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

<8ddb6dd3-a045-4d96-8812-537671656f30n@googlegroups.com>

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
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by: Fritz Feldhase - Thu, 25 Aug 2022 21:50 UTC

On Thursday, August 25, 2022 at 11:41:57 PM UTC+2, Fritz Feldhase wrote:

> What's the matter with you man, these are just some trivial variants of terminology.

To make a long story short:

Mückenheim just calls a set sequence (S_n)_(n e IN) "inclusion monotonic" iff

An e IN: S_n c S_(n+1) (*)

An e IN: S_(n+1) c S_n. (**)

Not that hard, is it?

Usually sequences of sets are called "monotone" iff (*) or (**) holds for them.
See: https://proofwiki.org/wiki/Definition:Monotone_Sequence_of_Sets

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 - Thu, 25 Aug 2022 22:08 UTC

On Thursday, August 25, 2022 at 11:49:42 PM UTC+2, Sergio wrote:

> OK, are these WN unique words and WM ideas ?
>
> FISON

Nope. IIRC "Virgil" coined that term. It 's just short for "finite initial sequence of natural numbers" or "finite initial sequence of IN".

> Endsegment

Nope. The notion exists in set theoy (formulated in german language.

> Inclusion Monotonic

Nope. The origin is the german word, "Inklusionsmonotony", but it's not "that common" to say the least. :-P

Mückenheim actually means "monotone" in this case.

> (WMs) Defined (def)

Yes.

> visable/dark

Yes.

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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 - Thu, 25 Aug 2022 22:10 UTC

On Thursday, August 25, 2022 at 11:49:42 PM UTC+2, Sergio wrote:

> OK, are these WN unique words and WM ideas ?
>
> FISON

Nope. IIRC "Virgil" coined that term. It 's just short for "finite initial sequence of natural numbers" or "finite initial sequence of IN".

> Endsegment

Nope. The notion exists in set theoy (formulated in german language.

> Inclusion Monotonic

Nope. The origin is the german word, "Inklusionsmonotonie", but it's not "that common" to say the least. :-P

Mückenheim actually means "monotone" in this case.

> (WMs) Defined (def)

Yes.

> visable/dark

Yes.

Re: Natural numbers and vases III

<1b9c5760-ee41-8417-ef40-9b0bc720bada@att.net>

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 25 Aug 2022 18:32:06 -0400
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by: Jim Burns - Thu, 25 Aug 2022 22:32 UTC

On 8/25/2022 5:50 PM, Fritz Feldhase wrote:
> On Thursday, August 25, 2022
> at 11:41:57 PM UTC+2, Fritz Feldhase wrote:

>> What's the matter with you man, these are
> just some trivial variants of terminology.
>
> To make a long story short:
>
> Mückenheim just calls a set sequence
> (S_n)_(n e IN) "inclusion monotonic"
> iff
> An e IN: S_n c S_(n+1) (*)
> or
> An e IN: S_(n+1) c S_n. (**)

No.
Mückenheim also requires a last set.

It's essential to his "proof" of dark numbers.
Because "our" sets don't include a last one,
the WM-necessarily-existing WM-last one
must be dark.

> Not that hard, is it?

None of this is _hard_

The problem is figuring out what the heck
he's _saying_

You know how he says "the intersection"
instead of "the intersection of all
end segment of ℕ" ?
Think of a car thief filing serial numbers
off of an engine.

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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 - Thu, 25 Aug 2022 22:33 UTC

On Friday, August 26, 2022 at 12:32:17 AM UTC+2, Jim Burns wrote:
> On 8/25/2022 5:50 PM, Fritz Feldhase wrote:
> > On Thursday, August 25, 2022
> > at 11:41:57 PM UTC+2, Fritz Feldhase wrote:
>
> >> What's the matter with you man, these are
> > just some trivial variants of terminology.
> >
> > To make a long story short:
> >
> > Mückenheim just calls a set sequence (S_n)_(n e IN) "inclusion monotonic" iff
> >
> > An e IN: S_n c S_(n+1) (*)
> >
> > or
> >
> > An e IN: S_(n+1) c S_n. (**)
> >
> No.

Yes. EOD

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 - Thu, 25 Aug 2022 22:35 UTC

On Friday, August 26, 2022 at 12:32:17 AM UTC+2, Jim Burns wrote:

> The problem is figuring out what the heck he's _saying_

That's an extremely easy task. Most of his utterings are just brain dead BS.

Re: Natural numbers and vases III

<te8vee$4rf$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 25 Aug 2022 18:09:00 -0500
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by: Sergio - Thu, 25 Aug 2022 23:09 UTC

On 8/25/2022 5:08 PM, Fritz Feldhase wrote:
> On Thursday, August 25, 2022 at 11:49:42 PM UTC+2, Sergio wrote:
>
>> OK, are these WN unique words and WM ideas ?
>>
>> FISON
>
> Nope. IIRC "Virgil" coined that term. It 's just short for "finite initial sequence of natural numbers" or "finite initial sequence of IN".

Virgil like in 2009 in a newsgroup ? or IIRC chat ?

https://groups.google.com/g/sci.logic/c/LJXoKzcMfE4 ?

- so FISON is not textbook stuff, not in a DOVER pub on set theory.

>
>> Endsegment
>
> Nope. The notion exists in set theoy (formulated in german language.

I got google hit on Mückenheim, a java code statement, math overflow....

I could not find a reference in a text book.... (did not look that hard)

>
>> Inclusion Monotonic
>
> Nope. The origin is the german word, "Inklusionsmonotony", but it's not "that common" to say the least. :-P

only hit on this is Mückenheim, and a french paper which discusses non-monotonic reasoning in AI

>
> Mückenheim actually means "monotone" in this case.

agree.

>
>> (WMs) Defined (def)
>
> Yes.
>
>> visable/dark
>
> Yes.

I was checking on how widely used these terms are... I think Mückenheim gets an ego tingle whenever one is used, as no one else uses them, and he does.
I think his math consists of about 10 vague words he considers his, and he bounces between them, incants them.

I think WM enjoys "owning" others in the newsgroups as they use "his terms".... and that is why we always get a return to his nonsense. (besides the
lost marbles thing)

(I did not search in German)

found this thing;
Trapezoid endsegment
Mn = #+ AB/2 mn(2) #=#+ab ab=#

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 - Fri, 26 Aug 2022 00:15 UTC

On Friday, August 26, 2022 at 1:09:14 AM UTC+2, Sergio wrote:
> On 8/25/2022 5:08 PM, Fritz Feldhase wrote:
> > On Thursday, August 25, 2022 at 11:49:42 PM UTC+2, Sergio wrote:
> >>
> >> OK, are these WN unique words and WM ideas ?
> >>
> >> FISON
> >
> > Nope. IIRC "Virgil" coined that term. It 's just short for "finite initial sequence of natural numbers" or "finite initial sequence of IN".
> >
> Virgil like in 2009 in a newsgroup ? or IIRC chat ?

Yes.

> - so FISON is not textbook stuff, not in a DOVER pub on set theory.

*sigh*

Not the word, I guess. But in german there's the notion "Anfangsabschnitt" or "Abschnitt" (Google trans. => beginning section)

But some authors allow for an infinte "Anfangsabschnitt" (initial section) too: IN.

If you want to exclude that you get the notion: _finite_ initial section (of IN). => FISON.

Again, this term was coined by Virgil, I guess.

> >> Endsegment
> >
> > Nope. The notion exists in set theory (formulated in german language).
> >
> I got google hit [...]

See https://www.math.uni-hamburg.de/spag/ml/Lehre/SS20_Ex8.pdf
for example.

This notion actually exists in the context of set theory.

> >> Inclusion Monotonic
> >
> > Nope. The origin is the german word, "Inklusionsmonotonie", but it's not "that common" to say the least. :-P
> >
> only ...

https://www.spektrum.de/lexikon/mathematik/inklusionsmonotonie/4189
https://matheraum.de/forum/wie_mag_ich_diese_Sprache/t287184

But it seems it does not mean the same as "monotone" (concening set sequences).

Good to know! Ha ha ha! What an idiot!

HOLY SHIT! (Wasn't aware of thtat fact!)

> > Mückenheim actually means "monotone" in this case.
> >
> agree.

Fine.

> >> (WMs) Defined (def)
> >
> > Yes.
> >
> >> visable/dark
> >
> > Yes.
> >
> I was checking on how widely used these terms are...

No one else uses them (in the same way).

> I think Mückenheim gets an ego tingle whenever one is used, as no one else uses them, and he does.

Agree.

> I think his math consists of about 10 vague words he considers his, and he bounces between them, incants them.

Yes. Like "inclusion monotonic" / "Inklusionsmonotonie".

> I think WM enjoys "owning" others in the newsgroups as they use "his terms".... and that is why we always get a return to his nonsense. (besides the
> lost marbles thing)

Agree!

Or rather: ACK 100%

Re: Natural numbers and vases III

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 25 Aug 2022 21:18:57 -0400
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by: FromTheRafters - Fri, 26 Aug 2022 01:18 UTC

Fritz Feldhase expressed precisely :
> On Thursday, August 25, 2022 at 11:49:42 PM UTC+2, Sergio wrote:
>
>> OK, are these WN unique words and WM ideas ?
>>
>> FISON
>
> Nope. IIRC "Virgil" coined that term. It 's just short for "finite initial
> sequence of natural numbers" or "finite initial sequence of IN".

The 'S' is for segment which is a part of a sequence.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: horand.g...@gmail.com (Gus Gassmann)
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by: Gus Gassmann - Fri, 26 Aug 2022 01:21 UTC

On Thursday, 25 August 2022 at 21:16:01 UTC-3, Fritz Feldhase wrote:
> On Friday, August 26, 2022 at 1:09:14 AM UTC+2, Sergio wrote:
> > On 8/25/2022 5:08 PM, Fritz Feldhase wrote:

> > > Nope. The origin is the german word, "Inklusionsmonotonie", but it's not "that common" to say the least. :-P
> > >
> > only ...
>
> https://www.spektrum.de/lexikon/mathematik/inklusionsmonotonie/4189
> https://matheraum.de/forum/wie_mag_ich_diese_Sprache/t287184

Thanks for these links. The first of these , from the Lexikon der Mathematik, simply says that for subsets X and Y of the domain of a continuous function it is true that

if X is a subset of Y then f(X) is a subset of f(Y).

Nothing there about the requirement that any of those sets has to be nonempty, but it seems that if X is nonempty, then the nonemptiness of f(X) follows from continuity.

> But it seems it does not mean the same as "monotone" (concening set sequences).

It doesn't look hard to extend this to sequences of sets X1, X2, X3, ... .

In fact, if you take S to be the successor function and X and Y to be end segments (over n and m, respectively), then it is true that E(n) c E(m) implies S(E(n)) = E(S(n)) c E(S(m)) = S(E(m)).

Kind of makes me wonder whether this is where WM gets his delusion about the continuity of the card() function.

Re: Natural numbers and vases III

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 25 Aug 2022 21:32:07 -0400
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by: FromTheRafters - Fri, 26 Aug 2022 01:32 UTC

Jim Burns laid this down on his screen :
> On 8/25/2022 5:50 PM, Fritz Feldhase wrote:
>> On Thursday, August 25, 2022
>> at 11:41:57 PM UTC+2, Fritz Feldhase wrote:
>
>>> What's the matter with you man, these are
>> just some trivial variants of terminology.
>>
>> To make a long story short:
>>
>> Mückenheim just calls a set sequence
>> (S_n)_(n e IN) "inclusion monotonic"
>> iff
>> An e IN: S_n c S_(n+1) (*)
>> or
>> An e IN: S_(n+1) c S_n. (**)
>
> No.
> Mückenheim also requires a last set.
>
> It's essential to his "proof" of dark numbers.
> Because "our" sets don't include a last one,
> the WM-necessarily-existing WM-last one
> must be dark.
>
>> Not that hard, is it?
>
> None of this is _hard_
>
> The problem is figuring out what the heck
> he's _saying_
>
> You know how he says "the intersection"
> instead of "the intersection of all
> end segment of ℕ" ?
> Think of a car thief filing serial numbers
> off of an engine.

I asked WM what he means by "complete" and Fritz hasn't answered me yet
:(

Re: Natural numbers and vases III

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Thu, 25 Aug 2022 21:03:28 -0500
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by: Sergio - Fri, 26 Aug 2022 02:03 UTC

On 8/25/2022 8:21 PM, Gus Gassmann wrote:
> On Thursday, 25 August 2022 at 21:16:01 UTC-3, Fritz Feldhase wrote:
>> On Friday, August 26, 2022 at 1:09:14 AM UTC+2, Sergio wrote:
>>> On 8/25/2022 5:08 PM, Fritz Feldhase wrote:
>
>>>> Nope. The origin is the german word, "Inklusionsmonotonie", but it's not "that common" to say the least. :-P
>>>>
>>> only ...
>>
>> https://www.spektrum.de/lexikon/mathematik/inklusionsmonotonie/4189
>> https://matheraum.de/forum/wie_mag_ich_diese_Sprache/t287184
>
> Thanks for these links. The first of these , from the Lexikon der Mathematik, simply says that for subsets X and Y of the domain of a continuous function it is true that
>
> if X is a subset of Y then f(X) is a subset of f(Y).
>
> Nothing there about the requirement that any of those sets has to be nonempty, but it seems that if X is nonempty, then the nonemptiness of f(X) follows from continuity.
>
>> But it seems it does not mean the same as "monotone" (concening set sequences).
>
> It doesn't look hard to extend this to sequences of sets X1, X2, X3, ... .
>
> In fact, if you take S to be the successor function and X and Y to be end segments (over n and m, respectively), then it is true that E(n) c E(m) implies S(E(n)) = E(S(n)) c E(S(m)) = S(E(m)).
>
> Kind of makes me wonder whether this is where WM gets his delusion about the continuity of the card() function.
>
>
>

from that second link, I ran into a series of youtube lectures, by Marcel Erné, 8 total 1.5 hrs long, heavy stuff!!

there is a series of lectures
https://www.youtube.com/watch?v=WsQyp7lU6O4&list=PL5rqYzyihIQ0nzfnsEKxxedCpbNQoifgg&index=1

from that above second link

I think this means 'inclusion monotone' (according to Marcel Erné, "Introduction to Order Theory", also: 'isotonic' or 'inclusion-preserving'). A
function $ f $ whose definition and value range are sets of sets (e.g. power sets) is called inclusion monotone exactly when $ A\subseteq B $ indicates
that $ f(A)\subseteq f(B) $.

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 - Fri, 26 Aug 2022 04:56 UTC

torsdag 25 augusti 2022 kl. 15:40:21 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Donnerstag, 25. August 2022 um 07:29:56 UTC+2:
> > onsdag 24 augusti 2022 kl. 14:22:06 UTC+2 skrev WM:
>
> > > All definable elements have ℵ₀ successors
> > > ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
> > That is again all of N, so N_def=N
> >
> > > All elements have no succesors
> >
> > False, all elements have infinitely many successors
> >
> > > ℕ \ {1, 2, 3, ...} = { }
> >
> > It is true for any set.
> What makes the difference between all elements and the set?
> S\S={}
> > So fucking what?
> This which a serious mathematician cannot deny:
> (1) The intersection of inclusion-monotonic infinite sets is infinite.

Not necessarily.

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

Only if you think in a step wise process which mathematics IS NOT!

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 - Fri, 26 Aug 2022 07:44 UTC

On Friday, August 26, 2022 at 3:32:23 AM UTC+2, FromTheRafters wrote:

> I asked WM what he means by "complete"

Well, we already had that discussion with WM - to no avail.

Hint: "/Complete/ may refer to:

_Mathematics_
Complete metric space, a metric space in which every Cauchy sequence converges
Complete uniform space, a uniform space where every Cauchy net in converges (or equivalently every Cauchy filter converges)
Complete measure, a measure space where every subset of every null set is measurable
Complete graph, an undirected graph in which every pair of vertices has exactly one edge connecting them
Complete category, a category C where every diagram from a small category to C has a limit; it is cocomplete if every such functor has a colimit
Complete variety, an algebraic variety that satisfies an analog of compactness
Complete orthonormal basis—see Orthonormal basis#Incomplete orthogonal sets
Complete sequence, a type of integer sequence

_Computing_
Complete (complexity), a notion referring to a problem in computational complexity theory that all other problems in a class reduce to
Turing complete set, a related notion from recursion theory
Complete search algorithm, a search algorithm that is guaranteed to find a solution if there is one

_Physics_
Complete set of commuting operators (or CSCO), a set of commuting operators in quantum mechanics whose eigenvalues are sufficient to specify the physical state of a system"

Source: https://en.wikipedia.org/wiki/Completeness

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 - Fri, 26 Aug 2022 14:57 UTC

William schrieb am Donnerstag, 25. August 2022 um 17:17:39 UTC+2:
> On Thursday, August 25, 2022 at 10:37:04 AM UTC-3, WM wrote:

> > each nonempty endsegment has at least one natnumber in common with all non-empty endsegments. Assume not.
> This assumption is true (and does not lead to a contradiction).
> >Assume for simplicity that every endsegment has only one element.
> This assumption may be simple but it is false. Unsurprisingly it leads to a contradiction.

It is not necessary for my proof.
Each nonempty endsegment has at least one natnumber in common with all non-empty endsegments. Assume not. Then there are at least two natnumbers a and b in endsegments A and B, such that
(1) a ∈ A
(2) b ∈ B
(3) a ∉ B
(4) b ∉ A.

(1) to (3) are satisfied by all endsegments. But (4) contradicts the definition of endsegment. Therefore the intersection of non-empty endsegments is non-empty.

Regards, WM

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 - Fri, 26 Aug 2022 15:05 UTC

Fritz Feldhase schrieb am Donnerstag, 25. August 2022 um 17:59:02 UTC+2:
> On Thursday, August 25, 2022 at 5:42:14 PM UTC+2, FromTheRafters wrote:
> > Fritz Feldhase was thinking very hard :
> > > 3. He just gave you the very same answer
> > >
> > So that puts you and he on equal footing.
> Concerning this "question", yes.
>
> It seems to me that this is one of the one or two things in math he really knows.

Two! Inclusion monotony of endsegments and the matrix
XOO...
XOO...
XOO...
....
Und mehr bedarfs nicht.

Regards, WM

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 - Fri, 26 Aug 2022 15:18 UTC

Jim Burns schrieb am Donnerstag, 25. August 2022 um 20:00:51 UTC+2:
> On 8/25/2022 11:20 AM, FromTheRafters wrote:
>
> > "Our intuition gained from finite sets
> > breaks down when dealing with infinite sets."
> > https://en.wikipedia.org/wiki/Cardinality#Infinite_sets
> One way to proceed despite broken down
> intuitions is to depend only upon such
> facts as hold in both the finite and the
> infinite realms.

Like exchanging X's and O's will never delete any X or O.
Yes, only such deep principles may be applied.

Regards, WM

Re: Natural numbers and vases III

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Newsgroups: sci.math
Date: Fri, 26 Aug 2022 08:22:17 -0700 (PDT)
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Subject: Re: Natural numbers and vases III
From: monteu...@t-online.de (WM)
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by: WM - Fri, 26 Aug 2022 15:22 UTC

Fritz Feldhase schrieb am Freitag, 26. August 2022 um 00:10:24 UTC+2:
> On Thursday, August 25, 2022 at 11:49:42 PM UTC+2, Sergio wrote:
>
> > OK, are these WN unique words and WM ideas ?
> >
> > FISON
> Nope. IIRC "Virgil" coined that term. It 's just short for "finite initial sequence of natural numbers" or "finite initial sequence of IN".

Yes, it is Virgil's word.

Regards, WM

Re: Natural numbers and vases III

<teaq96$1rqv$1@gioia.aioe.org>

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 26 Aug 2022 10:53:08 -0500
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by: Sergio - Fri, 26 Aug 2022 15:53 UTC

On 8/26/2022 10:18 AM, WM wrote:
> Jim Burns schrieb am Donnerstag, 25. August 2022 um 20:00:51 UTC+2:
>> On 8/25/2022 11:20 AM, FromTheRafters wrote:
>>
>>> "Our intuition gained from finite sets
>>> breaks down when dealing with infinite sets."
>>> https://en.wikipedia.org/wiki/Cardinality#Infinite_sets
>> One way to proceed despite broken down
>> intuitions is to depend only upon such
>> facts as hold in both the finite and the
>> infinite realms.
>
> Like exchanging X's and O's will never delete any X or O.
> Yes, only such deep principles may be applied.

wrong, yours is not math, and it is wrong as it does not agree with Cantor who proved the one to one mapping of the rationals to the naturals.

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: Fri, 26 Aug 2022 10:56:24 -0500
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by: Sergio - Fri, 26 Aug 2022 15:56 UTC

On 8/26/2022 9:57 AM, WM wrote:
> William schrieb am Donnerstag, 25. August 2022 um 17:17:39 UTC+2:
>> On Thursday, August 25, 2022 at 10:37:04 AM UTC-3, WM wrote:
>
>>> each nonempty endsegment has at least one natnumber in common with all non-empty endsegments. Assume not.
>> This assumption is true (and does not lead to a contradiction).
>>> Assume for simplicity that every endsegment has only one element.
>> This assumption may be simple but it is false. Unsurprisingly it leads to a contradiction.
>
> It is not necessary for my spoof.
> Each nonempty endsegment has at least one natnumber in common with all non-empty endsegments. Assume not. Then there are at least two natnumbers a and b in endsegments A and B, such that
> (1) a ∈ A
> (2) b ∈ B
> (3) a ∉ B
> (4) b ∉ A.
>
> (1) to (3) are satisfied by all endsegments.

wrong. a is not in E(A+1), fail.

> But (4) contradicts the definition of endsegment. Therefore the intersection of non-empty endsegments is non-empty.

again you prove you are just making bullshit up on the fly.

>
> Regards, troll WM

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 26 Aug 2022 10:57:19 -0500
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by: Sergio - Fri, 26 Aug 2022 15:57 UTC

On 8/26/2022 10:22 AM, WM wrote:
> Fritz Feldhase schrieb am Freitag, 26. August 2022 um 00:10:24 UTC+2:
>> On Thursday, August 25, 2022 at 11:49:42 PM UTC+2, Sergio wrote:
>>
>>> OK, are these WN unique words and WM ideas ?
>>>
>>> FISON
>> Nope. IIRC "Virgil" coined that term. It 's just short for "finite initial sequence of natural numbers" or "finite initial sequence of IN".
>
> Yes, it is Virgil's word.

some other troll on the internet.

>
> 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 - Fri, 26 Aug 2022 16:20 UTC

On Friday, August 26, 2022 at 5:57:29 PM UTC+2, Sergio wrote:
> On 8/26/2022 10:22 AM, WM wrote:
> > Fritz Feldhase schrieb am Freitag, 26. August 2022 um 00:10:24 UTC+2:
> >> On Thursday, August 25, 2022 at 11:49:42 PM UTC+2, Sergio wrote:
> >>
> >>> OK, are these WN unique words and WM ideas ?
> >>>
> >>> FISON
> >>
> >> Nope. IIRC "Virgil" coined that term. It 's just short for "finite initial segment of natural numbers" or "finite initial segment of IN".
> >
> > Yes, it is Virgil's word.
> >
> some other troll on the internet.

Fuck you, you silly idiot.

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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 - Fri, 26 Aug 2022 16:35 UTC

On Friday, 26 August 2022 at 00:56:21 UTC-4, zelos idiot wrote:
> torsdag 25 augusti 2022 kl. 15:40:21 UTC+2 skrev WM:
> schrieb am Donnerstag, 25. August 2022 um 07:29:56 UTC+2:
> > > onsdag 24 augusti 2022 kl. 14:22:06 UTC+2 skrev WM:
> >
> > > > All definable elements have ℵ₀ successors
> > > > ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
> > > That is again all of N, so N_def=N
> > >
> > > > All elements have no succesors
> > >
> > > False, all elements have infinitely many successors
> > >
> > > > ℕ \ {1, 2, 3, ...} = { }
> > >
> > > It is true for any set.
> > What makes the difference between all elements and the set?
> > S\S={}
> > > So fucking what?
> > This which a serious mathematician cannot deny:
> > (1) The intersection of inclusion-monotonic infinite sets is infinite.
> Not necessarily.
>
> >
> > (2) By exchanging X and O the matrix
> > XOO...
> > XOO...
> > XOO...
> > ...
> > cannot lose any O.
> >
> > Regards, WM
>
> Only if you think in a step wise process which mathematics IS NOT!

Newsflash: Everything in mathematics is a stepwise process. Set theory is not mathematics.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: Gus Gassmann - Fri, 26 Aug 2022 16:40 UTC

On Friday, 26 August 2022 at 12:57:29 UTC-3, Sergio wrote:
[...]
> > Yes, it is Virgil's word.
> some other troll on the internet.

Actually, no. Not everyone who contributes to sci.math is a troll. Virgil wasn't (at leat the posts that I read).

Re: Natural numbers and vases III

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From: james.g....@att.net (Jim Burns)
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Subject: Re: Natural numbers and vases III
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by: Jim Burns - Fri, 26 Aug 2022 16:42 UTC

On 8/26/2022 10:57 AM, WM wrote:

> It is not necessary for my proof.
> Each nonempty endsegment has at least one
> natnumber in common with all non-empty
> endsegments.
> Assume not.

Assume not.
Assume no natural number is in common
with all non-empty end segments.

A is a non-empty end segment.
There is some a ∈ A
and some non-empty B, a ∉ B

But B is also non-empty.
There is some b ∈ B
and some non-empty C, b ∉ C

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

How do you know A = C?

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

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