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Re: Natural numbers and vases III

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

<72565622-2ce4-4c09-9898-d77800f08638n@googlegroups.com>

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Tue, 23 Aug 2022 14:05 UTC

Jim Burns schrieb am Montag, 22. August 2022 um 22:48:33 UTC+2:
> On 8/22/2022 9:30 AM, WM wrote:

> | A FISON is
> | a collection with a counting-order
> | which begins at 0
> | and which ends _somewhere_

ℵo numbers befor omega.

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

About each natural number ℵo numbers befor omega.

Regards, WM

Re: Natural numbers and vases III

<f74c6d8d-b575-adba-6f49-fd456147a98f@att.net>

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https://www.novabbs.com/tech/article-flat.php?id=110002&group=sci.math#110002

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 23 Aug 2022 10:06:11 -0400
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by: Jim Burns - Tue, 23 Aug 2022 14:06 UTC

On 8/23/2022 9:53 AM, WM wrote:
> William schrieb ...

> How many elements can be subtracted
> without removing the set?

Remove one element and it's a different set.

Remove all but one element and
what's left is not the empty set.

As a matter of curiosity, is either of those
an answer to your intended question?

Re: Natural numbers and vases III

<44e5a0bb-5101-49a7-bc74-da7ea04f8ba9n@googlegroups.com>

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Tue, 23 Aug 2022 14:08 UTC

zelos...@gmail.com schrieb am Dienstag, 23. August 2022 um 06:55:48 UTC+2:
> måndag 22 augusti 2022 kl. 15:47:51 UTC+2 skrev WM:

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

> Which is ALL of them.

No. ℵo numbers are missing, but when removing the set then also these ℵo numbers are are removed. So there is a difference.

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 - Tue, 23 Aug 2022 14:12 UTC

On Tuesday, August 23, 2022 at 1:52:11 PM UTC+2, Eram semper recta wrote:

> To have ALL, it is required that ALL elements can be listed.

No, it isn't.

Hint: The real numbers can't be "listed".

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Tue, 23 Aug 2022 14:15 UTC

Jim Burns schrieb am Dienstag, 23. August 2022 um 16:06:24 UTC+2:
> On 8/23/2022 9:53 AM, WM wrote:
> > William schrieb ...
> > How many elements can be subtracted
> > without removing the set?
> Remove one element and it's a different set.
>
> Remove all but one element and
> what's left is not the empty set.
>
> As a matter of curiosity, is either of those
> an answer to your intended question?

Remove all elements which leave ℵo successors,
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
i.e. the set remove the subset ℕ_def.What remains?

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 - Tue, 23 Aug 2022 14:28 UTC

On Tuesday, August 23, 2022 at 4:15:11 PM UTC+2, WM wrote:

1.) "IN_def" is NOT defined be the expression
> ∀n ∈ IN_def: |IN \ {1, 2, 3, ..., n}| = ℵo

2.) {n e IN : |IN \ {1, 2, 3, ..., n}| = ℵo} is the set of
> all elements [in IN] which ["]leave ℵo successors["]

Hint: {n e IN : |IN \ {1, 2, 3, ..., n}| = ℵo} = IN.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: Sergio - Tue, 23 Aug 2022 14:38 UTC

On 8/23/2022 8:51 AM, WM wrote:
> FredJeffries schrieb am Montag, 22. August 2022 um 19:48:08 UTC+2:
>>> On Monday, August 22, 2022 at 3:36:34 PM UTC+2, WM wrote:
>>
>>>> there are ℵo natural numbers but most of them cannot be counted.
>> How do you know that there are ℵo of them if they cannot be counted?
>
> I use ℵo as expressing actual infinity (i.e. more than every finite number).
>
> Regards, WM

evasive

Re: Natural numbers and vases III

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by: Sergio - Tue, 23 Aug 2022 14:41 UTC

On 8/23/2022 9:03 AM, WM wrote:
> FromTheRafters schrieb am Montag, 22. August 2022 um 21:17:27 UTC+2:
>> WM pretended :
>
>>>> Each number greater than zero can be 'reached' by the successor
>>>> function, this is not induction.
>>>
>>> It is the same principle.
>> No, it isn't. That there is a next is given axiomatically, that there
>> is *always* a next is given by theorem using proof by induction.
>
> That there is always a next is proven by induction since n is arbitrary.
>
> |ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo

trivial, endsegments are infinite

>
> Regards, WM

and there is no n in your equations, very sloppy.

Re: Natural numbers and vases III

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 23 Aug 2022 09:42:32 -0500
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by: Sergio - Tue, 23 Aug 2022 14:42 UTC

On 8/23/2022 9:08 AM, WM wrote:
> zelos...@gmail.com schrieb am Dienstag, 23. August 2022 um 06:55:48 UTC+2:
>> måndag 22 augusti 2022 kl. 15:47:51 UTC+2 skrev WM:
>
>>> Fact is that induction proves that ℵo numbers are lurking behind every number reached by induction.
>
>> Which is ALL of them.
>
> No. ℵo numbers are missing,

Wrong. your knowledge of Math is missing

> but when removing the set then also these ℵo numbers are are removed. So there is a difference.

Failure.

>
> Regards, WM
>

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 - Tue, 23 Aug 2022 14:56 UTC

On Tuesday, August 23, 2022 at 10:53:32 AM UTC-3, WM wrote:
> William schrieb am Montag, 22. August 2022 um 20:24:39 UTC+2:
> > On Monday, August 22, 2022 at 1:53:05 PM UTC-3, WM wrote:
> > > how many elements are not the set?
> > Evasion. The answer does not change the fact that "all its elements" is the set
> How many elements can be subtracted without removing the set?

"all its elements" is the set, so any subset can be "subtracted" without "subtracting" "all its elements", i.e. the set. Note that for any n, {1,2,3...,n} is an strict subset that can be "subracted without removing the set"

Re: Natural numbers and vases III

<te2q0e$30v1q$1@dont-email.me>

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 23 Aug 2022 10:59:21 -0400
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by: FromTheRafters - Tue, 23 Aug 2022 14:59 UTC

WM pretended :
> William schrieb am Montag, 22. August 2022 um 20:24:39 UTC+2:
>> On Monday, August 22, 2022 at 1:53:05 PM UTC-3, WM wrote:
>>> how many elements are not the set?
>> Evasion. The answer does not change the fact that "all its elements" is the
>> set
>
> How many elements can be subtracted without removing the set?

You only 'subtract' elements from the 'all its elements' which you are
'considering' for inclusion in *another* set. The sets themselves don't
change.

The set of natural numbers, |N, has elements which I want to include
and exclude from a set I am building. I consider *all of the elements*
and remove from consideration the ones I wish to exclude from the new
set. For example those elements of |N which are not composite numbers
can be a set since each element of the set is defined and is itself a
set. Those elements of the collection which you deem unworthy (the
so-called undefinables) don't form a set or a subset *because* they are
undefined.

Re: Natural numbers and vases III

<te2q3m$1rgf$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 23 Aug 2022 10:01:10 -0500
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by: Sergio - Tue, 23 Aug 2022 15:01 UTC

On 8/23/2022 8:57 AM, WM wrote:
> FromTheRafters schrieb am Montag, 22. August 2022 um 20:34:54 UTC+2:
>> WM was thinking very hard :
>
>>> All of them satisfy ∀n ∈ ℕ: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
>>> Collecting them together we get |ℕ \ {1, 2, 3, ...}| = ℵo.
>>> The set satisfies |ℕ \ ℕ| = 0
>>> What causes the difference?
>
> Regards, WM

(hint: |ℕ \ {1, 2, 3, ...}| = ℵo. is wrong)

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: Tue, 23 Aug 2022 10:02:51 -0500
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by: Sergio - Tue, 23 Aug 2022 15:02 UTC

On 8/23/2022 9:15 AM, WM wrote:
> Jim Burns schrieb am Dienstag, 23. August 2022 um 16:06:24 UTC+2:
>> On 8/23/2022 9:53 AM, WM wrote:
>>> William schrieb ...
>>> How many elements can be subtracted
>>> without removing the set?
>> Remove one element and it's a different set.
>>
>> Remove all but one element and
>> what's left is not the empty set.
>>
>> As a matter of curiosity, is either of those
>> an answer to your intended question?
>
> Remove all elements which leave ℵo successors,
> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo

that only "removes" n elements from ℕ, not all, nor each and every.

Having problems this AM ?
>
>
> Regards, WM

Re: Natural numbers and vases III

<te2qdc$310gh$1@dont-email.me>

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From: FTR...@nomail.afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 23 Aug 2022 11:06:16 -0400
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by: FromTheRafters - Tue, 23 Aug 2022 15:06 UTC

Fritz Feldhase pretended :
> On Tuesday, August 23, 2022 at 1:52:11 PM UTC+2, Eram semper recta wrote:
>
>> To have ALL, it is required that ALL elements can be listed.
>
> No, it isn't.
>
> Hint: The real numbers can't be "listed".

If I'm not mistaken, to him the reals don't exist.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
Date: Tue, 23 Aug 2022 11:15:12 -0400
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by: FromTheRafters - Tue, 23 Aug 2022 15:15 UTC

WM explained on 8/23/2022 :
> FromTheRafters schrieb am Montag, 22. August 2022 um 21:17:27 UTC+2:
>> WM pretended :
>
>>>> Each number greater than zero can be 'reached' by the successor
>>>> function, this is not induction.
>>>
>>> It is the same principle.
>> No, it isn't. That there is a next is given axiomatically, that there
>> is *always* a next is given by theorem using proof by induction.
>
> That there is always a next is proven by induction since n is arbitrary.
>
>> ℕ \ {1, 2, 3, ..., k}| = ℵo ==> |ℕ \ {1, 2, 3, ..., k, k+1}| = ℵo

I don't see any 'n' here, is it one of your dark numbers?

1 through k and 1 through k+1 are both collections of finitely many
elements being removed from consideration for inclusion in your newly
created sets. For most of us whom have heard of cardinal arithmetic,
removing finitely many from infinitely many leaves infinitely many
still being considered for your new set.

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Tue, 23 Aug 2022 15:52:24 +0000
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by: Fritz Feldhase - Tue, 23 Aug 2022 15:52 UTC

On Tuesday, August 23, 2022 at 4:56:23 PM UTC+2, William wrote:

> "all its elements" is the set

No, you sily dumbfuck, the numbers 1, 2, 3 "are" not the set {1, 2, 3}.

STOP TALKING NONSENSE, MAN!

Holy shit!

Re: Natural numbers and vases III

<0f07b03c-19bd-65cc-0ada-e98481e41127@att.net>

copy mid

https://www.novabbs.com/tech/article-flat.php?id=110024&group=sci.math#110024

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Tue, 23 Aug 2022 11:56:32 -0400
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by: Jim Burns - Tue, 23 Aug 2022 15:56 UTC

On 8/23/2022 9:57 AM, WM wrote:
> FromTheRafters schrieb am Montag,
> 22. August 2022 um 20:34:54 UTC+2:
>> WM was thinking very hard :

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

𝐹ₙ∪⟨n+1⟩ is also a FISON.

By definition,
for each FISON 𝐹ₙ
there is some n in 𝐹ₙ
such that n+1 is not in 𝐹ₙ

However,
because 𝐹ₙ∪⟨n+1⟩ is also a FISON,
there is another FISON which n is in.

ℕ is the union of FISONs.
The n+1 which is not in 𝐹ₙ
is in ℕ
because 𝐹ₙ∪⟨n+1⟩ is also a FISON,

The properties you ask about arise from
n+1 also being in ℕ, always.
[1]

n+1 also being in ℕ, always, arises from
𝐹ₙ∪⟨n+1⟩ also being a FISON, always.

[1]
The properties you ask about...

If
n is in a FISON
then
n+1 is in a FISON

Define
m+(n+1) = (m+n)+1

If
m and n are in FISONs
then
m+n is in a FISON

Define
m*(n+1) = (m+n)+m

If
m and n are in FISONs
then
m*n is in a FISON

For each fraction p/q
if
p and q are in FISONs, p > 0, q > 0,
then
the fraction-index k = (p+q-1)*(p+q-2)/2+p
is in a FISON, k>0

If
k is in a FISON, k>0
and
iₖ is largest i =< k such that
(i-1)*(i-2)/2 < k
then, for
p = k-(iₖ+1)*iₖ/2
q = iₖ+2-p
p and q are in FISONs
and
p/q is the fraction indexed by k

𝐹ₙ∪⟨n+1⟩ also being a FISON
is why
infinitely-many X,O swaps can leave Bob
outside all the FISONs,
even though each swap leaves Bob
in some FISON

Re: Natural numbers and vases III

<895699de-2317-4162-bcd6-ad20fc009ce2n@googlegroups.com>

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Subject: Re: Natural numbers and vases III
From: fredjeff...@gmail.com (FredJeffries)
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by: FredJeffries - Tue, 23 Aug 2022 15:59 UTC

On Tuesday, August 23, 2022 at 6:51:55 AM UTC-7, WM wrote:
> FredJeffries schrieb am Montag, 22. August 2022 um 19:48:08 UTC+2:
> > > On Monday, August 22, 2022 at 3:36:34 PM UTC+2, WM wrote:
> >
> > > > there are ℵo natural numbers but most of them cannot be counted.
> > How do you know that there are ℵo of them if they cannot be counted?
> I use ℵo as expressing actual infinity (i.e. more than every finite number).

Who cares what you 'use'?

I'll rephrase the question: How do you know that there are 'more than every finite number' of them if they cannot be counted?

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Tue, 23 Aug 2022 16:01 UTC

On Tuesday, August 23, 2022 at 5:06:29 PM UTC+2, FromTheRafters wrote:
> Fritz Feldhase pretended :
> > On Tuesday, August 23, 2022 at 1:52:11 PM UTC+2, Eram semper recta wrote:
> > >
> > > To have ALL, it is required that ALL elements can be listed.
> > >
> > No, it isn't.
> >
> > Hint: The real numbers can't be "listed".
> >
> If I'm not mistaken, to him the reals don't exist.

Ok. In such a restricted (mathematical) universe the elements of any set might indeed be "listable". :-P

On the other hand all elements in IN _can be_ "listed" (in principle).

Actually, Chuck Norris already counted them all - twice!

Re: Natural numbers and vases III

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
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by: Sergio - Tue, 23 Aug 2022 16:07 UTC

On 8/23/2022 10:52 AM, Fritz Feldhase wrote:
> On Tuesday, August 23, 2022 at 4:56:23 PM UTC+2, William wrote:
>
>> "all its elements" is the set
>
> No, you sily dumbfuck, the numbers 1, 2, 3 "are" not the set {1, 2, 3}.
>
> STOP TALKING NONSENSE, MAN!
>
> Holy shit!

counted and labled sheeps are 1,2,3 However, their pen is { }

Therefore a Set of sheeps is {1,2,3}

See serious super sheeps slipping sideways suddenly stop succinctly in a set.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: monteu...@t-online.de (WM)
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by: WM - Tue, 23 Aug 2022 16:28 UTC

FredJeffries schrieb am Dienstag, 23. August 2022 um 17:59:40 UTC+2:
> On Tuesday, August 23, 2022 at 6:51:55 AM UTC-7, WM wrote:
> > FredJeffries schrieb am Montag, 22. August 2022 um 19:48:08 UTC+2:
> > > > On Monday, August 22, 2022 at 3:36:34 PM UTC+2, WM wrote:
> > >
> > > > > there are ℵo natural numbers but most of them cannot be counted.
> > > How do you know that there are ℵo of them if they cannot be counted?
> > I use ℵo as expressing actual infinity (i.e. more than every finite number).
> Who cares what you 'use'?

You.
>
> I'll rephrase the question: How do you know that there are 'more than every finite number' of them if they cannot be counted?

I know it because they cannot be counted. Every finite number of numbers can be counted.

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 - Tue, 23 Aug 2022 17:09 UTC

On Tuesday, August 23, 2022 at 6:01:19 PM UTC+2, Fritz Feldhase wrote:
> On Tuesday, August 23, 2022 at 5:06:29 PM UTC+2, FromTheRafters wrote:
> > Fritz Feldhase pretended :
> > > On Tuesday, August 23, 2022 at 1:52:11 PM UTC+2, Eram semper recta wrote:
> > > >
> > > > To have ALL, it is required that ALL elements can be listed.
> > > >
> > > No, it isn't.
> > >
> > > Hint: The real numbers can't be "listed".
> > >
> > If I'm not mistaken, to him the reals don't exist.
> Ok. In such a restricted (mathematical) universe the elements of any set might indeed be "listable". :-P
>
> On the other hand all elements in IN _can be_ "listed" (in principle).

Ooops, I meant /the/ elements in IN.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: Sergio - Tue, 23 Aug 2022 18:07 UTC

On 8/23/2022 11:28 AM, WM wrote:
> FredJeffries schrieb am Dienstag, 23. August 2022 um 17:59:40 UTC+2:
>> On Tuesday, August 23, 2022 at 6:51:55 AM UTC-7, WM wrote:
>>> FredJeffries schrieb am Montag, 22. August 2022 um 19:48:08 UTC+2:
>>>>> On Monday, August 22, 2022 at 3:36:34 PM UTC+2, WM wrote:
>>>>
>>>>>> there are ℵo natural numbers but most of them cannot be counted.
>>>> How do you know that there are ℵo of them if they cannot be counted?
>>> I use ℵo as expressing actual infinity (i.e. more than every finite number).
>> Who cares what you 'use'?
>
> You.
>>
>> I'll rephrase the question: How do you know that there are 'more than every finite number' of them if they cannot be counted?
>
> I know it because they cannot be counted.

Wrong, the natural numbers are countable. google is your fiend

> Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: thenewca...@gmail.com (Eram semper recta)
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by: Eram semper recta - Tue, 23 Aug 2022 22:42 UTC

On Tuesday, 23 August 2022 at 08:28:41 UTC-4, zelos moron wrote:
> tisdag 23 augusti 2022 kl. 13:52:11 UTC+2 skrev Eram semper recta:
> > On Monday, 22 August 2022 at 12:53:05 UTC-4, WM wrote:
> > > William schrieb am Montag, 22. August 2022 um 17:47:08 UTC+2:
> > > > On Monday, August 22, 2022 at 10:30:55 AM UTC-3, WM wrote:
> > > > > William schrieb am Samstag, 20. August 2022 um 16:30:41 UTC+2:
> > > > > > On Saturday, August 20, 2022 at 10:48:54 AM UTC-3, WM wrote:
> > > > > >
> > > > > > > I am not interested in the set but only in all its elements.
> > > > > > Piffle "all its elements" is the set.
> > > > > How man natural numbers can be used without using the set |N?
> > > > Irrelevant Piffle that has no bearing on the fact that "all its elements" is the set
> > > But how many elements are not the set?
> > They want to claim [A] The set N has no largest element and [B] N contains ALL of its elements. They refuse to accept that these statements are mutually exclusive.
> Because they aren't.

Anyone with a modicum of intelligence knows those two statements are mutually exclusive. You have none.

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

Strawman argument and not even relevant whether they can be written down or not. It's obvious you understood exactly nothing from the above paragraph. You can't claim all the members are distinct if you don't know what they are, you retard!

Don't project your feeble thoughts onto others.

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

You can keep dreaming. Set theory will in the not-too-distant future be excluded from all mathematics courses.

>
> >
> > >
> > > Regards, WM

Re: Natural numbers and vases III

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https://www.novabbs.com/tech/article-flat.php?id=110075&group=sci.math#110075

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From: pc+use...@asdf.org (Phil Carmody)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Wed, 24 Aug 2022 01:41:10 +0300
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by: Phil Carmody - Tue, 23 Aug 2022 22:41 UTC

Gus Gassmann <horand.gassmann@gmail.com> writes:
>> Presumably, every "for all" will be mapped in his head, via
>> "for each" and "for each in turn", into a procedure.
>>
>> I which case every single bit of formal set theory collapses
>> into a procedure, even the axioms and axiom schemata.
>>
>> Presumably, this includes his own version of set theory too.
>> So he needs to throw that out as well. He's nuking his own
>> feet.
>>
>> However, I'll start him off with a new formal set theory, as
>> a helpful starting point, because I'm that kind of guy:
>>
>> Axiom 0: There exists an empty set. Its definition is everything
>> sensible that WM's ever said about mathematics.
>
> Think again. Just yesterday he said that the empty set is a set from
> which all elements have been removed. He is even procedural about
> this.

Did he do this without a "for all" or invoking an axiom with a "for
all"? Finite sets are vanishingly rare in our universe of discourse,
(for every finite one he can specify, anyone with more than half a brain
can specify an uncountable infinitude of transfinite ones). He's taking
quite a risk at adopting that procedure for creating an empty set, given
the arguments he touts.

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

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

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