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"Faith: not *wanting* to know what is true." -- Friedrich Nietzsche

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

<tdqvlq$1vsss$1@dont-email.me>

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sat, 20 Aug 2022 11:47:00 -0400
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by: FromTheRafters - Sat, 20 Aug 2022 15:47 UTC

Fritz Feldhase laid this down on his screen :
> On Saturday, August 20, 2022 at 5:04:50 PM UTC+2, FromTheRafters wrote:
>> Sergio formulated the question :
>>> On 8/20/2022 8:51 AM, WM wrote:
>>>> Jim Burns schrieb am Freitag, 19. August 2022 um 18:52:27 UTC+2:
>>>>> On 8/19/2022 7:56 AM, WM wrote:
>>>>>> That does never end and
>>>>>> never become larger than every FISON.
>>>>>> there cannot be more FISONs than
>>>>>> at least one of the FISONs can distinguish.
>>>>> No.
>>>>> There are more FISONs than
>>>>> any FISON can distinguish.
>>>>
>>>> Then there is a surplus that cannot distinguished.
>>>>
>>>> Regards, WM
>>>
>>> NEW ANTS !!!
>>>
>>> Surplus Ants
>>> Surplus Ants that cannot distinguished.
>>>
>> Threshold Ants
>
> All its elements Ants

I'm sure you noticed that he wants to keep 'all of its elements'
separate from 'the set' here and now after previouly claiming that a
set is 'nothing more' than 'all of its elements'.

Maybe he has two axioms, the Axiom of Because I Said So, and the Axiom
of Convenience. actually, that second one should just be a theorem.

Re: Natural numbers and vases III

<tdr1je$1aka$1@gioia.aioe.org>

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https://www.novabbs.com/tech/article-flat.php?id=109690&group=sci.math#109690

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sat, 20 Aug 2022 11:19:56 -0500
Organization: Aioe.org NNTP Server
Message-ID: <tdr1je$1aka$1@gioia.aioe.org>
References: <8af77f99-b24b-48f1-9452-3ac841463047n@googlegroups.com>
<47073890-ff5f-4e73-aec4-7ca19976f27cn@googlegroups.com>
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by: Sergio - Sat, 20 Aug 2022 16:19 UTC

On 8/20/2022 10:47 AM, FromTheRafters wrote:
> Fritz Feldhase laid this down on his screen :
>> On Saturday, August 20, 2022 at 5:04:50 PM UTC+2, FromTheRafters wrote:
>>> Sergio formulated the question :
>>>> On 8/20/2022 8:51 AM, WM wrote:
>>>>> Jim Burns schrieb am Freitag, 19. August 2022 um 18:52:27 UTC+2:
>>>>>> On 8/19/2022 7:56 AM, WM wrote:
>>>>>>> That does never end and never become larger than every FISON. there cannot be more FISONs than at least one of the FISONs can distinguish.
>>>>>> No. There are more FISONs than any FISON can distinguish.
>>>>>
>>>>> Then there is a surplus that cannot distinguished.
>>>>> Regards, WM
>>>>
>>>> NEW ANTS !!!
>>>> Surplus Ants Surplus Ants that cannot distinguished.
>>>>
>>> Threshold Ants
>>
>> All its elements Ants
>
> I'm sure you noticed that he wants to keep 'all of its elements' separate from 'the set' here and now after previouly claiming that a set is 'nothing
> more' than 'all of its elements'.
>
> Maybe he has two axioms, the Axiom of Because I Said So, and the Axiom of Convenience. actually, that second one should just be a theorem.

I think he practices bulldozer math, just blindly bulldoze over what was there before, then do it again, no thinking needed.

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 - Sat, 20 Aug 2022 17:03 UTC

On Saturday, August 20, 2022 at 5:39:51 PM UTC+2, FromTheRafters wrote:
> Fritz Feldhase expressed precisely :
> >
> > Actually, all elements in {1, 2, 3} are natural numbers, but the set {1, 2, 3} is NOT a natural number.
> >
> I believe it is the natural number 3, under Frege's construction
> matching (equinumerosity) cardinal numbers to the naturals.

Nope. Frege's construction the number 3 would be (the class)

{{0, 1, 2}, {1, 2, 3}, ... {7, 19, 25}, ...{Sun, Earth, Moon}, {Spock, Kirk, Scotty}, ...}

(ignoring the problem with foundation for the sake of the argument).

In other words, 3 = {{0, 1, 2}, {1, 2, 3}, ... {7, 19, 25}, ...{Sun, Earth, Moon}, {Spock, Kirk, Scotty}, ...}

Then for any finite set M: |M| = 3 <-> M e 3.

So all we would get is |{1, 2, 3}| = 3 (which looks right) but not {1, 2, 3} = 3.

Don't mix this up with von Neumann's approach. There we actually, would have, say, {0, 1, 2} = 3. :-P

So there the set {0, 1, 2} of natural numbers would be a natural number. Ok.

Still, "the elements in this set would not be this set." (Whatever this may mean.)

At least we can tell: 0 =/= {0, 1, 2}, 1 =/= {0, 1, 2} and 2 =/= {0, 1, 2}.

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: Sat, 20 Aug 2022 12:46:07 -0500
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by: Sergio - Sat, 20 Aug 2022 17:46 UTC

On 8/20/2022 9:56 AM, FromTheRafters wrote:
> William was thinking very hard :
>> On Saturday, August 20, 2022 at 10:48:54 AM UTC-3, WM wrote:
>>
>>> I am not interested in the set but only in all its elements.
>>
>> Piffle "all its elements" is the set.
>
> Not all muckysets are sets in the ZFC sense. He has a muckyset of counting numbers some of which have been 'used' and are thus 'defined' and some which
> have not been used yet which are 'undefined' and some that are so huge that he calls them 'undefinable' as if they could never conceivably be used.
>
> "All muckyset elements" is not necessarily 'the (ZFC) set' -- that is to say that 'all elements of a collection of objects some of which are
> undefinable' is not a set in ZFC despite that fact that everything *in* ZFC is a set.

yes, the following WM "defined" ANTS already exist;

1088 Untouchable Ants
1089 unused natural Ants
1090 Upward Direction Ants
1091 Used Ants that are sticky
1092 Used Ants are NOT returnable
1093 vacuous Ants

149 Ants counter intuitive to some delusional internet troll
150 Ants do not care about forming a FISON
151 Ants Finished with Omega
152 Ants of the First Bunch
153 Ants of the First Bunch Not Counted
154 Ants that are not making sausages,
155 Ants that are going insane in N
156 Ants that are Imprecise
157 Ants that attach Electrodes to Chickens

206 Beginning to End Insanity Ants
207 Beyond all Ants, there is no Ant

180 Ants that violate arithmetic
181 Ants too stupid and moronic to do mathematics
182 Ants with a Deep Misunderstanding of Math
183 Ants With Headlights that shoot Dark Number Ants on sight
184 Ants witout the slightest clue
185 Ants WM Pants

Re: Natural numbers and vases III

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by: Sergio - Sat, 20 Aug 2022 18:07 UTC

On 8/20/2022 10:39 AM, FromTheRafters wrote:
> Fritz Feldhase expressed precisely :
>> On Saturday, August 20, 2022 at 4:30:41 PM UTC+2, William wrote:
>>> On Saturday, August 20, 2022 at 10:48:54 AM UTC-3, WM wrote:
>>>>
>>>> I am not interested in the set but only in all its elements.
>>>>
>>> Piffle "all its elements" is the set.
>>
>> No, it is't, you silly asshole.
>>
>> Hint: Consider the set {1, 2, 3}. The numbers 1, 2, and 3 are "all its elements". But the numbers 1, 2, and 3 AREN'T the set {1, 2, 3}.
>>
>> Actually, all elements in {1, 2, 3} are natural numbers, but the set {1, 2, 3} is NOT a natural number.
>
> I believe it is the natural number 3, under Frege's construction matching (equinumerosity) cardinal numbers to the naturals. Of course, WM and William
> were not thinking about this, I assume.

agree, 3 it is. Not 4, not 2, but three. Three it shall be. Thrice is nice. (ala monte pythonisk)

is 3 the set ? {3} ? or {x,y,z} or 6/2 a Cantor Rational ?

(yep, Math nomenclature again...)

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
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Subject: Re: Natural numbers and vases III
Date: Sat, 20 Aug 2022 13:09:49 -0500
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by: Sergio - Sat, 20 Aug 2022 18:09 UTC

On 8/20/2022 9:39 AM, FromTheRafters wrote:
> WM expressed precisely :
>> William schrieb am Freitag, 19. August 2022 um 14:31:56 UTC+2:
>>> On Friday, August 19, 2022 at 8:48:16 AM UTC-3, WM wrote:
>>>
>>>> The set of numbers [that can be written down] is finite but with not upper threshold.
>>>
>>> Absolute nonsense. There is no such thing as a finite set with no upper threshold.
>
> Threshold? Are we making hay now?
>
>> What is the upper threshold of the set of n defined by
>>> ℕ \ {1, 2, 3, ..., n}| = ℵo ?
>> It cannot be ℵo-infinite because ℵo elements are following.
>
> Balderdash! It is exactly why. There is no last element and you are taking only a finite subset of it out of consideration in your new 'still inductive'
> set.
>
>>> It cannot be ℵo-infinite because
>>>> ∀k ∈ ℕ: |ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo.
>>> So what? A statement that every *element* of |N has some property, does not imply that the *set* has this property.
>>
>> I am not interested in the set but only in all its elements.
>
> How do you determine if a particular element qualifies to be in the set?

to qualify you have to have qualifiers.

Re: Natural numbers and vases III

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by: Dutch Vacca - Sat, 20 Aug 2022 18:15 UTC

Sergio wrote:

>> How do you determine if a particular element qualifies to be in the
>> set?
>
> to qualify you have to have qualifiers.

lol, the nazi uKraine is calling capitalist geaormony *drug_addicts* due
its gas dependence from Russia.

fuck, the *nazi_uKraine* is already bigger than capitalist geaormony.

Re: Natural numbers and vases III

<b6ddc9ba-9dca-c311-2e1c-6c2a820b70fa@att.net>

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sat, 20 Aug 2022 15:14:50 -0400
Organization: A noiseless patient Spider
Lines: 102
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by: Jim Burns - Sat, 20 Aug 2022 19:14 UTC

On 8/20/2022 9:51 AM, WM wrote:
> Jim Burns schrieb
> am Freitag, 19. August 2022 um 18:52:27 UTC+2:
>> On 8/19/2022 7:56 AM, WM wrote:

>>> That does never end and
>>> never become larger than every FISON.
>>> there cannot be more FISONs than
>>> at least one of the FISONs can distinguish.
>>
>> No.
>> There are more FISONs than
>> any FISON can distinguish.
>
> Then there is
> a surplus that cannot distinguished.

No.
Remember what a FISON is.
[1]

lemma.
Each FISON can be distinguished.

| Assume otherwise.
| Assume FISON 𝐹ₙ cannot be distinguished.
| | Axioms of Distinction
|| Let 𝐹ᵢ be a FISON which ends at i
|| Let 𝐹ᵢ₊₁ = 𝐹ᵢ∪⟨i+1⟩
||
|| If 𝐹ᵢ can be distinguished,
|| then 𝐹ᵢ₊₁ can be distinguished.
||
|| ⟨0⟩ can be distinguished.
| | Each FISON 𝐹ₙ ends somewhere: at n
| | For each FISON 𝐹ₙ
| a FISON-sequence ⟨ ⟨0⟩,⋯,𝐹ₙ ⟩ exists
| such that,
| for each split,
| a step 𝐹ᵢ,𝐹ᵢ₊₁ exists such that
| 𝐹ᵢ is last before the split,
| 𝐹ᵢ₊₁ is first after the split,
| 𝐹ᵢ₊₁ = 𝐹ᵢ∪⟨i+1⟩
| and
| ⟨ ⟨0⟩,⋯,𝐹ₙ ⟩ begins at ⟨0⟩
| and
| ⟨ ⟨0⟩,⋯,𝐹ₙ ⟩ ends at 𝐹ₙ
| | Define the split
| AFTER =
| { 𝐹 : ∃𝐹'=<𝐹 ∧ 𝐹' cannot be distinguished }
| BEFORE =
| { 𝐹 : ∀𝐹'=<𝐹 ∧ 𝐹' can be distinguished }
| | A step 𝐹ᵢ,𝐹ᵢ₊₁ exists from BEFORE to AFTER
| Arising from the definitions of BEFORE,AFTER
| 𝐹ᵢ can be distinguished, and
| 𝐹ᵢ₊₁ cannot be distinguished.
| | However,
| if 𝐹ᵢ can be distinguished,
| then 𝐹ᵢ₊₁ can be distinguished.
| Contradiction.

Therefore,
each FISON can be distinguished.

> Then there is
> a surplus that cannot distinguished.

No.
There is no surplus.
Each FISON can be distinguished.

No FISON can distinguish all FISONs
because 𝐹ₙ∪⟨n+1⟩ is also a FISON.

[1]
Remember what a FISON is.

A FISON 𝐹 is
a collection 𝐹 with a counting-order
such that
𝐹 begins at 0
and
𝐹 ends _somewhere_

A counting order of 𝐹 is
a total order such that,
for each split,
a step i,i+1 exists such that
i is last before the split, and
i+1 is first after the split.

Note that
each i ∈ 𝐹ₙ ends a FISON 𝐹ᵢ
𝐹ᵢ ⊆ 𝐹ₙ

Re: Natural numbers and vases III

<tdri9p$232oa$1@dont-email.me>

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sat, 20 Aug 2022 17:04:50 -0400
Organization: Peripheral Visions
Lines: 34
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by: FromTheRafters - Sat, 20 Aug 2022 21:04 UTC

Sergio expressed precisely :
> On 8/20/2022 10:39 AM, FromTheRafters wrote:
>> Fritz Feldhase expressed precisely :
>>> On Saturday, August 20, 2022 at 4:30:41 PM UTC+2, William wrote:
>>>> On Saturday, August 20, 2022 at 10:48:54 AM UTC-3, WM wrote:
>>>>>
>>>>> I am not interested in the set but only in all its elements.
>>>>>
>>>> Piffle "all its elements" is the set.
>>>
>>> No, it is't, you silly asshole.
>>>
>>> Hint: Consider the set {1, 2, 3}. The numbers 1, 2, and 3 are "all its
>>> elements". But the numbers 1, 2, and 3 AREN'T the set {1, 2, 3}.
>>>
>>> Actually, all elements in {1, 2, 3} are natural numbers, but the set {1,
>>> 2, 3} is NOT a natural number.
>>
>> I believe it is the natural number 3, under Frege's construction matching
>> (equinumerosity) cardinal numbers to the naturals. Of course, WM and
>> William were not thinking about this, I assume.
>
> agree, 3 it is. Not 4, not 2, but three. Three it shall be. Thrice is nice.
> (ala monte pythonisk)
>
> is 3 the set ? {3} ? or {x,y,z} or 6/2 a Cantor Rational ?
>
> (yep, Math nomenclature again...)

Yep, like Fritz says, {x,y,z} is in the same equivalence class as
{1,2,3} when set size is the only consideration for inclusion in the
class.

Still, the sets are not equal, just of equal cardinality.

Re: Natural numbers and vases III

<tdrige$234fl$1@dont-email.me>

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sat, 20 Aug 2022 17:08:23 -0400
Organization: Peripheral Visions
Lines: 37
Message-ID: <tdrige$234fl$1@dont-email.me>
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by: FromTheRafters - Sat, 20 Aug 2022 21:08 UTC

Sergio presented the following explanation :
> On 8/20/2022 9:39 AM, FromTheRafters wrote:
>> WM expressed precisely :
>>> William schrieb am Freitag, 19. August 2022 um 14:31:56 UTC+2:
>>>> On Friday, August 19, 2022 at 8:48:16 AM UTC-3, WM wrote:
>>>>
>>>>> The set of numbers [that can be written down] is finite but with not
>>>>> upper threshold.
>>>>
>>>> Absolute nonsense. There is no such thing as a finite set with no upper
>>>> threshold.
>>
>> Threshold? Are we making hay now?
>>
>>> What is the upper threshold of the set of n defined by
>>>> ℕ \ {1, 2, 3, ..., n}| = ℵo ?
>>> It cannot be ℵo-infinite because ℵo elements are following.
>>
>> Balderdash! It is exactly why. There is no last element and you are taking
>> only a finite subset of it out of consideration in your new 'still
>> inductive' set.
>>
>>>> It cannot be ℵo-infinite because
>>>>> ∀k ∈ ℕ: |ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| =
>>>>> ℵo.
>>>> So what? A statement that every *element* of |N has some property, does
>>>> not imply that the *set* has this property.
>>>
>>> I am not interested in the set but only in all its elements.
>>
>> How do you determine if a particular element qualifies to be in the set?
>
>
> to qualify you have to have qualifiers.

Indeed, you need to be able to tell if an element is indeed qualified
to be in the desired set. Can he have a subset of odd dark numbers?

Re: Natural numbers and vases III

<454bfce4-1816-8a1f-f225-8906be0cd41f@att.net>

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Path: i2pn2.org!i2pn.org!eternal-september.org!reader01.eternal-september.org!.POSTED!not-for-mail
From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sat, 20 Aug 2022 18:25:23 -0400
Organization: A noiseless patient Spider
Lines: 96
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by: Jim Burns - Sat, 20 Aug 2022 22:25 UTC

On 8/20/2022 5:08 PM, FromTheRafters wrote:
> Sergio presented the following explanation :
>> On 8/20/2022 9:39 AM, FromTheRafters wrote:
>>> WM expressed precisely :
>>>> William schrieb am Freitag,
>>>> 19. August 2022 um 14:31:56 UTC+2:
>>>>> On Friday, August 19, 2022
>>>>> at 8:48:16 AM UTC-3, WM wrote:

>>>>>> The set of numbers [that can be written down]
>>>>>> is finite but with not upper threshold.
>>>>>
>>>>> Absolute nonsense. There is no such thing as
>>>>> a finite set with no upper threshold.
>>>
>>> Threshold? Are we making hay now?
>>>
>>>> What is the upper threshold of
>>>> the set of n defined by
>>>>> ℕ \ {1, 2, 3, ..., n}| = ℵo ?
>>>> It cannot be ℵo-infinite because
>>>> ℵo elements are following.
>>>
>>> Balderdash! It is exactly why.
>>> There is no last element and you are
>>> taking only a finite subset of it
>>> out of consideration in your new
>>> 'still inductive' set.
>>>
>>>>>> It cannot be ℵo-infinite because
>>>>>> ∀k ∈ ℕ: |ℕ \ {1, 2, 3, ..., k}| = ℵo ==>
>>>>>> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo.
>>>>> So what? A statement that
>>>>> every *element* of |N has some property,
>>>>> does not imply that the *set* has this property.
>>>>
>>>> I am not interested in the set
>>>> but only in all its elements.

Each FISON is
a collection with a counting-order
which begins at 0
and ends _somewhere_

For each FISON 𝐹
there is some n ∈ 𝐹 such that n+1 ∉ 𝐹

∀𝐹 ∈ 𝓕, (∃n∈𝐹: n+1∉𝐹)

| because a FISON ends somewhere.

For each n
if n is in some FISON,
then n+1 is in some FISON,
sometimes a different FISON.

∀n:( ∃𝐹∈𝓕: n∈𝐹 -> ∃𝐹'∈𝓕: n+1∈𝐹' )

| because 𝐹' = 𝐹ₙ∪⟨n+1⟩ is also a FISON.

Define
∀n:( n ∈ ⋃𝓕 <-> ∃𝐹∈𝓕: n∈𝐹 )

That makes the previous claim
∀n:( n ∈ ⋃𝓕 -> n+1 ∈ ⋃𝓕 )

| because 𝐹' = 𝐹ₙ∪⟨n+1⟩ is also a FISON,
| ⋃𝓕 does not end somewhere.

~(∃n∈⋃𝓕: n+1∉⋃𝓕)
∀𝐹 ∈ 𝓕, (∃n∈𝐹: n+1∉𝐹)

∀𝐹 ∈ 𝓕, 𝐹 ≠ ⋃𝓕

⋃𝓕 ∉ 𝓕
⋃𝓕 is not a FISON.

>>> How do you determine if
>>> a particular element qualifies to be in the set?
>>
>> to qualify you have to have qualifiers.
>
> Indeed, you need to be able to tell
> if an element is indeed qualified to be
> in the desired set.
> Can he have a subset of odd dark numbers?

I think that he thinks he can.
I think that he mixes together
"this is described" and "this exists".
Consider
| finite but with not upper threshold

I think that he thinks that
we (or Cantor?) do as he does.

Re: Natural numbers and vases III

<tdro37$dna$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Sat, 20 Aug 2022 17:43:50 -0500
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by: Sergio - Sat, 20 Aug 2022 22:43 UTC

On 8/20/2022 5:25 PM, Jim Burns wrote:
> On 8/20/2022 5:08 PM, FromTheRafters wrote:
>> Sergio presented the following explanation :
>>> On 8/20/2022 9:39 AM, FromTheRafters wrote:
>>>> WM expressed precisely :
>>>>> William schrieb am Freitag,
>>>>> 19. August 2022 um 14:31:56 UTC+2:
>>>>>> On Friday, August 19, 2022
>>>>>> at 8:48:16 AM UTC-3, WM wrote:
>
>>>>>>> The set of numbers [that can be written down]
>>>>>>> is finite but with not upper threshold.
>>>>>>
>>>>>> Absolute nonsense. There is no such thing as
>>>>>> a finite set with no upper threshold.
>>>>
>>>> Threshold? Are we making hay now?
>>>>
>>>>> What is the upper threshold of
>>>>> the set of n defined by
>>>>>> ℕ \ {1, 2, 3, ..., n}| = ℵo ?
>>>>> It cannot be ℵo-infinite because
>>>>> ℵo elements are following.
>>>>
>>>> Balderdash! It is exactly why.
>>>> There is no last element and you are taking only a finite subset of it
>>>> out of consideration in your new 'still inductive' set.
>>>>
>>>>>>> It cannot be ℵo-infinite because
>>>>>>> ∀k ∈ ℕ: |ℕ \ {1, 2, 3, ..., k}| = ℵo ==>
>>>>>>> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo.
>>>>>> So what? A statement that
>>>>>> every *element* of |N has some property, does not imply that the *set* has this property.
>>>>>
>>>>> I am not interested in the set
>>>>> but only in all its elements.
>
> Each FISON is
> a collection with a counting-order
> which begins at 0
> and ends _somewhere_
>
> For each FISON 𝐹
> there is some n ∈ 𝐹 such that n+1 ∉ 𝐹
>
> ∀𝐹 ∈ 𝓕, (∃n∈𝐹: n+1∉𝐹)
>
> | because a FISON ends somewhere.
>
> For each n
> if n is in some FISON,
> then n+1 is in some FISON,
> sometimes a different FISON.
>
> ∀n:( ∃𝐹∈𝓕: n∈𝐹 -> ∃𝐹'∈𝓕: n+1∈𝐹' )
>
> | because 𝐹' = 𝐹ₙ∪⟨n+1⟩ is also a FISON.
>
> Define
> ∀n:( n ∈ ⋃𝓕 <-> ∃𝐹∈𝓕: n∈𝐹 )
>
> That makes the previous claim
> ∀n:( n ∈ ⋃𝓕 -> n+1 ∈ ⋃𝓕 )
>
> | because 𝐹' = 𝐹ₙ∪⟨n+1⟩ is also a FISON,
> | ⋃𝓕 does not end somewhere.
>
> ~(∃n∈⋃𝓕: n+1∉⋃𝓕)
> ∀𝐹 ∈ 𝓕, (∃n∈𝐹: n+1∉𝐹)
>
> ∀𝐹 ∈ 𝓕, 𝐹 ≠ ⋃𝓕
>
> ⋃𝓕 ∉ 𝓕
> ⋃𝓕 is not a FISON.
>
>>>> How do you determine if
>>>> a particular element qualifies to be in the set?
>>>
>>> to qualify you have to have qualifiers.
>>
>> Indeed, you need to be able to tell
>> if an element is indeed qualified to be
>> in the desired set.
>> Can he have a subset of odd dark numbers?
>
> I think that he thinks he can.
> I think that he mixes together
> "this is described" and "this exists".
> Consider
> | finite but with not upper threshold
>
> I think that he thinks that
> we (or Cantor?) do as he does.
>

WM doesn't care, he chums out whatever, then argues for his bad math.
like slinging spaghetti on the wall to see what sticks.
He ignores proofs that show his math is a crock.
It is what trolls do.

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, 22 Aug 2022 05:01 UTC

fredag 19 augusti 2022 kl. 13:35:48 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Freitag, 19. August 2022 um 09:10:07 UTC+2:
> > torsdag 18 augusti 2022 kl. 16:08:13 UTC+2 skrev WM:
> > > William schrieb am Mittwoch, 17. August 2022 um 17:57:29 UTC+2:
>
> > > > The fact that the *set* of successors cannnot be subtracted by a stepwise process does not mean there is an *element* of the set of successors that cannot be subtracted by a stepwise process.
> > > There are infinitely many as is proved here
> > > ∀n ∈ ℕ: |ℕ \ {1, 2, 3, ..., n}| = ℵo
> > > and here
> > > |ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo.
> > >
> > > This does never change. But you cannot define any element that must be remaining. That shows dark numbers.
> > >
> > No it doesn't! It just shows that cardinal arithmetic works different from ordinary arithmetic
> Logic works the same. This statement

You do not fucking understand logic

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

Saysn othing of what you want.

> says that ℵo numbers are lurking behind all definable numbers. So they are undefinable.

False, your "definable" is MEANINGLESS!

>
> 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, 22 Aug 2022 13:30 UTC

William schrieb am Samstag, 20. August 2022 um 16:30:41 UTC+2:
> On Saturday, August 20, 2022 at 10:48:54 AM UTC-3, WM wrote:
>
> > I am not interested in the set but only in all its elements.
> Piffle "all its elements" is the set.

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

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, 22 Aug 2022 13:36 UTC

Fritz Feldhase schrieb am Samstag, 20. August 2022 um 17:03:33 UTC+2:
> On Saturday, August 20, 2022 at 3:48:54 PM UTC+2, WM was talking about
>
> > the set of n [e IN] defined by |ℕ \ {1, 2, 3, ..., n}| = ℵo

> > It cannot be ℵo-infinite because ℵo elements are following.

> Actually, "it" is infinit and has cardinality ℵo, since IN is infinite and has cardinality ℵo.

Up to every n it is finite.

How man natural numbers can be defined individually without having an ℵo-infinite set of natural numbers?
>
> Hint: There are countably-infinitely many natural numbers in IN.

No, there are ℵo natural numbers but most of them cannot be counted..
How man can be counted?

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, 22 Aug 2022 13:42 UTC

Jim Burns schrieb am Samstag, 20. August 2022 um 21:15:00 UTC+2:

> Each FISON can be distinguished

by elements of FISONs. There are finitely many, i.e., less than ℵo.

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, 22 Aug 2022 13:47 UTC

zelos...@gmail.com schrieb am Montag, 22. August 2022 um 07:01:27 UTC+2:
> fredag 19 augusti 2022 kl. 13:35:48 UTC+2 skrev WM:

> > > No it doesn't! It just shows that cardinal arithmetic works different from ordinary arithmetic
> > Logic works the same. This statement
> > |ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo
> > says that ℵo numbers are lurking behind all definable numbers. So they are undefinable.
>
> False, your "definable" is MEANINGLESS!

Fact is that induction proves that ℵo numbers are lurking behind every number reached by induction.

Regards, WM

Re: Natural numbers and vases III

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 22 Aug 2022 09:53:11 -0400
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by: FromTheRafters - Mon, 22 Aug 2022 13:53 UTC

WM wrote :
> William schrieb am Samstag, 20. August 2022 um 16:30:41 UTC+2:
>> On Saturday, August 20, 2022 at 10:48:54 AM UTC-3, WM wrote:
>>
>>> I am not interested in the set but only in all its elements.
>> Piffle "all its elements" is the set.
>
> How man natural numbers can be used without using the set |N?

All of them.

Re: Natural numbers and vases III

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 22 Aug 2022 09:55:21 -0400
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by: FromTheRafters - Mon, 22 Aug 2022 13:55 UTC

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

Each number greater than zero can be 'reached' by the successor
function, this is not induction.

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 22 Aug 2022 08:56:29 -0500
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by: Sergio - Mon, 22 Aug 2022 13:56 UTC

On 8/22/2022 8:36 AM, WM wrote:
> Fritz Feldhase schrieb am Samstag, 20. August 2022 um 17:03:33 UTC+2:
>> On Saturday, August 20, 2022 at 3:48:54 PM UTC+2, WM was talking about
>>
>>> the set of n [e IN] defined by |ℕ \ {1, 2, 3, ..., n}| = ℵo
>
>>> It cannot be ℵo-infinite because ℵo elements are following.
>
>> Actually, "it" is infinit and has cardinality ℵo, since IN is infinite and has cardinality ℵo.
>
> Up to every n it is finite.

Wrong, you remove a finite set from an infinite set, you still have an infinite set.

>
> How man natural numbers can be defined individually without having an ℵo-infinite set of natural numbers?

you remain permanently confused.

>>
>> Hint: There are countably-infinitely many natural numbers in IN.
>
> No, there are ℵo natural numbers but most of them cannot be counted.
> How man can be counted?

you have 'counting' confused with 'countablility'

I do not have the time to teach you math. you are not smart enough to learn math anyway, go use google.

>
> Regards, WM

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Subject: Re: Natural numbers and vases III
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by: Sergio - Mon, 22 Aug 2022 13:57 UTC

On 8/22/2022 8:30 AM, WM wrote:
> William schrieb am Samstag, 20. August 2022 um 16:30:41 UTC+2:
>> On Saturday, August 20, 2022 at 10:48:54 AM UTC-3, WM wrote:
>>
>>> I am not interested in the set but only in all its elements.
>> Piffle "all its elements" is the set.
>
> How man natural numbers can be used without using the set |N?

how many sheeps do you have?

>
> Regards, WM

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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, 22 Aug 2022 14:28 UTC

On Monday, August 22, 2022 at 3:36:34 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Samstag, 20. August 2022 um 17:03:33 UTC+2:
> >
> > Hint: There are countably-infinitely many natural numbers in IN.
> >
> No

Yes, a trival set-theoretic fact.

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

Wrong! Note that Chuck Norris counted to infinity - twice!

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 - Mon, 22 Aug 2022 15:47 UTC

On Monday, August 22, 2022 at 10:30:55 AM UTC-3, WM wrote:
> William schrieb am Samstag, 20. August 2022 um 16:30:41 UTC+2:
> > On Saturday, August 20, 2022 at 10:48:54 AM UTC-3, WM wrote:
> >
> > > I am not interested in the set but only in all its elements.
> > Piffle "all its elements" is the set.
> How man natural numbers can be used without using the set |N?

Irrelevant Piffle that has no bearing on the fact that "all its elements" is the set

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Mon, 22 Aug 2022 16:53 UTC

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

But how many elements are not the set?

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, 22 Aug 2022 16:58 UTC

FromTheRafters schrieb am Montag, 22. August 2022 um 15:53:23 UTC+2:
> WM wrote :
> > William schrieb am Samstag, 20. August 2022 um 16:30:41 UTC+2:
> >> On Saturday, August 20, 2022 at 10:48:54 AM UTC-3, WM wrote:
> >>
> >>> I am not interested in the set but only in all its elements.
> >> Piffle "all its elements" is the set.
> >
> > How man natural numbers can be used without using the set |N?
> All of them.

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

Regards, WM

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

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