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All syllogisms have three parts, therefore this is not a syllogism.


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

SubjectAuthor
* Natural numbers and vasesWilliam
+- Re: Natural numbers and vasesRoss A. Finlayson
+* Re: Natural numbers and vasesWM
|+* Re: Natural numbers and vasesWilliam
||`* Re: Natural numbers and vasesWM
|| +- Re: Natural numbers and vasessergio
|| `* Re: Natural numbers and vasesWilliam
||  `* Re: Natural numbers and vasesWM
||   +- Re: Natural numbers and vasessergio
||   `* Re: Natural numbers and vasesWilliam
||    `* Re: Natural numbers and vasesWM
||     +- Re: Natural numbers and vasessergio
||     `* Re: Natural numbers and vasesWilliam
||      +- Re: Natural numbers and vasesFritz Feldhase
||      `* Re: Natural numbers and vasesWM
||       +* Re: Natural numbers and vasesWilliam
||       |+* Re: Natural numbers and vasesGus Gassmann
||       ||`* Re: Natural numbers and vasesFritz Feldhase
||       || `- Re: Natural numbers and vasesGus Gassmann
||       |`* Re: Natural numbers and vasesWM
||       | +- Re: Natural numbers and vasesGus Gassmann
||       | +* Re: Natural numbers and vasesWilliam
||       | |+* Re: Natural numbers and vasesWM
||       | ||+* Re: Natural numbers and vasesWilliam
||       | |||`* Re: Natural numbers and vasesWM
||       | ||| `* Re: Natural numbers and vasesWilliam
||       | |||  +* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |`- Re: Natural numbers and vasessergio
||       | |||  +* Re: Natural numbers and vasesGus Gassmann
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||+- Re: Natural numbers and vasesFromTheRafters
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesGus Gassmann
||       | |||  ||`- Re: Natural numbers and vasesChris M. Thomasson
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||+* Re: Natural numbers and vasesJim Burns
||       | |||  |||`* Re: Natural numbers and vasesWM
||       | |||  ||| +* Re: Natural numbers and vasesJim Burns
||       | |||  ||| |`* Re: Natural numbers and vasesWM
||       | |||  ||| | +* Re: Natural numbers and vasesJim Burns
||       | |||  ||| | |`* Re: Natural numbers and vasesWM
||       | |||  ||| | | +* Re: Natural numbers and vasesJim Burns
||       | |||  ||| | | |`* Re: Natural numbers and vasesWM
||       | |||  ||| | | | `- Re: Natural numbers and vasessergio
||       | |||  ||| | | `- Re: Natural numbers and vasessergio
||       | |||  ||| | `- Re: Natural numbers and vasessergio
||       | |||  ||| `- Re: Natural numbers and vasessergio
||       | |||  ||`* Re: Natural numbers and vasessergio
||       | |||  || `- Re: Natural numbers and vasesChet Hirasi
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+* Re: Natural numbers and vasesGus Gassmann
||       | |||  ||`- Re: Natural numbers and vasesChet Hirasi
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`* Re: Natural numbers and vasessergio
||       | |||  || `* Re: Natural numbers and vasesWM
||       | |||  ||  `* Re: Natural numbers and vasessergio
||       | |||  ||   +* Re: Natural numbers and vasessergio
||       | |||  ||   |`* Re: Natural numbers and vasesFredJeffries
||       | |||  ||   | `- Re: Natural numbers and vasessergio
||       | |||  ||   `* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||    `* Re: Natural numbers and vasessergio
||       | |||  ||     +* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||     |`- Re: Natural numbers and vasessergio
||       | |||  ||     `* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||      `* Re: Natural numbers and vasessergio
||       | |||  ||       `* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||        +* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  ||        |`- Re: Natural numbers and vasessergio
||       | |||  ||        `- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||`- Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  ||+- Re: Natural numbers and vasessergio
||       | |||  ||`* Re: Natural numbers and vasesChris M. Thomasson
||       | |||  || +* Re: Natural numbers and vasesFromTheRafters
||       | |||  || `* Re: Natural numbers and vasessergio
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesGus Gassmann
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesGus Gassmann
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWilliam
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |+- Re: Natural numbers and vasesWM
||       | |||  |+* Re: Natural numbers and vasesWM
||       | |||  |`* Re: Natural numbers and vasesWM
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vasesFritz Feldhase
||       | |||  +- Re: Natural numbers and vaseszelos...@gmail.com
||       | |||  `- Re: Natural numbers and vaseszelos...@gmail.com
||       | ||`- Re: Natural numbers and vasessergio
||       | |`* Re: Natural numbers and vasesWM
||       | +- Re: Natural numbers and vasessergio
||       | `* Re: Natural numbers and vasesJim Burns
||       `- Re: Natural numbers and vasessergio
|+- Re: Natural numbers and vasesRoss A. Finlayson
|`- Re: Natural numbers and vasesFritz Feldhase
+* Re: Natural numbers and vasesChris M. Thomasson
+* Re: Natural numbers and vasesMostowski Collapse
`- Re: Natural numbers and vasesSocratis T.n.p.

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Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Sun, 12 Jun 2022 17:02 UTC

$\mathbb{N}$ and $\emptyset$ by $x=x$ and $x < x$
William schrieb am Sonntag, 12. Juni 2022 um 16:27:03 UTC+2:
> > >
> > > For every element of "the set |N of all n": f(n)=n
> > >
> > > defines a bijection.
> > Here the universal quantifier works perfectly such that no n is missing..
> Indeed, no n, element of the set "all n", is missing.

in f(n)=n. But here many are missing here
∀n ∈ ℕ: |ℕ \ {1, 2, 3, ..., n}| = ℵo
although all are advertised.

Regards, WM

Re: Natural numbers and vases

<4c0915a8-9324-4aff-b051-b896e0c32995n@googlegroups.com>

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Subject: Re: Natural numbers and vases
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Sun, 12 Jun 2022 17:20:09 +0000
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 by: Fritz Feldhase - Sun, 12 Jun 2022 17:20 UTC

On Sunday, June 12, 2022 at 6:58:30 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Sonntag, 12. Juni 2022 um 16:32:30 UTC+2:
> > On Sunday, June 12, 2022 at 2:43:30 PM UTC+2, WM wrote:
> > > FromTheRafters schrieb am Sonntag, 12. Juni 2022 um 02:09:28 UTC+2:
> > > > WM was thinking very hard:
> > > > >
> > > > > Note that well-order is the basis for bijection.
> > > > >
> > > > Is there a bijection between sets {elephant, donkey, walrus} and
> > > > {monkey, garden hoe, geode}?
> > > >
> > > > Are these 'well ordered' sets?
> > > >
> > > Every extensionally given set is well-ordered by the oder of writing.
> > >
> > No, it isn't
> >
> > {elephant, donkey, walrus} = {donkey, elephant, walrus} = {walrus, donkey, elephant} = ...
> >
> This yields three well-orderings. One is sufficient.

Look, you psychotic piece of shit, your claim was: "Every extensionally given set is well-ordered by the order of writing."

Now let M = {elephant, donkey, walrus} = {donkey, elephant, walrus} = {walrus, donkey, elephant} = ...

Which *is* the smallest element in M?

Man, your really are full of shit!

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
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 by: William - Sun, 12 Jun 2022 17:48 UTC

On Sunday, June 12, 2022 at 2:02:37 PM UTC-3, WM wrote:

> advertised.

nonsense

--
William Hughes

Re: Natural numbers and vases

<t85bq4$fbv$1@dont-email.me>

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sun, 12 Jun 2022 14:37:54 -0400
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 by: FromTheRafters - Sun, 12 Jun 2022 18:37 UTC

After serious thinking WM wrote :
>
> Fritz Feldhase schrieb am Sonntag, 12. Juni 2022 um 16:32:30 UTC+2:
>> On Sunday, June 12, 2022 at 2:43:30 PM UTC+2, WM wrote:
>>> FromTheRafters schrieb am Sonntag, 12. Juni 2022 um 02:09:28 UTC+2:
>>>> WM was thinking very hard:
>>>>>
>>>>> Note that well-order is the basis for bijection.
>>>>>
>>>> Is there a bijection between sets {elephant, donkey, walrus} and
>>>> {monkey, garden hoe, geode}?
>>>>
>>>> Are these 'well ordered' sets?
>>>>
>>> Every extensionally given set is well-ordered by the order of writing.
>> No, it isn't
>>
>> {elephant, donkey, walrus} = {donkey, elephant, walrus} = {walrus, donkey,
>> elephant} = ...
>
> This yields three well-orderings. One is sufficient.

Because changing the listed order (permutation) of the elements does
not affect bijection. Now you say well-order is the basis for it?

Is a donkey less than a walrus but greater than an elephant?

Re: Natural numbers and vases

<t85i3c$ba8$1@gioia.aioe.org>

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From: inva...@invalid.com (sergi o)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sun, 12 Jun 2022 15:25:14 -0500
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 by: sergi o - Sun, 12 Jun 2022 20:25 UTC

On 6/12/2022 1:37 PM, FromTheRafters wrote:
> After serious thinking WM wrote :
>>
>> Fritz Feldhase schrieb am Sonntag, 12. Juni 2022 um 16:32:30 UTC+2:
>>> On Sunday, June 12, 2022 at 2:43:30 PM UTC+2, WM wrote:
>>>> FromTheRafters schrieb am Sonntag, 12. Juni 2022 um 02:09:28 UTC+2:
>>>>> WM was thinking very hard:
>>>>>>
>>>>>> Note that well-order is the basis for bijection.
>>>>> Is there a bijection between sets {elephant, donkey, walrus} and {monkey, garden hoe, geode}?
>>>>> Are these 'well ordered' sets?
>>>> Every extensionally given set is well-ordered by the order of writing.
>>> No, it isn't
>>>
>>> {elephant, donkey, walrus} = {donkey, elephant, walrus} = {walrus, donkey, elephant} = ...
>>
>> This yields three well-orderings. One is sufficient.
>
> Because changing the listed order (permutation) of the elements does not affect bijection. Now you say well-order is the basis for it?
>
> Is a donkey less than a walrus but greater than an elephant?

Well order by;

intelligence?

volume ?

average specific gravity ?

Weight ?

# of letters in its name ?

Year of discovery ?

Number of legs/feet/flippers ?

surface area ?

Amount of sparkles it can have applied ?

longest add on unicorn horn ?

demonstrable knowledge of Maths ?

Re: Natural numbers and vases

<87v8t5mx6u.fsf@bsb.me.uk>

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Sun, 12 Jun 2022 21:41:29 +0100
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 by: Ben Bacarisse - Sun, 12 Jun 2022 20:41 UTC

sergi o <invalad@invalid.com> writes:

> On 6/12/2022 10:43 AM, Ben Bacarisse wrote:
>> sergi o <invalad@invalid.com> writes:
>>
>>> On 6/12/2022 7:43 AM, WM wrote:
>>
>>>> Every finite set can be well-ordered.
>>>
>>> no. "Every finite totally ordered set is well ordered."
>>> "A totally ordered set (A,<=) is said to be well ordered (or have a
>>> well-founded order) iff every nonempty subset of A has a least
>>> element."
>> I'm not sure what your objection here is. That a finite set A "can be
>> well-ordered" just means that there exists some relation R on A such
>> that R is a well-founded order.
>
> he is too general
>
> {stamps, letters, envelopes} is a finite set...

....and it can be well-ordered.

--
Ben.

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Sun, 12 Jun 2022 21:04 UTC

On Sunday, June 12, 2022 at 6:55:21 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Sonntag, 12. Juni 2022 um 17:14:42 UTC+2:
> > On Saturday, June 11, 2022 at 11:10:38 PM UTC+2, WM wrote:
> > >
> > > well-order is the basis for bijection.
> > >
> > Huh?
> >
> "Zwei ..."

Look you silly idiot,

the function f: [0, 1] --> [1, 2] defined with f(x) = x + 1 (for all x e [0, 1]) is a bijection,

which well-order "is the basis for this bijection?"

You are dumb like shit, you silly asshole.

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Sun, 12 Jun 2022 22:01 UTC

On Sunday, June 12, 2022 at 10:41:38 PM UTC+2, Ben Bacarisse wrote:
> sergi o <inv...@invalid.com> writes:
> >
> > {stamps, letters, envelopes} is a finite set...
> >
> ...and it can be well-ordered.

Actually, it's a theorem in ZFC (proven by Zermelo in the context of Z), that each and every set "can be well-ordered". I guess Sergi O knows that.

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
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 by: Ben Bacarisse - Sun, 12 Jun 2022 22:39 UTC

Fritz Feldhase <franz.fritschee.ff@gmail.com> writes:

> On Sunday, June 12, 2022 at 10:41:38 PM UTC+2, Ben Bacarisse wrote:
>> sergi o <inv...@invalid.com> writes:
>> >
>> > {stamps, letters, envelopes} is a finite set...
>> >
>> ...and it can be well-ordered.
>
> Actually, it's a theorem in ZFC (proven by Zermelo in the context of
> Z), that each and every set "can be well-ordered".

Yup, but I didn't want to muddy the waters by extending the claim from
the one sergi o said "no" to.

> I guess Sergi O knows that.

I'd have thought so, but the first word he wrote in reply to "every
finite set can be well-ordered" was "no".

--
Ben.

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
Date: Sun, 12 Jun 2022 22:47:47 -0500
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 by: sergi o - Mon, 13 Jun 2022 03:47 UTC

On 6/12/2022 5:39 PM, Ben Bacarisse wrote:
> Fritz Feldhase <franz.fritschee.ff@gmail.com> writes:
>
>> On Sunday, June 12, 2022 at 10:41:38 PM UTC+2, Ben Bacarisse wrote:
>>> sergi o <inv...@invalid.com> writes:
>>>>
>>>> {stamps, letters, envelopes} is a finite set...
>>>>
>>> ...and it can be well-ordered.
>>
>> Actually, it's a theorem in ZFC (proven by Zermelo in the context of
>> Z), that each and every set "can be well-ordered".
>
> Yup, but I didn't want to muddy the waters by extending the claim from
> the one sergi o said "no" to.
>
>> I guess Sergi O knows that.
>
> I'd have thought so, but the first word he wrote in reply to "every
> finite set can be well-ordered" was "no".
>
>

I was going on this from Wolfram; https://www.wolframalpha.com/input?i=well+ordered+set

"Every finite totally ordered set is well ordered."
"A totally ordered set (A,<=) is said to be well ordered (or have a well-founded order) iff every nonempty subset of A has a least element."
"the set of integers Z, which has no least element, is an example of a set that is not well ordered."

VS

Whereas WM stated "Every finite set can be well-ordered."

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Mon, 13 Jun 2022 04:12 UTC

On Monday, June 13, 2022 at 5:48:02 AM UTC+2, sergi o wrote:

> Whereas WM stated "Every finite set can be well-ordered."

So what? "_Every set_ can be well-ordered."

See: http://scihi.org/ernst-zermelo/

And: https://en.m.wikipedia.org/wiki/Well-ordering_theorem

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Subject: Re: Natural numbers and vases
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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 by: zelos...@gmail.com - Mon, 13 Jun 2022 07:09 UTC

torsdag 9 juni 2022 kl. 16:52:55 UTC+2 skrev WM:
> William schrieb am Mittwoch, 8. Juni 2022 um 22:36:41 UTC+2:
> > On Wednesday, June 8, 2022 at 4:17:44 PM UTC-3, WM wrote:
>
> > > Look, in the beginning we have this matrix:
> > >
> > > XOOO...
> > > XOOO...
> > > XOOO...
> > > XOOO...
> > > ...
> > You cannot get rid of the O's by applying exchanges. So what?
> You cannot enumerate fractions without applying natural indexes and, in my language, without applying exchanges.
> > You cannot get the bijection by applying exchanges.
> That means you cannot get the bijection.
>
> By the way, dark numbers are also evident in this example:
>
> ∀n∈N:|N \ {1,2,3,...,n}| = ℵo.

that in no way shows anything "dark".

>
> Almost all natural numbers remain. According to the universal quantifier this is valid for all natural numbers. Apply one after the other. Nothing will change. Always ℵo natural numbers will be left.

But none of that means any of them are "Dark"

>
> But if it is done too fast, simultaneously say, then nothing remains
>
> N− \ {1,2,3,...}=∅.
>
> This indicates either dark numbers or a time dependence of ZF. What do you prefer?
>
> Regards, WM

Re: Natural numbers and vases

<87bkuwn6zh.fsf@bsb.me.uk>

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From: ben.use...@bsb.me.uk (Ben Bacarisse)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Mon, 13 Jun 2022 12:22:10 +0100
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 by: Ben Bacarisse - Mon, 13 Jun 2022 11:22 UTC

sergi o <invalad@invalid.com> writes:

> On 6/12/2022 5:39 PM, Ben Bacarisse wrote:
>> Fritz Feldhase <franz.fritschee.ff@gmail.com> writes:
>>
>>> On Sunday, June 12, 2022 at 10:41:38 PM UTC+2, Ben Bacarisse wrote:
>>>> sergi o <inv...@invalid.com> writes:
>>>>>
>>>>> {stamps, letters, envelopes} is a finite set...
>>>>>
>>>> ...and it can be well-ordered.
>>>
>>> Actually, it's a theorem in ZFC (proven by Zermelo in the context of
>>> Z), that each and every set "can be well-ordered".
>> Yup, but I didn't want to muddy the waters by extending the claim from
>> the one sergi o said "no" to.
>>
>>> I guess Sergi O knows that.
>> I'd have thought so, but the first word he wrote in reply to "every
>> finite set can be well-ordered" was "no".
>
> I was going on this from Wolfram;
> https://www.wolframalpha.com/input?i=well+ordered+set
>
> "Every finite totally ordered set is well ordered."
> "A totally ordered set (A,<=) is said to be well ordered (or have a
> well-founded order) iff every nonempty subset of A has a least
> element." "the set of integers Z, which has no least element, is an
> example of a set that is not well ordered."
>
> VS
>
> Whereas WM stated "Every finite set can be well-ordered."

There is no need for the "whereas". wolframalpha is not wrong and
neither is WM. I don't see where you see any conflict between them.

--
Ben.

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
Injection-Date: Mon, 13 Jun 2022 13:49:21 +0000
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 by: WM - Mon, 13 Jun 2022 13:49 UTC

zelos...@gmail.com schrieb am Montag, 13. Juni 2022 um 09:09:35 UTC+2:
> torsdag 9 juni 2022 kl. 16:52:55 UTC+2 skrev WM:

> > By the way, dark numbers are also evident in this example:
> >
> > ∀n∈N:|N \ {1,2,3,...,n}| = ℵo.
>
> that in no way shows anything "dark".
>
> >
> > Almost all natural numbers remain. According to the universal quantifier this is valid for all natural numbers. Apply one after the other. Nothing will change. Always ℵo natural numbers will be left.
>
> But none of that means any of them are "Dark"

You can't subtract FISONs without remainder:
∀n∈N:|N −{1,2,3,...,n}|=ℵ0.
But allegedly you can biject natnumbers and FISONs without remainder. And if you subtract all indexed FISONs from N then nothing remains.

Think over it.

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
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 by: William - Mon, 13 Jun 2022 14:08 UTC

On Monday, June 13, 2022 at 10:49:27 AM UTC-3, WM wrote:

> You can't subtract FISONs without remainder:
> ∀n∈N:|N −{1,2,3,...,n}|=ℵ0.

Correct, subtracting any *element* of the set of FISONS leaves a remainder of cardinaliity aleph_0

> But allegedly you can biject natnumbers and FISONs without remainder. And if you subtract all indexed FISONs from N then nothing remains.

Correct if you subtract the *set* , "all indexed FISONs ", from |N then nothing remains.

You are on a fruitless search to find the element that makes |N infinite.

--
William Hughes

Re: Natural numbers and vases

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From: inva...@invalid.com (sergi o)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Mon, 13 Jun 2022 09:12:41 -0500
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 by: sergi o - Mon, 13 Jun 2022 14:12 UTC

On 6/13/2022 8:49 AM, WM wrote:
> zelos...@gmail.com schrieb am Montag, 13. Juni 2022 um 09:09:35 UTC+2:
>> torsdag 9 juni 2022 kl. 16:52:55 UTC+2 skrev WM:
>
>>> By the way, dark numbers are also evident in this example:
>>>
>>> ∀n∈N:|N \ {1,2,3,...,n}| = ℵo.
>>
>> that in no way shows anything "dark".
>>
>>>
>>> Almost all natural numbers remain. According to the universal quantifier this is valid for all natural numbers. Apply one after the other. Nothing will change. Always ℵo natural numbers will be left.
>>
>> But none of that means any of them are "Dark"
>
>
> You can't subtract FISONs without remainder:
> ∀n∈N:|N −{1,2,3,...,n}|=ℵ0.

Endsegment.

> But allegedly you can biject natnumbers and FISONs without remainder.

can you show the equations for that ?

> And if you subtract all indexed FISONs from N then nothing remains.

How would you prove that ? any ideas ?

(hint: assume a number is present, and show it cant be)

>
> Think over it.

go read a beginning algebra book

>
> Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Mon, 13 Jun 2022 14:16 UTC

FromTheRafters schrieb am Sonntag, 12. Juni 2022 um 20:38:06 UTC+2:
> After serious thinking WM wrote :
> >
> > Fritz Feldhase schrieb am Sonntag, 12. Juni 2022 um 16:32:30 UTC+2:
> >> On Sunday, June 12, 2022 at 2:43:30 PM UTC+2, WM wrote:
> >>> FromTheRafters schrieb am Sonntag, 12. Juni 2022 um 02:09:28 UTC+2:
> >>>> WM was thinking very hard:
> >>>>>
> >>>>> Note that well-order is the basis for bijection.
> >>>>>
> >>>> Is there a bijection between sets {elephant, donkey, walrus} and
> >>>> {monkey, garden hoe, geode}?
> >>>>
> >>>> Are these 'well ordered' sets?
> >>>>
> >>> Every extensionally given set is well-ordered by the order of writing.
> >> No, it isn't

It is a list!

> >>
> >> {elephant, donkey, walrus} = {donkey, elephant, walrus} = {walrus, donkey,
> >> elephant} = ...
> >
> > This yields three well-orderings. One is sufficient.
> Because changing the listed order (permutation) of the elements does
> not affect bijection. Now you say well-order is the basis for it?

Yes, but one is enough.
>
> Is a donkey less than a walrus but greater than an elephant?

Well-order has nothing to do with largeness. 3, 2, 1 is also well-ordered.

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Mon, 13 Jun 2022 14:21 UTC

Fritz Feldhase schrieb am Sonntag, 12. Juni 2022 um 19:20:14 UTC+2:
> On Sunday, June 12, 2022 at 6:58:30 PM UTC+2, WM wrote:

> your claim was: "Every extensionally given set is well-ordered by the order of writing."
>
> Now let M = {elephant, donkey, walrus} = {donkey, elephant, walrus} = {walrus, donkey, elephant} = ...

Three different well-orders do not disprove the existence of one.
>
> Which *is* the smallest element in M?
>
Well-order has nothing to do with largeness.

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Mon, 13 Jun 2022 14:22 UTC

William schrieb am Sonntag, 12. Juni 2022 um 19:48:40 UTC+2:

You can't subtract FISONs without remainder:
∀n∈N:|N −{1,2,3,...,n}|=ℵ0.
But allegedly you can biject natnumbers and FISONs without remainder. And if you subtract all indexed FISONs from N then nothing remains.

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Mon, 13 Jun 2022 14:37 UTC

William schrieb am Montag, 13. Juni 2022 um 16:09:06 UTC+2:
> On Monday, June 13, 2022 at 10:49:27 AM UTC-3, WM wrote:
>
> > You can't subtract FISONs without remainder:
> > ∀n∈N:|N −{1,2,3,...,n}|=ℵ0.
> Correct, subtracting any *element* of the set of FISONS leaves a remainder of cardinaliity aleph_0

By ∀n∈N all elements are addressed.

> > But allegedly you can biject natnumbers and FISONs without remainder. And if you subtract all indexed FISONs from N then nothing remains.
> Correct if you subtract the *set* ,

No, I subtract all FISONs, not a set.

> "all indexed FISONs ", from |N then nothing remains.

That contradicts that all indexed FISONs leave remainders:
∀n∈N:|N −{1,2,3,...,n}|=ℵ0.
>
> You are on a fruitless search to find the element that makes |N infinite.

I have found them: infinitely many dark numbers. Any finite number belongs to a finite set and cannot cause infinity.

Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
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 by: William - Mon, 13 Jun 2022 14:38 UTC

On Monday, June 13, 2022 at 11:23:04 AM UTC-3, WM wrote:
> William schrieb am Sonntag, 12. Juni 2022 um 19:48:40 UTC+2:
>
> You can't subtract FISONs without remainder:
> ∀n∈N:|N −{1,2,3,...,n}|=ℵ0.
> But allegedly you can biject natnumbers and FISONs without remainder. And if you subtract all indexed FISONs from N then nothing remains.

Indeed, you cannot subtract any *element* of the set of FISONs, "all indexed FISONs", without remainder, but you can subtract the set.
All your arguments boil down, to, no element of |N makes |N infinite, therefore there must be something else that makes |N infinite.

--
William Hughes

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: wpihug...@gmail.com (William)
Injection-Date: Mon, 13 Jun 2022 14:45:10 +0000
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 by: William - Mon, 13 Jun 2022 14:45 UTC

On Monday, June 13, 2022 at 11:37:53 AM UTC-3, WM wrote:
> William schrieb am Montag, 13. Juni 2022 um 16:09:06 UTC+2:

> > ... if you subtract the *set* ,
> No, I subtract all FISONs, not a set.

Piffle, you subtract "all indexed FISONs", the set of all FISONS

> > You are on a fruitless search to find the element that makes |N infinite.
> I have found them: infinitely many dark numbers.

Piffle. A Peano set is infinite, A Peano set does not contain "dark" elements

--
William Hughes

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: askaske...@gmail.com (WM)
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 by: WM - Mon, 13 Jun 2022 15:05 UTC

William schrieb am Montag, 13. Juni 2022 um 16:45:15 UTC+2:
> On Monday, June 13, 2022 at 11:37:53 AM UTC-3, WM wrote:
> > William schrieb am Montag, 13. Juni 2022 um 16:09:06 UTC+2:
> > > ... if you subtract the *set* ,
> > No, I subtract all FISONs, not a set.
> Piffle, you subtract "all indexed FISONs", the set of all FISONS

No. This set cannot accomplish more than its elements: Inclusion-monotony!

But there is a difference. All indexed FISONs leave infinite remainders:

∀n∈N:|N \ {1,2,3,...,n}|=ℵ0.

The set N does not leave anything N \ {1,2,3,...} = { }.

This shows that the set N contains more than the union of all FISONs.

> A Peano set is infinite, A Peano set does not contain "dark" elements

Like the set of all FISONs. It does not contain dark elements. Therefore it cannot exhaust the dark elements of N when being subtracted.

Regards, WM

Re: Natural numbers and vases

<t87lf6$107b$1@gioia.aioe.org>

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases
Date: Mon, 13 Jun 2022 10:35:00 -0500
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 by: sergi o - Mon, 13 Jun 2022 15:35 UTC

On 6/13/2022 10:05 AM, WM wrote:
> William schrieb am Montag, 13. Juni 2022 um 16:45:15 UTC+2:
>> On Monday, June 13, 2022 at 11:37:53 AM UTC-3, WM wrote:
>>> William schrieb am Montag, 13. Juni 2022 um 16:09:06 UTC+2:
>>>> ... if you subtract the *set* ,
>>> No, I subtract all FISONs, not a set.
>> Piffle, you subtract "all indexed FISONs", the set of all FISONS
>
> No. This set cannot accomplish more than its elements: Inclusion-monotony!

red herring.

>
> But there is a difference. All indexed FISONs leave infinite remainders:
>
> ∀n∈N:|N \ {1,2,3,...,n}|=ℵ0.

yes, you took out a set called a FISON out of N, so now its an Endsegment,
they are infinite sets...

>
> The set N does not leave anything N \ {1,2,3,...} = { }.

yes, you took every element out of N, nothing left.

>
> This shows that the set N contains more than the union of all FISONs.

nope, where is your equation that shows that ?

>
>
>> A Peano set is infinite, A Peano set does not contain "dark" elements
>
> Like the set of all FISONs. It does not contain dark elements. Therefore it cannot exhaust the dark elements of N when being subtracted.

there are no dark elements.

For years you have failed to prove your dark numbers exist.

>
> Regards, WM

Re: Natural numbers and vases

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Subject: Re: Natural numbers and vases
From: franz.fr...@gmail.com (Fritz Feldhase)
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 by: Fritz Feldhase - Mon, 13 Jun 2022 18:01 UTC

On Monday, June 13, 2022 at 4:21:57 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Sonntag, 12. Juni 2022 um 19:20:14 UTC+2:
> > On Sunday, June 12, 2022 at 6:58:30 PM UTC+2, WM wrote:
> >
> > Look, you psychotic asshole, your claim was: "Every extensionally given set is well-ordered by the order of writing."
> >
> > Now let M = {elephant, donkey, walrus} = {donkey, elephant, walrus} = {walrus, donkey, elephant} = ...
> >
> > Which *is* the smallest element in M?
> >
> Well-order has nothing to do with largeness.

Oh, really?

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