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Re: Natural numbers and vases III

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

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Re: Natural numbers and vases III

<teg448$llk1$1@dont-email.me>

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 28 Aug 2022 12:11:50 -0400
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by: FromTheRafters - Sun, 28 Aug 2022 16:11 UTC

WM wrote on 8/28/2022 :
> FromTheRafters schrieb am Samstag, 27. August 2022 um 17:00:34 UTC+2:
>> on 8/27/2022, WM supposed :
>>> FromTheRafters schrieb am Freitag, 26. August 2022 um 21:31:11 UTC+2:
>>>
>>>> Okay, so it is about your reluctance to accept an infinite set?
>>>
>>> I do accept infinite sets!
>> Then what was the relevance of those quotes using the word 'complete'?
>
> You asked for an explanation of that word.
>>
>> I had asked what you meant by complete. It seems to still mean 'has a
>> last element' to you.
>
> It means the same to me as to everyone who is informed about the difference
> between potential and actual (complete) infinity. But most matheologians deny
> to understand the difference because it leads to inconsistencies.
> Matheologians always need the opportunity to say that they have meant
> potential infinity when they are shown the inconsistencies, After a while
> they will come back with actual infinity - until they are tied down again.
>
> Complete does not mean a last element, but all elements are there, none can
> be added.

Then what is a set?

Re: Natural numbers and vases III

<teg4af$107k$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 28 Aug 2022 11:15:10 -0500
Organization: Aioe.org NNTP Server
Message-ID: <teg4af$107k$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
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by: Sergio - Sun, 28 Aug 2022 16:15 UTC

On 8/28/2022 8:49 AM, WM wrote:
> William schrieb am Samstag, 27. August 2022 um 17:07:27 UTC+2:
>> On Saturday, August 27, 2022 at 10:33:32 AM UTC-3, WM wrote:
>>> William schrieb am Freitag, 26. August 2022 um 21:16:08 UTC+2:
>>>> On Friday, August 26, 2022 at 4:03:03 PM UTC-3, WM wrote:
>>>>> William schrieb am Freitag, 26. August 2022 um 20:55:21 UTC+2:
>>>>>> On Friday, August 26, 2022 at 3:47:09 PM UTC-3, WM wrote:
>>>>>>> ... by
>>>>>>> ∀k ∈ ℕ: E(k+1) = E(k) \ {k}
>>>>>>> there must be a first natural number which is not followed by an infinite endsegment.
>>>>>> Nope, does not follow and is not true.
>>>>>>
>>>>> It follows because above you see the universal quantifier.
>>>>>
>>>> Nope, There is no last |N so the fact that there is a universal quantifier means
>>>> ∀k ∈ ℕ: | E(k)|= aleph_0
>>> We need no last n in ℕ, but there are all endsegments. None is missing. And for all the equation E(k+1) = E(k) \ {k} is valid. That means that the infinite intersection cannot be reduced in one step to the empty set. It can be reduced only one by one. Hence *if* the intersection is emptied [by a stepwise process],there must be finite intersections.
>>
>> Vacuously true. The intersection cannot "be emptied" by a stepwise process. So what?
>
> Every definable endsegment decreases the intersection by one natnumber:
>
> ∀k ∈ ℕ_def : ∩{E(1), E(2), ..., E(k+1)} = ∩{E(1), E(2), ..., E(k)} \ {k}.

corrected:

∀k ∈ ℕ : ∩{E(1), E(2), ..., E(k+1)} = ℵo
∩{E(1), E(2), ..., E(k)} \ {k} = ℵo

>
> If this stepwise deleting cannot be carried through with the whole set of endsegments, then there must be a reason.

the reason is you stop at k+1, and k, and you do not understand the material.

>
> Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Sun, 28 Aug 2022 16:23 UTC

On Sunday, August 28, 2022 at 6:15:20 PM UTC+2, Sergio wrote:
> On 8/28/2022 8:49 AM, WM wrote:
> > William schrieb am Samstag, 27. August 2022 um 17:07:27 UTC+2:
> >> On Saturday, August 27, 2022 at 10:33:32 AM UTC-3, WM wrote:
> >>> William schrieb am Freitag, 26. August 2022 um 21:16:08 UTC+2:
> >>>> On Friday, August 26, 2022 at 4:03:03 PM UTC-3, WM wrote:
> >>>>> William schrieb am Freitag, 26. August 2022 um 20:55:21 UTC+2:
> >>>>>> On Friday, August 26, 2022 at 3:47:09 PM UTC-3, WM wrote:
> >>>>>>> ... by
> >>>>>>> ∀k ∈ ℕ: E(k+1) = E(k) \ {k}
> >>>>>>> there must be a first natural number which is not followed by an infinite endsegment.
> >>>>>> Nope, does not follow and is not true.
> >>>>>>
> >>>>> It follows because above you see the universal quantifier.
> >>>>>
> >>>> Nope, There is no last |N so the fact that there is a universal quantifier means
> >>>> ∀k ∈ ℕ: | E(k)|= aleph_0
> >>> We need no last n in ℕ, but there are all endsegments. None is missing. And for all the equation E(k+1) = E(k) \ {k} is valid. That means that the infinite intersection cannot be reduced in one step to the empty set. It can be reduced only one by one. Hence *if* the intersection is emptied [by a stepwise process],there must be finite intersections.
> >>
> >> Vacuously true. The intersection cannot "be emptied" by a stepwise process. So what?
> >
> > Every definable endsegment decreases the intersection by one natnumber:
> >
> > ∀k ∈ ℕ_def : ∩{E(1), E(2), ..., E(k+1)} = ∩{E(1), E(2), ..., E(k)} \ {k}.

> corrected:

Huh?!

Was correct, you wrote nonsense:

> ∀k ∈ ℕ : ∩{E(1), E(2), ..., E(k+1)} = ℵo

Hint:
> ∩{E(1), E(2), ..., E(k)} \ {k} = ℵ

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 - Sun, 28 Aug 2022 16:27 UTC

On Sunday, August 28, 2022 at 10:52:02 AM UTC-3, WM wrote:
> William schrieb am Samstag, 27. August 2022 um 17:19:36 UTC+2:
> > On Saturday, August 27, 2022 at 10:44:04 AM UTC-3, WM wrote:
> > > ... you must find an endsegment which contains some elements not in a predecessor.
> >
> > Nope. No such endsegment is needed in order to get an empty intersection
> It is needed if all endsegments are nonempty. The only alternative would be an empty endsegment.

Piffle. There is also the alternative that there is no last endsegment.

--
William Hughes

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Sun, 28 Aug 2022 16:28 UTC

On Sunday, August 28, 2022 at 6:23:27 PM UTC+2, Fritz Feldhase wrote:
> On Sunday, August 28, 2022 at 6:15:20 PM UTC+2, Sergio wrote:
> > On 8/28/2022 8:49 AM, WM wrote:
> > > William schrieb am Samstag, 27. August 2022 um 17:07:27 UTC+2:
> > >> On Saturday, August 27, 2022 at 10:33:32 AM UTC-3, WM wrote:
> > >>> William schrieb am Freitag, 26. August 2022 um 21:16:08 UTC+2:
> > >>>> On Friday, August 26, 2022 at 4:03:03 PM UTC-3, WM wrote:
> > >>>>> William schrieb am Freitag, 26. August 2022 um 20:55:21 UTC+2:
> > >>>>>> On Friday, August 26, 2022 at 3:47:09 PM UTC-3, WM wrote:
> > >>>>>>> ... by
> > >>>>>>> ∀k ∈ ℕ: E(k+1) = E(k) \ {k}
> > >>>>>>> there must be a first natural number which is not followed by an infinite endsegment.
> > >>>>>> Nope, does not follow and is not true.
> > >>>>>>
> > >>>>> It follows because above you see the universal quantifier.
> > >>>>>
> > >>>> Nope, There is no last |N so the fact that there is a universal quantifier means
> > >>>> ∀k ∈ ℕ: | E(k)|= aleph_0
> > >>> We need no last n in ℕ, but there are all endsegments. None is missing. And for all the equation E(k+1) = E(k) \ {k} is valid. That means that the infinite intersection cannot be reduced in one step to the empty set. It can be reduced only one by one. Hence *if* the intersection is emptied [by a stepwise process],there must be finite intersections.
> > >>
> > >> Vacuously true. The intersection cannot "be emptied" by a stepwise process. So what?
> > >
> > > Every definable endsegment decreases the intersection by one natnumber:
> > >
> > > ∀k ∈ ℕ_def : ∩{E(1), E(2), ..., E(k+1)} = ∩{E(1), E(2), ..., E(k)} \ {k}.
>
> > corrected:
> Huh?!
>
> Was correct, you wrote nonsense:

> > ∀k ∈ ℕ : ∩{E(1), E(2), ..., E(k+1)} = ℵo

Hint: ∀k ∈ ℕ: ∩{E(1), E(2), ..., E(k+1)} = E(k+1)

I guess you meant: ∀k ∈ ℕ: |∩{E(1), E(2), ...., E(k+1)}| = ℵo

> > ∩{E(1), E(2), ..., E(k)} \ {k} = ℵo

Same, and missing quantifier.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Sun, 28 Aug 2022 16:44 UTC

On Sunday, August 28, 2022 at 4:24:11 PM UTC+2, WM wrote:
> Jim Burns schrieb am Samstag, 27. August 2022 um 20:14:07 UTC+2:
> >
> > Elements [for] which [there is an endsegment they are not-in]
> > are not-in [the] intersection [of all endsegments]

Right. All elements in IN are

> such elements

>> a ∈ A and a ∉ B

Especially, n ∈ E(n) and n ∉ E(n+1) for all n e IN.

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sun, 28 Aug 2022 11:49:14 -0500
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by: Sergio - Sun, 28 Aug 2022 16:49 UTC

On 8/28/2022 11:23 AM, Fritz Feldhase wrote:
> On Sunday, August 28, 2022 at 6:15:20 PM UTC+2, Sergio wrote:
>> On 8/28/2022 8:49 AM, WM wrote:
>>> William schrieb am Samstag, 27. August 2022 um 17:07:27 UTC+2:
>>>> On Saturday, August 27, 2022 at 10:33:32 AM UTC-3, WM wrote:
>>>>> William schrieb am Freitag, 26. August 2022 um 21:16:08 UTC+2:
>>>>>> On Friday, August 26, 2022 at 4:03:03 PM UTC-3, WM wrote:
>>>>>>> William schrieb am Freitag, 26. August 2022 um 20:55:21 UTC+2:
>>>>>>>> On Friday, August 26, 2022 at 3:47:09 PM UTC-3, WM wrote:
>>>>>>>>> ... by
>>>>>>>>> ∀k ∈ ℕ: E(k+1) = E(k) \ {k}
>>>>>>>>> there must be a first natural number which is not followed by an infinite endsegment.
>>>>>>>> Nope, does not follow and is not true.
>>>>>>>>
>>>>>>> It follows because above you see the universal quantifier.
>>>>>>>
>>>>>> Nope, There is no last |N so the fact that there is a universal quantifier means
>>>>>> ∀k ∈ ℕ: | E(k)|= aleph_0
>>>>> We need no last n in ℕ, but there are all endsegments. None is missing. And for all the equation E(k+1) = E(k) \ {k} is valid. That means that the infinite intersection cannot be reduced in one step to the empty set. It can be reduced only one by one. Hence *if* the intersection is emptied [by a stepwise process],there must be finite intersections.
>>>>
>>>> Vacuously true. The intersection cannot "be emptied" by a stepwise process. So what?
>>>
>>> Every definable endsegment decreases the intersection by one natnumber:
>>>
>>> ∀k ∈ ℕ_def : ∩{E(1), E(2), ..., E(k+1)} = ∩{E(1), E(2), ..., E(k)} \ {k}.
>
>> corrected:
>
> Huh?!
>
> Was correct, you wrote nonsense:
>
>> ∀k ∈ ℕ : ∩{E(1), E(2), ..., E(k+1)} = ℵo

agree, no coffee yet

>
> Hint:
>> ∩{E(1), E(2), ..., E(k)} \ {k} = ℵ

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: Sun, 28 Aug 2022 13:32:33 -0400
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by: Jim Burns - Sun, 28 Aug 2022 17:32 UTC

On 8/28/2022 10:24 AM, WM wrote:
> Jim Burns schrieb am Samstag,
> 27. August 2022 um 20:14:07 UTC+2:
>> On 8/27/2022 9:44 AM, WM wrote:
>>> Jim Burns schrieb am Freitag,
>>> 26. August 2022 um 21:56:30 UTC+2:
>>>> On 8/26/2022 2:51 PM, WM wrote:

>>>>>>> Then there are at least two natnumbers
>>>>>>> a and b in endsegments A and B, such that
>>>>>>> (1) a ∈ A
>>>>>>> (2) b ∈ B
>>>>>>> (3) a ∉ B
>>>>>>> (4) b ∉ A.

>>> But a ∈ A and a ∈ B
>>
>> See above.
>> a ∈ A and a ∉ B
>
> Then b ∈ A and b ∈ B.

Suppose b ∈ A
If b ∉ C and c ∈ C then b is not in
the intersection of all end segments.

> The conditions (1) to (4) cannot be satisfied
> together with non-empty endsegnments.

Conditions (1) to (4) don't need to be
satisfied for their intersection to be empty.

For an empty intersection of all,
we only need each element in any end segment
to be not-in some other end segment.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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by: zelos...@gmail.com - Mon, 29 Aug 2022 05:08 UTC

fredag 26 augusti 2022 kl. 18:35:33 UTC+2 skrev Eram semper recta:
> On Friday, 26 August 2022 at 00:56:21 UTC-4, zelos idiot wrote:
> > torsdag 25 augusti 2022 kl. 15:40:21 UTC+2 skrev WM:
> > 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..
> > Not necessarily.
> >
> > >
> > > (2) By exchanging X and O the matrix
> > > XOO...
> > > XOO...
> > > XOO...
> > > ...
> > > cannot lose any O.
> > >
> > > Regards, WM
> >
> > Only if you think in a step wise process which mathematics IS NOT!
> Newsflash: Everything in mathematics is a stepwise process. Set theory is not mathematics.
Newsflash: You're wrong as always.
Things are not a process in mathematics and set theory is very much mathematics.

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, 29 Aug 2022 09:15 UTC

FromTheRafters schrieb am Sonntag, 28. August 2022 um 18:12:02 UTC+2:
> WM wrote on 8/28/2022 :

> > Complete does not mean a last element, but all elements are there, none can
> > be added.
> Then what is a set?

As I said: All elements are there, none can be added.
Contrary to the collection of definable endsegments which contains only those endsegments which have a nonempty intersection:
∩{E(n) | n ∈ ℕ_def} =/= { }.
You cannot complete them.

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 - Mon, 29 Aug 2022 09:20 UTC

William schrieb am Sonntag, 28. August 2022 um 18:27:31 UTC+2:
> On Sunday, August 28, 2022 at 10:52:02 AM UTC-3, WM wrote:
> > William schrieb am Samstag, 27. August 2022 um 17:19:36 UTC+2:
> > > On Saturday, August 27, 2022 at 10:44:04 AM UTC-3, WM wrote:
> > > > ... you must find an endsegment which contains some elements not in a predecessor.
> > >
> > > Nope. No such endsegment is needed in order to get an empty intersection
> > It is needed if all endsegments are nonempty. The only alternative would be an empty endsegment.
> Piffle. There is also the alternative that there is no last endsegment.

All endsegments which are there fail to satisfy
(1) a ∈ A
(2) b ∈ B
(3) a ∉ B
(4) b ∉ A.
It is irrelevant whether there is a last one if all fail. All which fail have an element in common.

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 - Mon, 29 Aug 2022 09:23 UTC

Fritz Feldhase schrieb am Sonntag, 28. August 2022 um 18:44:44 UTC+2:
> On Sunday, August 28, 2022 at 4:24:11 PM UTC+2, WM wrote:
> > Jim Burns schrieb am Samstag, 27. August 2022 um 20:14:07 UTC+2:
> > >
> > > Elements [for] which [there is an endsegment they are not-in]
> > > are not-in [the] intersection [of all endsegments]
>
> Right. All elements in IN are
>
> > such elements
> >> a ∈ A and a ∉ B
> Especially, n ∈ E(n) and n ∉ E(n+1) for all n e IN.

All endsegments which are there fail to satisfy
(1) a ∈ A
(2) b ∈ B
(3) a ∉ B
(4) b ∉ A.
All which fail have an element in common.

Regards, WM

Re: Natural numbers and vases III

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by: WM - Mon, 29 Aug 2022 09:26 UTC

Jim Burns schrieb am Sonntag, 28. August 2022 um 19:32:44 UTC+2:
> On 8/28/2022 10:24 AM, WM wrote:

> > The conditions (1) to (4) cannot be satisfied
> > together with non-empty endsegnments.
> Conditions (1) to (4) don't need to be
> satisfied for their intersection to be empty.
>
> For an empty intersection of all,
> we only need each element in any end segment
> to be not-in some other end segment.

But that is wrong without an empty endsegment, contradicted by

(1) a ∈ A
(2) b ∈ B
(3) a ∉ B
(4) b ∉ A.
All which fail and are not empty have an element in common.

Regards, WM

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Mon, 29 Aug 2022 09:28 UTC

zelos...@gmail.com schrieb am Montag, 29. August 2022 um 07:09:03 UTC+2:
> fredag 26 augusti 2022 kl. 18:35:33 UTC+2 skrev Eram semper recta:
> > On Friday, 26 August 2022 at 00:56:21 UTC-4, zelos idiot wrote:
> > > Only if you think in a step wise process which mathematics IS NOT!
> > Newsflash: Everything in mathematics is a stepwise process. Set theory is not mathematics.
> Newsflash: You're wrong as always.
> Things are not a process in mathematics and set theory is very much mathematics.

All sequences are stepwise processes and are stepwise analyzable as long as the terms can be individually defined. The others are dark. Otherwise they could be checked stepwise.

Regards, WM

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 - Mon, 29 Aug 2022 09:56 UTC

On Monday, August 29, 2022 at 11:29:04 AM UTC+2, WM wrote:
> zelos...@gmail.com schrieb am Montag, 29. August 2022 um 07:09:03 UTC+2:
> > fredag 26 augusti 2022 kl. 18:35:33 UTC+2 skrev Eram semper recta:
> > >
> > > Newsflash: Everything in mathematics is a stepwise process. Set theory is not mathematics.

Complete nonsense. But proofs indeed consists of steps. We proceed in steps when proving a theorem, you know.

> > Newsflash: You're wrong as always.

Indeed! :-)

> > Things are not a process in mathematics and set theory is very much mathematics.

Of course

> All sequences are stepwise processes

Holy shit!

> and are stepwise analyzable as long as the terms can be individually defined.

So what? Who cares?

You know, we usually don't check infinitely many mathematical facts, when doing proofs. Actually, that's why we USE proofs.

We can prove that for all natural numbers n: n + n = 2*n.

We DON'T prove this by explicitly checking that

1 + 1 = 2 = 2*1, 2 + 2 = 4 = 2*2, 3 + 3 = 6 = 2*3, ad infinitum

Seems that you are confusing mathematics with using a pocket calculator.

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, 29 Aug 2022 06:17:01 -0400
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by: FromTheRafters - Mon, 29 Aug 2022 10:17 UTC

WM laid this down on his screen :
> FromTheRafters schrieb am Sonntag, 28. August 2022 um 18:12:02 UTC+2:
>> WM wrote on 8/28/2022 :
>
>>> Complete does not mean a last element, but all elements are there, none can
>>> be added.
>> Then what is a set?
>
> As I said: All elements are there, none can be added.

That's a property of a set, what does complete mean again?

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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by: zelos...@gmail.com - Mon, 29 Aug 2022 10:31 UTC

måndag 29 augusti 2022 kl. 11:26:27 UTC+2 skrev WM:
> Jim Burns schrieb am Sonntag, 28. August 2022 um 19:32:44 UTC+2:
> > On 8/28/2022 10:24 AM, WM wrote:
>
> > > The conditions (1) to (4) cannot be satisfied
> > > together with non-empty endsegnments.
> > Conditions (1) to (4) don't need to be
> > satisfied for their intersection to be empty.
> >
> > For an empty intersection of all,
> > we only need each element in any end segment
> > to be not-in some other end segment.
> But that is wrong without an empty endsegment, contradicted by
> (1) a ∈ A
> (2) b ∈ B
> (3) a ∉ B
> (4) b ∉ A.
> All which fail and are not empty have an element in common.
>
> Regards, WM
you still do not understand how intersections work

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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by: zelos...@gmail.com - Mon, 29 Aug 2022 10:32 UTC

måndag 29 augusti 2022 kl. 11:29:04 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Montag, 29. August 2022 um 07:09:03 UTC+2:
> > fredag 26 augusti 2022 kl. 18:35:33 UTC+2 skrev Eram semper recta:
> > > On Friday, 26 August 2022 at 00:56:21 UTC-4, zelos idiot wrote:
>
> > > > Only if you think in a step wise process which mathematics IS NOT!
> > > Newsflash: Everything in mathematics is a stepwise process. Set theory is not mathematics.
> > Newsflash: You're wrong as always.
> > Things are not a process in mathematics and set theory is very much mathematics.
> All sequences are stepwise processes and are stepwise analyzable as long as the terms can be individually defined. The others are dark. Otherwise they could be checked stepwise.
>
> Regards, WM
A sequence is not a stepwise process. It is a function from N to S.

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 - Mon, 29 Aug 2022 10:41 UTC

On Monday, August 29, 2022 at 11:23:15 AM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Sonntag, 28. August 2022 um 18:44:44 UTC+2:
> > On Sunday, August 28, 2022 at 4:24:11 PM UTC+2, WM wrote:
> > > Jim Burns schrieb am Samstag, 27. August 2022 um 20:14:07 UTC+2:
> > > >
> > > > Elements [for] which [there is an endsegment they are not-in]
> > > > are not-in [the] intersection [of all endsegments]
> > > >
> > Right. All elements in IN are
> >
> > > such elements
> > > >
> > > > a ∈ A and a ∉ B
> > > >
> > Especially, n ∈ E(n) and n ∉ E(n+1) for all n e IN.
> >
> All endsegments which are there fail to satisfy
> (1) a ∈ A
> (2) b ∈ B
> (3) a ∉ B
> (4) b ∉ A.
> All which fail have an element in common.

Hint: This mumbo jumbo does not "invalidate" the fact that

for all n e IN: n ∈ E(n) and n ∉ E(n+1), or simply: for all n e IN: n ∉ E(n+1)

and hence

for all n e IN: there is a k e IN such that: n ∉ E(k)

and hence

for all n e IN: n ∉ INTERSECTION {E(i) : i e IN} ,

since

> > > > Elements [for] which [there is an endsegment they are not-in]
> > > > are not-in [the] intersection [of all endsegments] .

Which just means

INTERSECTION {E(i) : i e IN} = { }

since INTERSECTION {E(i) : i e IN} c IN.

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From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Mon, 29 Aug 2022 11:00 UTC

On Monday, August 29, 2022 at 12:31:44 PM UTC+2, zelos...@gmail.com wrote:

> you still do not understand how intersections work

@Mückenheim, hint:

For any sets A_k (k e IN) and each and every x:

x !e INTERSECTION {A_k : k e IN} <-> Ek e IN: x !e A_k. (*)

BY DEFINITION OF THE NOTION ___INTERSECTION___.

Now from An e IN: n !e E(n+1) we GET that for each and every natural number n:

Ek e IN: n !e E(k) ,

hence by (*) for each and every natural number n:

n !e INTERSECTION {E(k) : k e IN} .

=> There is no natural number in INTERSECTION {E(k) : k e IN}.

Now look, you silly idiot, THIS RESULT DOES NOT DEPEND on the assumption (or fact) that all endsegments are finite/infinite/empty, whatever. ALL that is needed for this result is that for each and every n e IN:

___ Ek e IN: n !e E(k)__.

Which is the case, since

Ak e IN: k !e E(k+1)

BY DEFINITION of (E(k))_k e IN.

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, 29 Aug 2022 07:53:08 -0400
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by: Jim Burns - Mon, 29 Aug 2022 11:53 UTC

On 8/29/2022 5:15 AM, WM wrote:
> FromTheRafters schrieb am Sonntag,
> 28. August 2022 um 18:12:02 UTC+2:
>> WM wrote on 8/28/2022 :

>>> Complete does not mean a last element,
>>> but all elements are there,
>>> none can be added.
>>
>> Then what is a set?
>
> As I said:
> All elements are there,
> none can be added.

Consider ___.

If 𝐹 is a FISON,
then 𝐹 is in ___.
If 𝐹 is in ___,
then 𝐹 is a FISON,

Is ___ a set?

If ___ is not a set,
then what can be added?
Nothing which is a FISON.
It's in ___,
Nothing which is not a FISON.
It's not in ___,

Is there something which
both is and is not a FISON,
or which
neither is nor is not a FISON?

> Contrary to
> the collection of definable endsegments

Let k be in a FISON.
Consider ______.

If m ends a FISON which k is in,
then m is in ______.
If m is in ______,
then m ends a FISON which k is in.

Is ______ a set?

If ______ is not a set,
is there something which
both does and does not
end a FISON which k is in,
or which
neither does nor does not
end a FISON which k is in?

> which contains only those endsegments
> which have a nonempty intersection:

Perhaps it would be better for you
to answer what is an intersection?

For everyone else,
it is collections or set of end segments
which have intersections.

> ∩{E(n) | n ∈ ℕ_def} =/= { }.

If 𝐸 is in some _________ which
contains only end segment and which
has a non-empty intersection,
then 𝐸 is in ____________.
If 𝐸 is in ____________,
then 𝐸 is in some _________ which
contains only end segment and which
has a non-empty intersection.

____________ contains only end segments.
However,
____________ is not non-empty.

> You cannot complete them.

You, above:
> All elements are there,
> none can be added.

What can be added to ___?
to ______?
to _________?
to ____________?

Re: Natural numbers and vases III

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From: james.g....@att.net (Jim Burns)
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Subject: Re: Natural numbers and vases III
Date: Mon, 29 Aug 2022 08:04:09 -0400
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by: Jim Burns - Mon, 29 Aug 2022 12:04 UTC

On 8/29/2022 7:53 AM, Jim Burns wrote:
> On 8/29/2022 5:15 AM, WM wrote:

>> ∩{E(n) | n ∈ ℕ_def} =/= { }.
>
> If 𝐸 is in some _________ which
> contains only end segment and which
> has a non-empty intersection,
> then 𝐸 is in ____________.
> If 𝐸 is in ____________,
> then 𝐸 is in some _________ which
> contains only end segment and which
> has a non-empty intersection.
>
> ____________ contains only end segments.
> However,
> ____________ is not non-empty.

What I meant to say
However,
____________ does not have
a non-empty intersection.

Re: Natural numbers and vases III

<b4992386-8c6d-4335-8b3c-3b04ac17b38an@googlegroups.com>

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Mon, 29 Aug 2022 13:27 UTC

Fritz Feldhase schrieb am Montag, 29. August 2022 um 11:56:37 UTC+2:
> On Monday, August 29, 2022 at 11:29:04 AM UTC+2, WM wrote:
> > zelos...@gmail.com schrieb am Montag, 29. August 2022 um 07:09:03 UTC+2:
> > > fredag 26 augusti 2022 kl. 18:35:33 UTC+2 skrev Eram semper recta:
> > > >
> > > > Newsflash: Everything in mathematics is a stepwise process. Set theory is not mathematics.
> Complete nonsense.

> > All sequences are stepwise processes
> > and are stepwise analyzable as long as the terms can be individually defined.
> So what? Who cares?

Everyone who wants to refute your above "complete nonsense" should care.
>
> You know, we usually don't check infinitely many mathematical facts, when doing proofs. Actually, that's why we USE proofs.

But you are not aware of the fact that dark numbers exist and that your proofs are invalid for dark numbers.
>
> We can prove that for all natural numbers n: n + n = 2*n.

And we can check that for each definable number.
>
> We DON'T prove this by explicitly checking that
>
> 1 + 1 = 2 = 2*1, 2 + 2 = 4 = 2*2, 3 + 3 = 6 = 2*3, ad infinitum

No-one does. But we know that for every definable number this can be done. For undefinable numbers it cannot be done.
>
> Seems that you are confusing mathematics with using a pocket calculator.

The pocket calculator contains more mathematics than all ZFC-matheology.

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 - Mon, 29 Aug 2022 13:28 UTC

FromTheRafters schrieb am Montag, 29. August 2022 um 12:17:14 UTC+2:
> WM laid this down on his screen :
> > FromTheRafters schrieb am Sonntag, 28. August 2022 um 18:12:02 UTC+2:
> >> WM wrote on 8/28/2022 :
> >
> >>> Complete does not mean a last element, but all elements are there, none can
> >>> be added.
> >> Then what is a set?
> >
> > As I said: All elements are there, none can be added.
> That's a property of a set, what does complete mean again?

Just that.

Regards, WM

Re: Natural numbers and vases III

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Newsgroups: sci.math
Date: Mon, 29 Aug 2022 06:30:50 -0700 (PDT)
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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
Injection-Date: Mon, 29 Aug 2022 13:30:51 +0000
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by: WM - Mon, 29 Aug 2022 13:30 UTC

zelos...@gmail.com schrieb am Montag, 29. August 2022 um 12:32:41 UTC+2:
> måndag 29 augusti 2022 kl. 11:29:04 UTC+2 skrev WM:
> > zelos...@gmail.com schrieb am Montag, 29. August 2022 um 07:09:03 UTC+2:
> > > fredag 26 augusti 2022 kl. 18:35:33 UTC+2 skrev Eram semper recta:
> > > > On Friday, 26 August 2022 at 00:56:21 UTC-4, zelos idiot wrote:
> >
> > > > > Only if you think in a step wise process which mathematics IS NOT!
> > > > Newsflash: Everything in mathematics is a stepwise process. Set theory is not mathematics.
> > > Newsflash: You're wrong as always.
> > > Things are not a process in mathematics and set theory is very much mathematics.
> > All sequences are stepwise processes and are stepwise analyzable as long as the terms can be individually defined. The others are dark. Otherwise they could be checked stepwise.
> >
> A sequence is not a stepwise process. It is a function from N to S.

ℕ is a stepwise ordered set.

Regards, WM

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

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