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"Jesus saves...but Gretzky gets the rebound!" -- Daniel Hinojosa (hinojosa@hp-sdd)

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
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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
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
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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
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
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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
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
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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
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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
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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
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	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

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Mon, 22 Aug 2022 17:00 UTC

FromTheRafters schrieb am Montag, 22. August 2022 um 15:55:34 UTC+2:
> WM was thinking very hard :

> >>>> No it doesn't! It just shows that cardinal arithmetic works different from
> >>>> ordinary arithmetic Logic works the same. This statement ℕ \ {1, 2, 3,
> >>>> ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo

> > Fact is that induction proves that ℵo numbers are lurking behind every number
> > reached by induction.
> Each number greater than zero can be 'reached' by the successor
> function, this is not induction.

It is the same principle. And it fails in the same way. Provable by induction.

Regards, WM

Re: Natural numbers and vases III

<a8055499-beed-4299-bca1-61274b2935cdn@googlegroups.com>

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Newsgroups: sci.math
Date: Mon, 22 Aug 2022 10:04:00 -0700 (PDT)
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Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
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by: Gus Gassmann - Mon, 22 Aug 2022 17:04 UTC

On Monday, 22 August 2022 at 13:58:07 UTC-3, WM wrote:
[...]
> All [natural numbers] satisfy ∀n ∈ ℕ: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
> Collecting them together we get |ℕ \ {1, 2, 3, ...}| = ℵo.

No, you do not, you fucking imbecile. Your second line requires justification through a limit, for instance, or some other mechanism.

> The set satisfies |ℕ \ ℕ}| = 0.
> What causes the difference?

Muckenheim's well-documented quantifier dyslexia, age-induced dementia, and general stupidity.

Re: Natural numbers and vases III

<te0cur$1qrk$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 22 Aug 2022 12:04:26 -0500
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by: Sergio - Mon, 22 Aug 2022 17:04 UTC

On 8/22/2022 11:58 AM, WM wrote:
> FromTheRafters schrieb am Montag, 22. August 2022 um 15:53:23 UTC+2:
>> WM wrote :
>>> William schrieb am Samstag, 20. August 2022 um 16:30:41 UTC+2:
>>>> On Saturday, August 20, 2022 at 10:48:54 AM UTC-3, WM wrote:
>>>>
>>>>> I am not interested in the set but only in all its elements.
>>>> Piffle "all its elements" is the set.
>>>
>>> How man natural numbers can be used without using the set |N?
>> All of them.
>
> All of them satisfy ∀n ∈ ℕ: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
> Collecting them together we get |ℕ \ {1, 2, 3, ...}| = ℵo.

wrong, ℕ = {1, 2, 3, ...}

What do you think you mean in terms of math by "Collecting them together" ?

> The set satisfies |ℕ \ ℕ}| = 0.
> What causes the difference?

your mistakes

>
> Regards, WM

Re: Natural numbers and vases III

<te0d36$1qrk$2@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 22 Aug 2022 12:06:45 -0500
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by: Sergio - Mon, 22 Aug 2022 17:06 UTC

On 8/22/2022 11:53 AM, WM wrote:
> William schrieb am Montag, 22. August 2022 um 17:47:08 UTC+2:
>> On Monday, August 22, 2022 at 10:30:55 AM UTC-3, WM wrote:
>>> William schrieb am Samstag, 20. August 2022 um 16:30:41 UTC+2:
>>>> On Saturday, August 20, 2022 at 10:48:54 AM UTC-3, WM wrote:
>>>>
>>>>> I am not interested in the set but only in all its elements.
>>>> Piffle "all its elements" is the set.
>>> How man natural numbers can be used without using the set |N?
>> Irrelevant Piffle that has no bearing on the fact that "all its elements" is the set
>
> But how many elements are not the set?

by "elements" do you mean natural numbers only ?

>
> Regards, WM

Re: Natural numbers and vases III

<te0d4v$1qrk$3@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 22 Aug 2022 12:07:42 -0500
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by: Sergio - Mon, 22 Aug 2022 17:07 UTC

On 8/22/2022 12:00 PM, WM wrote:
> FromTheRafters schrieb am Montag, 22. August 2022 um 15:55:34 UTC+2:
>> WM was thinking very hard :
>
>>>>>> No it doesn't! It just shows that cardinal arithmetic works different from
>>>>>> ordinary arithmetic Logic works the same. This statement ℕ \ {1, 2, 3,
>>>>>> ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo
>
>>> Fact is that induction proves that ℵo numbers are lurking behind every number
>>> reached by induction.
>> Each number greater than zero can be 'reached' by the successor
>> function, this is not induction.
>
> It is the same principle. And it fails in the same way. Provable by induction.
>
> Regards, WM

more bad math tossed in like chum into a newsgroup by a troll

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, 22 Aug 2022 17:48 UTC

> On Monday, August 22, 2022 at 3:36:34 PM UTC+2, WM wrote:

> > there are ℵo natural numbers but most of them cannot be counted..

How do you know that there are ℵo of them if they cannot be counted?

Re: Natural numbers and vases III

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copy mid

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Subject: Re: Natural numbers and vases III
From: wpihug...@gmail.com (William)
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by: William - Mon, 22 Aug 2022 18:24 UTC

On Monday, August 22, 2022 at 1:53:05 PM UTC-3, WM wrote:
> how many elements are not the set?
Evasion. The answer does not change the fact that "all its elements" is the set

Re: Natural numbers and vases III

<te0i84$2ns2h$1@dont-email.me>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=109943&group=sci.math#109943

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From: FTR...@nomail.afraid.org (FromTheRafters)
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Subject: Re: Natural numbers and vases III
Date: Mon, 22 Aug 2022 14:34:42 -0400
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by: FromTheRafters - Mon, 22 Aug 2022 18:34 UTC

WM was thinking very hard :
> FromTheRafters schrieb am Montag, 22. August 2022 um 15:53:23 UTC+2:
>> WM wrote :
>>> William schrieb am Samstag, 20. August 2022 um 16:30:41 UTC+2:
>>>> On Saturday, August 20, 2022 at 10:48:54 AM UTC-3, WM wrote:
>>>>
>>>>> I am not interested in the set but only in all its elements.
>>>> Piffle "all its elements" is the set.
>>>
>>> How man natural numbers can be used without using the set |N?
>> All of them.
>
> All of them satisfy ∀n ∈ ℕ: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
> Collecting them together we get |ℕ \ {1, 2, 3, ...}| = ℵo.

My reply pane treated your second line with Aleph_zero and |N
differently from the first one. Anyway, the difference set between the
set |N without zero represented by its special symbol (which you got
wrong) and the set of positive naturals represented by the roster form
{1,2,3,...} is the empty set.

> The set satisfies |ℕ \ ℕ}| = 0.

One curly bracket?

> What causes the difference?

What difference?

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 22 Aug 2022 14:43:55 -0400
Organization: Peripheral Visions
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by: FromTheRafters - Mon, 22 Aug 2022 18:43 UTC

on 8/22/2022, WM supposed :
> William schrieb am Montag, 22. August 2022 um 17:47:08 UTC+2:
>> On Monday, August 22, 2022 at 10:30:55 AM UTC-3, WM wrote:
>>> William schrieb am Samstag, 20. August 2022 um 16:30:41 UTC+2:
>>>> On Saturday, August 20, 2022 at 10:48:54 AM UTC-3, WM wrote:
>>>>
>>>>> I am not interested in the set but only in all its elements.
>>>> Piffle "all its elements" is the set.
>>> How man natural numbers can be used without using the set |N?
>> Irrelevant Piffle that has no bearing on the fact that "all its elements" is
>> the set
>
> But how many elements are not the set?

Infinitely many, because only elements which qualify for inclusion in
the set are in the set. This means of course that, in the naturals,
there are no dark numbers. To include a dark number, you would have to
invoke it and determine its worthiness to be included, which means it
is not dark.

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: Mon, 22 Aug 2022 14:50:31 -0400
Organization: Peripheral Visions
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by: FromTheRafters - Mon, 22 Aug 2022 18:50 UTC

Sergio used his keyboard to write :
> On 8/22/2022 11:53 AM, WM wrote:
>> William schrieb am Montag, 22. August 2022 um 17:47:08 UTC+2:
>>> On Monday, August 22, 2022 at 10:30:55 AM UTC-3, WM wrote:
>>>> William schrieb am Samstag, 20. August 2022 um 16:30:41 UTC+2:
>>>>> On Saturday, August 20, 2022 at 10:48:54 AM UTC-3, WM wrote:
>>>>>
>>>>>> I am not interested in the set but only in all its elements.
>>>>> Piffle "all its elements" is the set.
>>>> How man natural numbers can be used without using the set |N?
>>> Irrelevant Piffle that has no bearing on the fact that "all its elements"
>>> is the set
>>
>> But how many elements are not the set?
>
> by "elements" do you mean natural numbers only ?

If so, he is just being facetious. My answer then would be one, because
he leaves the zero out of his notion of natural numbers when it
conveniences him.

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 22 Aug 2022 15:08:42 -0400
Organization: Peripheral Visions
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by: FromTheRafters - Mon, 22 Aug 2022 19:08 UTC

William formulated on Monday :
> On Monday, August 22, 2022 at 1:53:05 PM UTC-3, WM wrote:
>> how many elements are not the set?
> Evasion. The answer does not change the fact that "all its elements" is the
> set

I disagree. Maybe just a nitpick. Given the set |N , which doesn't
change, I can consider all of the elements in |N for inclusion in a new
set and filter out the ones I don't want to include, for example the
composite numbers.

Is this a new set? No, it is just a collection of elements. ZFC axioms
can be shown to validate the (proper subset) collection as a set. Then
you can put the curly brackets around the new collection and put roster
form or set builder notation inside the brackets.

Elephant, giraffe, Grizzly Bear <-- the beginnings of a zoo
{Elephant, Giraffe, Grizzly Bear} <-- a set with three elements

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: Mon, 22 Aug 2022 15:13:14 -0400
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by: FromTheRafters - Mon, 22 Aug 2022 19:13 UTC

It happens that FredJeffries formulated :
>> On Monday, August 22, 2022 at 3:36:34 PM UTC+2, WM wrote:
>
>>> there are ℵo natural numbers but most of them cannot be counted.
>
> How do you know that there are ℵo of them if they cannot be counted?

Because he had Chuck Norris count Aleph_zero minus one of them and then
he added one.

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 22 Aug 2022 15:17:15 -0400
Organization: Peripheral Visions
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by: FromTheRafters - Mon, 22 Aug 2022 19:17 UTC

WM pretended :
> FromTheRafters schrieb am Montag, 22. August 2022 um 15:55:34 UTC+2:
>> WM was thinking very hard :
>
>>>>>> No it doesn't! It just shows that cardinal arithmetic works different
>>>>>> from ordinary arithmetic Logic works the same. This statement ℕ \ {1,
>>>>>> 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo
>
>>> Fact is that induction proves that ℵo numbers are lurking behind every
>>> number reached by induction.
>> Each number greater than zero can be 'reached' by the successor
>> function, this is not induction.
>
> It is the same principle.

No, it isn't. That there is a next is given axiomatically, that there
is *always* a next is given by theorem using proof by induction.

> And it fails in the same way. Provable by induction.

Wrong, or not even wrong.

Re: Natural numbers and vases III

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 22 Aug 2022 16:48:21 -0400
Organization: A noiseless patient Spider
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by: Jim Burns - Mon, 22 Aug 2022 20:48 UTC

On 8/22/2022 9:30 AM, WM wrote:

> How man natural numbers can be used
> without using the set |N?

That describes all natural numbers.
ℕ was not used here to describe them.

By reasoning from that description,
we can draw conclusions about each natural number.
Without using ℕ

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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 - Tue, 23 Aug 2022 04:55 UTC

måndag 22 augusti 2022 kl. 15:47:51 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Montag, 22. August 2022 um 07:01:27 UTC+2:
> > fredag 19 augusti 2022 kl. 13:35:48 UTC+2 skrev WM:
>
> > > > No it doesn't! It just shows that cardinal arithmetic works different from ordinary arithmetic
> > > Logic works the same. This statement
> > > |ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo
> > > says that ℵo numbers are lurking behind all definable numbers.. So they are undefinable.
> >
> > False, your "definable" is MEANINGLESS!
> Fact is that induction proves that ℵo numbers are lurking behind every number reached by induction.
>
> Regards, WM

Which is ALL of them. It just means that the set is infinite! nothing else!

Re: Natural numbers and vases III

<87v8qjffhu.fsf@zotaspaz.fatphil.org>

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https://www.novabbs.com/tech/article-flat.php?id=109980&group=sci.math#109980

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From: pc+use...@asdf.org (Phil Carmody)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 23 Aug 2022 12:58:37 +0300
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by: Phil Carmody - Tue, 23 Aug 2022 09:58 UTC

FromTheRafters <FTR@nomail.afraid.org> writes:
> WM explained on 8/14/2022 :
>> FromTheRafters schrieb am Samstag, 13. August 2022 um 19:27:50 UTC+2:
>>> WM was thinking very hard :
>>>> FromTheRafters schrieb am Freitag, 12. August 2022 um 19:27:37
>>>> UTC+2:
>>>>
>>>>>> But when following the process, which first has to establish
>>>>>> this bijection, then it turns out that this claim is wrong.
>>>>> The 'process' does not establish the bijection, the bijection is
>>>>> already there.
>>>>
>>>> In your delusions but not in mathematics.
>>> So, there is no bijection between {elephant, giraffe, aardvark} and
>>> {jackrabbit, antelope, firetruck} ?
>>
>> It is now, after you have processed the procedure.
>
> What procedure are you imagining has been processed?

Presumably, every "for all" will be mapped in his head, via
"for each" and "for each in turn", into a procedure.

I which case every single bit of formal set theory collapses
into a procedure, even the axioms and axiom schemata.

Presumably, this includes his own version of set theory too.
So he needs to throw that out as well. He's nuking his own
feet.

However, I'll start him off with a new formal set theory, as
a helpful starting point, because I'm that kind of guy:

Axiom 0: There exists an empty set. Its definition is everything
sensible that WM's ever said about mathematics.

Phil
--
We are no longer hunters and nomads. No longer awed and frightened, as we have
gained some understanding of the world in which we live. As such, we can cast
aside childish remnants from the dawn of our civilization.
-- NotSanguine on SoylentNews, after Eugen Weber in /The Western Tradition/

Re: Natural numbers and vases III

<a715612a-9098-4a9b-88ff-325b401edb4fn@googlegroups.com>

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Newsgroups: sci.math
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Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
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by: Gus Gassmann - Tue, 23 Aug 2022 10:27 UTC

On Tuesday, 23 August 2022 at 07:14:57 UTC-3, Phil Carmody wrote:
> FromTheRafters <F...@nomail.afraid.org> writes:
> > WM explained on 8/14/2022 :
> >> FromTheRafters schrieb am Samstag, 13. August 2022 um 19:27:50 UTC+2:
> >>> WM was thinking very hard :
> >>>> FromTheRafters schrieb am Freitag, 12. August 2022 um 19:27:37
> >>>> UTC+2:
> >>>>
> >>>>>> But when following the process, which first has to establish
> >>>>>> this bijection, then it turns out that this claim is wrong.
> >>>>> The 'process' does not establish the bijection, the bijection is
> >>>>> already there.
> >>>>
> >>>> In your delusions but not in mathematics.
> >>> So, there is no bijection between {elephant, giraffe, aardvark} and
> >>> {jackrabbit, antelope, firetruck} ?
> >>
> >> It is now, after you have processed the procedure.
> >
> > What procedure are you imagining has been processed?
>
> Presumably, every "for all" will be mapped in his head, via
> "for each" and "for each in turn", into a procedure.
>
> I which case every single bit of formal set theory collapses
> into a procedure, even the axioms and axiom schemata.
>
> Presumably, this includes his own version of set theory too.
> So he needs to throw that out as well. He's nuking his own
> feet.
>
> However, I'll start him off with a new formal set theory, as
> a helpful starting point, because I'm that kind of guy:
>
> Axiom 0: There exists an empty set. Its definition is everything
> sensible that WM's ever said about mathematics.

Think again. Just yesterday he said that the empty set is a set from which all elements have been removed. He is even procedural about this.

Re: Natural numbers and vases III

<te2di4$2vnal$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: Tue, 23 Aug 2022 07:26:56 -0400
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by: FromTheRafters - Tue, 23 Aug 2022 11:26 UTC

Phil Carmody presented the following explanation :
> FromTheRafters <FTR@nomail.afraid.org> writes:
>> WM explained on 8/14/2022 :
>>> FromTheRafters schrieb am Samstag, 13. August 2022 um 19:27:50 UTC+2:
>>>> WM was thinking very hard :
>>>>> FromTheRafters schrieb am Freitag, 12. August 2022 um 19:27:37
>>>>> UTC+2:
>>>>>
>>>>>>> But when following the process, which first has to establish
>>>>>>> this bijection, then it turns out that this claim is wrong.
>>>>>> The 'process' does not establish the bijection, the bijection is
>>>>>> already there.
>>>>>
>>>>> In your delusions but not in mathematics.
>>>> So, there is no bijection between {elephant, giraffe, aardvark} and
>>>> {jackrabbit, antelope, firetruck} ?
>>>
>>> It is now, after you have processed the procedure.
>>
>> What procedure are you imagining has been processed?
>
> Presumably, every "for all" will be mapped in his head, via
> "for each" and "for each in turn", into a procedure.
>
> I which case every single bit of formal set theory collapses
> into a procedure, even the axioms and axiom schemata.
>
> Presumably, this includes his own version of set theory too.
> So he needs to throw that out as well. He's nuking his own
> feet.
>
> However, I'll start him off with a new formal set theory, as
> a helpful starting point, because I'm that kind of guy:
>
> Axiom 0: There exists an empty set. Its definition is everything
> sensible that WM's ever said about mathematics.
>
> Phil

Hi Phil, very well put. We need a simpleton function for his set theory
too. :D

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 - Tue, 23 Aug 2022 11:32 UTC

On Monday, August 22, 2022 at 8:24:39 PM UTC+2, William wrote:

> The answer does not change the fact that "all its elements" is the set.

That's not "a fact", but BS.

Re: Natural numbers and vases III

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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 - Tue, 23 Aug 2022 11:52 UTC

On Monday, 22 August 2022 at 12:53:05 UTC-4, WM wrote:
> William schrieb am Montag, 22. August 2022 um 17:47:08 UTC+2:
> > On Monday, August 22, 2022 at 10:30:55 AM UTC-3, WM wrote:
> > > William schrieb am Samstag, 20. August 2022 um 16:30:41 UTC+2:
> > > > On Saturday, August 20, 2022 at 10:48:54 AM UTC-3, WM wrote:
> > > >
> > > > > I am not interested in the set but only in all its elements.
> > > > Piffle "all its elements" is the set.
> > > How man natural numbers can be used without using the set |N?
> > Irrelevant Piffle that has no bearing on the fact that "all its elements" is the set
> But how many elements are not the set?

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.

One of the first properties of "sets" is that their elements are **distinct**. As you say, if they are mostly not there, then one can't even begin to talk about distinctness (definable or dark numbers as you call them). Just saying n ∈ N means n is a **distinct** element of N given the property that n is a fraction with denominator the unit. The statement says nothing about "ALL". To have ALL, it is required that ALL elements can be listed. This is not the case with the junk concept called "infinite set".

Whichever way one looks at it, they are basically screwed because ∈ implies membership meaning a set whose members are ALL known.

Set theory is not mathematics.

>
> Regards, WM

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 - Tue, 23 Aug 2022 12:28 UTC

tisdag 23 augusti 2022 kl. 13:52:11 UTC+2 skrev Eram semper recta:
> On Monday, 22 August 2022 at 12:53:05 UTC-4, WM wrote:
> > William schrieb am Montag, 22. August 2022 um 17:47:08 UTC+2:
> > > On Monday, August 22, 2022 at 10:30:55 AM UTC-3, WM wrote:
> > > > William schrieb am Samstag, 20. August 2022 um 16:30:41 UTC+2:
> > > > > On Saturday, August 20, 2022 at 10:48:54 AM UTC-3, WM wrote:
> > > > >
> > > > > > I am not interested in the set but only in all its elements.
> > > > > Piffle "all its elements" is the set.
> > > > How man natural numbers can be used without using the set |N?
> > > Irrelevant Piffle that has no bearing on the fact that "all its elements" is the set
> > But how many elements are not the set?
> 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.

>
> One of the first properties of "sets" is that their elements are **distinct**. As you say, if they are mostly not there, then one can't even begin to talk about distinctness (definable or dark numbers as you call them). Just saying n ∈ N means n is a **distinct** element of N given the property that n is a fraction with denominator the unit. The statement says nothing about "ALL". To have ALL, it is required that ALL elements can be listed. This is not the case with the junk concept called "infinite set".

If your complain is that we cannot write it down on a piece of paper you are truly a fucking moron.

>
> Whichever way one looks at it, they are basically screwed because ∈ implies membership meaning a set whose members are ALL known.
>
> Set theory is not mathematics.

It very much is.

>
> >
> > 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 - Tue, 23 Aug 2022 13:51 UTC

FredJeffries schrieb am Montag, 22. August 2022 um 19:48:08 UTC+2:
> > On Monday, August 22, 2022 at 3:36:34 PM UTC+2, WM wrote:
>
> > > there are ℵo natural numbers but most of them cannot be counted.
> How do you know that there are ℵo of them if they cannot be counted?

I use ℵo as expressing actual infinity (i.e. more than every finite number).

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 - Tue, 23 Aug 2022 13:53 UTC

William schrieb am Montag, 22. August 2022 um 20:24:39 UTC+2:
> On Monday, August 22, 2022 at 1:53:05 PM UTC-3, WM wrote:
> > how many elements are not the set?
> Evasion. The answer does not change the fact that "all its elements" is the set

How many elements can be subtracted without removing the set?

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 - Tue, 23 Aug 2022 13:57 UTC

FromTheRafters schrieb am Montag, 22. August 2022 um 20:34:54 UTC+2:
> WM was thinking very hard :

> > All of them satisfy ∀n ∈ ℕ: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
> > Collecting them together we get |ℕ \ {1, 2, 3, ...}| = ℵo.
> > The set satisfies |ℕ \ ℕ| = 0
> > What causes the difference?

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 - Tue, 23 Aug 2022 14:03 UTC

FromTheRafters schrieb am Montag, 22. August 2022 um 21:17:27 UTC+2:
> WM pretended :

> >> Each number greater than zero can be 'reached' by the successor
> >> function, this is not induction.
> >
> > It is the same principle.
> No, it isn't. That there is a next is given axiomatically, that there
> is *always* a next is given by theorem using proof by induction.

That there is always a next is proven by induction since n is arbitrary.

|ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo

Regards, WM

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

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