> Some sources:
> https://proofwiki.org/wiki/Definition:Monotone_Sequence_of_Sets
> https://en.wikipedia.org/wiki/Set-theoretic_limit#Monotone_sequences

Funny, no mention of *inclusion* monotonic. Each new set in this
particular case is a *proper subset* since each time another element is
missing. They are *not equal* except in cardinality. What is 'inclusion
monotonic' about that sequence?

Hint: two sets are *equal* if they have the *same* elements, and two
sets are of *equal size* if there is a *bijection* between them.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: Jim Burns - Thu, 25 Aug 2022 18:25 UTC

On 8/25/2022 9:40 AM, WM wrote:

> What makes the difference between
> all elements and the set?

I think that this gets answered very well
with _pluralities_ which you and I have
been giving the local name of "collections"

https://en.wikipedia.org/wiki/Plural_quantification
https://plato.stanford.edu/entries/plural-quant/

Elements are in collections.

A collection is not an element.
An element is not a collection.
They are separate domains.

With collections, we can do things
like describe one of the natural numbers,
so that, by reasoning from our description,
we can reason about all infinitely-many
of them.

----
Sets aren't like that, typically.
Sets can be in sets.
In some theories, like ZFC,
It's _only_ sets which can be in sets,
since there are only sets.

Even so, even in ZFC, a set as _container_
and a set as _contained_ are different roles.
omega contains all finite ordinals.
omega is not a finite ordinal.

I think collections (pluralities) are
better for explaining because, there,
they aren't different _roles_ they are
different _objects_

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 - Thu, 25 Aug 2022 21:41 UTC

On Thursday, August 25, 2022 at 8:17:46 PM UTC+2, FromTheRafters wrote:
> Fritz Feldhase explained on 8/25/2022 :

> Funny, no mention of *inclusion* monotonic.

Mückenheim's "inclusion" monotonic just points ot that the relevant order-realation is "inclusion" (is_subset, is_superset) and not, say, some order relation < or > (which may take into account cardinality or ordinality)..

> What is 'inclusion monotonic' about that sequence?

HOLY SHIT! Man, are you joking? JUST IGNORE MÜCKENHEIM'S "inclusion":

The sequence (E(n))_(n e IN) defined with E(n) = {m e IN : m >= n} for all n e IN is a ***monotone sequence of sets**. (Actually. it's a _decreasing_ sequence.)
See: https://proofwiki.org/wiki/Definition:Monotone_Sequence_of_Sets

This is just what Mückenheim means with his notion of "inclusion monotonic".

What's the matter with you man, these are just some trivial variants of terminology.

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 25 Aug 2022 16:49:30 -0500
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by: Sergio - Thu, 25 Aug 2022 21:49 UTC

On 8/25/2022 4:41 PM, Fritz Feldhase wrote:
> On Thursday, August 25, 2022 at 8:17:46 PM UTC+2, FromTheRafters wrote:
>> Fritz Feldhase explained on 8/25/2022 :
>
>> Funny, no mention of *inclusion* monotonic.
>
> Mückenheim's "inclusion" monotonic just points ot that the relevant order-realation is "inclusion" (is_subset, is_superset) and not, say, some order relation < or > (which may take into account cardinality or ordinality).
>
>> What is 'inclusion monotonic' about that sequence?
>
> HOLY SHIT! Man, are you joking? JUST IGNORE MÜCKENHEIM'S "inclusion":
>
> The sequence (E(n))_(n e IN) defined with E(n) = {m e IN : m >= n} for all n e IN is a ***monotone sequence of sets**. (Actually. it's a _decreasing_ sequence.)
> See: https://proofwiki.org/wiki/Definition:Monotone_Sequence_of_Sets
>
> This is just what Mückenheim means with his notion of "inclusion monotonic".
>
> What's the matter with you man, these are just some trivial variants of terminology.

OK, are these WN unique words and WM ideas ?

FISON
Endsegment
Inclusion Monotonic
(WMs) Defined (def)
visable/dark

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

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