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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
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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	FredJeffries
Re: Natural numbers and vases III	WM
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	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	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	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	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
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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	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	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	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
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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
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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	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
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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	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

<te65bc$1k23$2@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 24 Aug 2022 16:31:24 -0500
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by: Sergio - Wed, 24 Aug 2022 21:31 UTC

On 8/24/2022 4:30 PM, Sergio wrote:
> On 8/24/2022 3:58 PM, WM wrote:
>> Fritz Feldhase schrieb am Mittwoch, 24. August 2022 um 22:16:39 UTC+2:
>>> On Wednesday, August 24, 2022 at 9:49:34 PM UTC+2, William wrote:
>>>> 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
>>> Actually, each and every natural number has ℵ₀ successors:
>>>
>>> ∀n ∈ ℕ: | ℕ \ {1, 2, 3, ..., n} | = ℵo
>>>> So what? They are not the same successors. So you cannot combine all these statements to form
>>>>
>>>> |ℕ_ def\ {1, 2, 3, ...}| = ℵo
>>> or to
>>>
>>> | ℕ \ {1, 2, 3, ...} | = ℵo .
>>>
>>> But MÜCKENHEIM can. By an application of
>>
>> of simple logic. All infinite endsegments have ℵo elements in common. Inclusion monotony.
>
> corrected: Endsegments have ℵo elements in common.

no that is wrong, because I cannot name any element that is common to all....

>
>>>
>>> | ℕ \ {1, 2, 3, ...}_def | = ℵo
>>>
>>> from
>>
>> a simple argument: Every natnumber which destroys this result is excluded from the set {1, 2, 3, ...}_def.
>
> ........way too many loose ends in that statement.
>
> Can you write an equation for that ? Or is that too much to ask?
>
>
>>
>> Regards, WM
>
>
> Ants that Destroy Results, and then get Excluded!

Re: Natural numbers and vases III

<1b33a9a2-03ad-4fdd-aff4-31b8b935dc79n@googlegroups.com>

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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 - Wed, 24 Aug 2022 22:13 UTC

On Wednesday, August 24, 2022 at 10:32:39 PM UTC+2, Sergio wrote:
> On 8/24/2022 3:16 PM, Fritz Feldhase wrote:
> >
> > | "Mückenheim's law":
> > |
> > | If An e IN: PHI[{1, ..., n}], then PHI[{1, 2, 3, ...}].
> >
> > So it's easy to derive
> >
> > | ℕ \ {1, 2, 3, ...} | = ℵo
> >
> > from
> >
> > ∀n ∈ ℕ: | ℕ \ {1, 2, 3, ..., n} | = ℵo .
> >
> > Just a simple application of Mückenheim's law.
> >
> >
> >
> I focus in on the area of concern;
>
> , ..., n}
>
> or
>
> , ...}

No, you did't get THE ESSENCE of Mückenheim's law:

An e IN: ... {1, 2, 3, ..., n} ...

implies (quite obviously)

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

Hope you got it now!

"Mückenheim's law" just allows for a formal application (as a "rule of derivation") of that obvious fact.

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 - Wed, 24 Aug 2022 22:17 UTC

On Wednesday, August 24, 2022 at 10:58:07 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Mittwoch, 24. August 2022 um 22:16:39 UTC+2:
> >
> > But MÜCKENHEIM can. By an application of
> >
> of simple logic.

Indeed! But actually it's called "Mückenheim's law", you know.

Hint: "Mückenheim's law" refers to the following rule of derivation:

| If An e IN: PHI[{1, ..., n}], then PHI[{1, 2, 3, ...}].

Re: Natural numbers and vases III

<te68s8$3ed69$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: Wed, 24 Aug 2022 18:31:31 -0400
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by: FromTheRafters - Wed, 24 Aug 2022 22:31 UTC

Sergio wrote on 8/24/2022 :
> On 8/24/2022 4:30 PM, Sergio wrote:
>> On 8/24/2022 3:58 PM, WM wrote:
>>> Fritz Feldhase schrieb am Mittwoch, 24. August 2022 um 22:16:39 UTC+2:
>>>> On Wednesday, August 24, 2022 at 9:49:34 PM UTC+2, William wrote:
>>>>> 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
>>>> Actually, each and every natural number has ℵ₀ successors:
>>>>
>>>> ∀n ∈ ℕ: | ℕ \ {1, 2, 3, ..., n} | = ℵo
>>>>> So what? They are not the same successors. So you cannot combine all
>>>>> these statements to form
>>>>>
>>>>> |ℕ_ def\ {1, 2, 3, ...}| = ℵo
>>>> or to
>>>>
>>>> | ℕ \ {1, 2, 3, ...} | = ℵo .
>>>>
>>>> But MÜCKENHEIM can. By an application of
>>>
>>> of simple logic. All infinite endsegments have ℵo elements in common.
>>> Inclusion monotony.
>>
>> corrected: Endsegments have ℵo elements in common.
>
> no that is wrong, because I cannot name any element that is common to all....

Which you 'could' do if it had a last element, which it doesn't.

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 - Wed, 24 Aug 2022 22:34 UTC

On Thursday, August 25, 2022 at 12:31:45 AM UTC+2, FromTheRafters wrote:
> Sergio wrote on 8/24/2022 :
> > On 8/24/2022 4:30 PM, Sergio wrote:
> >> On 8/24/2022 3:58 PM, WM wrote:
> >>> Fritz Feldhase schrieb am Mittwoch, 24. August 2022 um 22:16:39 UTC+2:
> >>>> On Wednesday, August 24, 2022 at 9:49:34 PM UTC+2, William wrote:
> >>>>> 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
> >>>> Actually, each and every natural number has ℵ₀ successors:
> >>>>
> >>>> ∀n ∈ ℕ: | ℕ \ {1, 2, 3, ..., n} | = ℵo
> >>>>> So what? They are not the same successors. So you cannot combine all
> >>>>> these statements to form
> >>>>>
> >>>>> |ℕ_ def\ {1, 2, 3, ...}| = ℵo
> >>>> or to
> >>>>
> >>>> | ℕ \ {1, 2, 3, ...} | = ℵo .
> >>>>
> >>>> But MÜCKENHEIM can. By an application of
> >>>
> >>> of simple logic. All infinite endsegments have ℵo elements in common.
> >>> Inclusion monotony.
> >>
> >> corrected: Endsegments have ℵo elements in common.
> >
> > no that is wrong, because I cannot name any element that is common to all...
> >
> Which you 'could' do if it had a last element, which it doesn't.

Did you mean "least"?

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: Wed, 24 Aug 2022 17:48:45 -0500
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by: Sergio - Wed, 24 Aug 2022 22:48 UTC

On 8/24/2022 3:52 PM, WM wrote:
> 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, you cannot name any number that is in common with all endsegments.

>
> Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
Date: Wed, 24 Aug 2022 17:51:16 -0500
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by: Sergio - Wed, 24 Aug 2022 22:51 UTC

On 8/24/2022 5:34 PM, Fritz Feldhase wrote:
> On Thursday, August 25, 2022 at 12:31:45 AM UTC+2, FromTheRafters wrote:
>> Sergio wrote on 8/24/2022 :
>>> On 8/24/2022 4:30 PM, Sergio wrote:
>>>> On 8/24/2022 3:58 PM, WM wrote:
>>>>> Fritz Feldhase schrieb am Mittwoch, 24. August 2022 um 22:16:39 UTC+2:
>>>>>> On Wednesday, August 24, 2022 at 9:49:34 PM UTC+2, William wrote:
>>>>>>> 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
>>>>>> Actually, each and every natural number has ℵ₀ successors:
>>>>>>
>>>>>> ∀n ∈ ℕ: | ℕ \ {1, 2, 3, ..., n} | = ℵo
>>>>>>> So what? They are not the same successors. So you cannot combine all
>>>>>>> these statements to form
>>>>>>>
>>>>>>> |ℕ_ def\ {1, 2, 3, ...}| = ℵo
>>>>>> or to
>>>>>>
>>>>>> | ℕ \ {1, 2, 3, ...} | = ℵo .
>>>>>>
>>>>>> But MÜCKENHEIM can. By an application of
>>>>>
>>>>> of simple logic. All infinite endsegments have ℵo elements in common.
>>>>> Inclusion monotony.
>>>>
>>>> corrected: Endsegments have ℵo elements in common.
>>>
>>> no that is wrong, because I cannot name any element that is common to all...
>>>
>> Which you 'could' do if it had a last element, which it doesn't.
>
> Did you mean "least"?

perhaps "universal" ?

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
Date: Wed, 24 Aug 2022 19:00:25 -0400
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by: FromTheRafters - Wed, 24 Aug 2022 23:00 UTC

Fritz Feldhase explained :
> On Thursday, August 25, 2022 at 12:31:45 AM UTC+2, FromTheRafters wrote:
>> Sergio wrote on 8/24/2022 :
>>> On 8/24/2022 4:30 PM, Sergio wrote:
>>>> On 8/24/2022 3:58 PM, WM wrote:
>>>>> Fritz Feldhase schrieb am Mittwoch, 24. August 2022 um 22:16:39 UTC+2:
>>>>>> On Wednesday, August 24, 2022 at 9:49:34 PM UTC+2, William wrote:
>>>>>>> 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
>>>>>> Actually, each and every natural number has ℵ₀ successors:
>>>>>>
>>>>>> ∀n ∈ ℕ: | ℕ \ {1, 2, 3, ..., n} | = ℵo
>>>>>>> So what? They are not the same successors. So you cannot combine all
>>>>>>> these statements to form
>>>>>>>
>>>>>>>> ℕ_ def\ {1, 2, 3, ...}| = ℵo
>>>>>> or to
>>>>>>
>>>>>>> ℕ \ {1, 2, 3, ...} | = ℵo .
>>>>>>
>>>>>> But MÜCKENHEIM can. By an application of
>>>>>
>>>>> of simple logic. All infinite endsegments have ℵo elements in common.
>>>>> Inclusion monotony.
>>>>
>>>> corrected: Endsegments have ℵo elements in common.
>>>
>>> no that is wrong, because I cannot name any element that is common to
>>> all...
>>>
>> Which you 'could' do if it had a last element, which it doesn't.
>
> Did you mean "least"?

No, I was just referring to the 'name an element common to all
endsegments' idea. Zero is not common to all of them, one is not common
to all of them, etcetera. Each and every number in turn gets removed
from consideration in the intersection. As long as this continues,
there will be *no* common element in all of the considered endsegments.

Only his notion of finite (his {3,4,5,...100D} or whatever it was)
endsegments, where there is a greatest/last element, will it stop.

{0,1,2,3,4,5}
{1,2,3,4,5}
{2,3,4,5}
{3,4,5}
{4,5}
{5}

The five being common to these 'finite endsegments' and also being the
last/greatest/rightmost element. He simply doesn't get the concept of
infinity as it is understood today.

Re: Natural numbers and vases III

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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 00:54 UTC

On Wednesday, August 24, 2022 at 5:16:39 PM UTC-3, Fritz Feldhase wrote:
> On Wednesday, August 24, 2022 at 9:49:34 PM UTC+2, William wrote:
> > 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
> Actually, each and every natural number has ℵ₀ successors:
>
> ∀n ∈ ℕ: | ℕ \ {1, 2, 3, ..., n} | = ℵo
> > So what? They are not the same successors. So you cannot combine all these statements to form
> >
> > |ℕ_ def\ {1, 2, 3, ...}| = ℵo
> or to
>
> | ℕ \ {1, 2, 3, ...} | = ℵo .
>
> But MÜCKENHEIM can. By an application of "Mückenheim's law":
>
> | If An e IN: PHI[{1, ..., n}], then PHI[{1, 2, 3, ...}].
>
> So it's easy to derive
>
> | ℕ \ {1, 2, 3, ...} | = ℵo
>
> from
>
> ∀n ∈ ℕ: | ℕ \ {1, 2, 3, ..., n} | = ℵo .
>
> Just a simple application of Mückenheim's law.

It only work if you include the Pink Elephant

Re: Natural numbers and vases III

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copy mid

https://www.novabbs.com/tech/article-flat.php?id=110192&group=sci.math#110192

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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 01:05 UTC

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.

--
William Hughes

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 - Thu, 25 Aug 2022 05:29 UTC

onsdag 24 augusti 2022 kl. 14:22:06 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Mittwoch, 24. August 2022 um 07:40:40 UTC+2:
> > tisdag 23 augusti 2022 kl. 16:08:34 UTC+2 skrev WM:
> > > zelos...@gmail.com schrieb am Dienstag, 23. August 2022 um 06:55:48 UTC+2:
> > > > måndag 22 augusti 2022 kl. 15:47:51 UTC+2 skrev WM:
> > >
> > > > > Fact is that induction proves that ℵo numbers are lurking behind every number reached by induction.
> > > > Which is ALL of them.
> > > No. ℵo numbers are missing, but when removing the set then also these ℵo numbers are are removed. So there is a difference.
> > >
> > There is nothing missing! There is no difference, you makae it up out of nothing
> nothing that you could understand.

There is nothing to understand, because everytime you say some property it applies to ALL of N!

>Nevertheless the difference exists:
>
> 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. S\S={}
So fucking what?

> > It is the same for ALL elements, this property is universal to ALL elements.
> Obviously not. But don't try to understand. It could damage your brain.

THere is nothing to understand because you just repeat things that is retarded

>
> 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 - Thu, 25 Aug 2022 13:19 UTC

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.

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 - Thu, 25 Aug 2022 13:22 UTC

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.

(2) By exchanging X and O the matrix
XOO...
XOO...
XOO...
....
cannot lose any O.

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 - Thu, 25 Aug 2022 13:26 UTC

FromTheRafters schrieb am Mittwoch, 24. August 2022 um 17:44:57 UTC+2:
> It happens that WM formulated :

> > n is an abbreviation for natural number, visible and dark. k is often used to
> > represent a natural number, bean-counter.
> You shouldn't blame others for your sloppiness. You have also used n as
> a real number in your 'real interval' attempt to show dark numbers
> exist.

I have used n = 6 in April and n =10 in June. Sorry for inconvenience if that is confusing you.

> > All visible natural numbers are ends of FISONs. They have ℵ₀ successors:
> > ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo .
> >
> > All natural numbers, i.e. the set ℕ, have no natural succesors:
> > ℕ \ {1, 2, 3, ...} = { } .
> Non-responsive,

But true and important.

Regards, WM

Re: Natural numbers and vases III

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by: FromTheRafters - Thu, 25 Aug 2022 13:30 UTC

on 8/25/2022, WM supposed :
> 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.

So what? What do you mean by 'complete' here?

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 - Thu, 25 Aug 2022 13:31 UTC

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

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 - Thu, 25 Aug 2022 13:36 UTC

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. 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. Assume for simplicity that every endsegment has only one element. Then there are at least two natnumbers a and b in endsegments A and B, such that a ∈ A and b ∈ B but a ∉ B and b ∉ A.

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 - Thu, 25 Aug 2022 13:40 UTC

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?

S\S={}
> So fucking what?

This which a serious mathematician cannot deny:

(1) The intersection of inclusion-monotonic infinite sets is infinite.

(2) By exchanging X and O the matrix
XOO...
XOO...
XOO...
....
cannot lose any O.

Regards, WM

Re: Natural numbers and vases III

<te7u6u$3li55$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 09:41:44 -0400
Organization: Peripheral Visions
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by: FromTheRafters - Thu, 25 Aug 2022 13:41 UTC

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 as is the case with their associated FISONs.

> (2) By exchanging X and O the matrix
> XOO...
> XOO...
> XOO...
> ...
> cannot lose any O.

Which has nothing to do with the topic.

Re: Natural numbers and vases III

<te7ue5$3liqu$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 09:45:35 -0400
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by: FromTheRafters - Thu, 25 Aug 2022 13:45 UTC

WM formulated on Thursday :
> FromTheRafters schrieb am Mittwoch, 24. August 2022 um 17:44:57 UTC+2:
>> It happens that WM formulated :
>
>>> n is an abbreviation for natural number, visible and dark. k is often used
>>> to represent a natural number, bean-counter.
>> You shouldn't blame others for your sloppiness. You have also used n as
>> a real number in your 'real interval' attempt to show dark numbers
>> exist.
>
> I have used n = 6 in April and n =10 in June. Sorry for inconvenience if that
> is confusing you.

Which has nothing to do with the fact that you claimed that n was a
natural when you use it (to be understood as such in your matheology)
but you are inconsistent with your terminology.

Re: Natural numbers and vases III

<te7upf$1v2l$1@gioia.aioe.org>

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https://www.novabbs.com/tech/article-flat.php?id=110234&group=sci.math#110234

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 25 Aug 2022 08:51:42 -0500
Organization: Aioe.org NNTP Server
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by: Sergio - Thu, 25 Aug 2022 13:51 UTC

On 8/25/2022 8:30 AM, FromTheRafters wrote:
> on 8/25/2022, WM supposed :
>> 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.
>
> So what? What do you mean by 'complete' here?

Complete Ants
No Complete Ants
Non-Complete Ants in linear order
Ordered Ants via Amazon, linearly
Reconciled No Complete Ants
Uncompleted Ants w no cheese left on their crackers

Re: Natural numbers and vases III

<te7uu6$1v2l$2@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 08:54:13 -0500
Organization: Aioe.org NNTP Server
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by: Sergio - Thu, 25 Aug 2022 13:54 UTC

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.

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 08:55:47 -0500
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by: Sergio - Thu, 25 Aug 2022 13:55 UTC

On 8/25/2022 8:36 AM, 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.

but it is not, so it is false.

> 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. Assume for simplicity that every endsegment has only one element. Then there are at least two natnumbers a and b in endsegments A and B, such that a ∈ A and b ∈ B but a ∉ B and b ∉ A.

wrong. Name the natural number that is common to all endsegments. Fail

>
> 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 - Thu, 25 Aug 2022 13:56 UTC

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.

> > (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. 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.

Regards, WM

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 25 Aug 2022 08:57:35 -0500
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by: Sergio - Thu, 25 Aug 2022 13:57 UTC

On 8/25/2022 8:40 AM, WM wrote:
> 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?

google for it.

>> So fucking what?
>
> This which a serious mathematician cannot deny:

you are never serious, you have a math mistake in Every Post!

>
> (1) The intersection of inclusion-monotonic infinite sets is infinite.
>
> (2) By exchanging X and O the matrix
> XOO...
> XOO...
> XOO...
> ...
> cannot lose any O.

wrong, and wrong

>
> Regards, WM

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

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