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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
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	FredJeffries
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
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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
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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
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
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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	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	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	FredJeffries
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	FredJeffries
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	Gus Gassmann
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	FromTheRafters
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Fritz Feldhase
Re: Natural numbers and vases III	zelos...@gmail.com
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Eduardo Faqtardo
Re: Natural numbers and vases III	Eram semper recta
Re: Natural numbers and vases III	Archimedes Plutonium
Re: Natural numbers and vases III	Archimedes Plutonium

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Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Mon, 1 Aug 2022 11:11 UTC

Gus Gassmann schrieb am Sonntag, 31. Juli 2022 um 15:44:23 UTC+2:
> On Sunday, 31 July 2022 at 09:08:42 UTC-3, WM wrote:
> [...]
> > That is the impression of blind lookers. There are many dark numbers before omega, alas they cannot be put in order. Their order cannot be discerned.
> And still none of them is the last,

As I said, they cannot be put in order.

Proof: Take the intersection of all endsegments which together have an infinite intersection. You cannot define other endsegments. But you claim that there are more, namely enough to yield an empty intersection. Dark endsegments.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Mon, 1 Aug 2022 11:16 UTC

William schrieb am Sonntag, 31. Juli 2022 um 17:03:35 UTC+2:
> On Sunday, July 31, 2022 at 8:20:01 AM UTC-3, WM wrote:
>
> indeed "all endsegments is {E(k) : k ∈ ℕ} but ∩{E(k) : k ∈ ℕ} is not the state of a stepwise process
> > you agree: all and nothing else. If there are all in a linear process or sequence,
> >but no last exists or can be determined,
> indeed, each element has a successor, so no element is the last.

But for most elements the successor cannot be named.

> > then there is a subset of elements which cannot be ordered or distinguished.
> No. Does not follow and is not True.

For proof take the intersection of all endsegments which together have an infinite intersection. You cannot define other endsegments. But you claim that there are more, namely enough to yield an empty intersection. Dark endsegments.

The fact that something does not exist does not mean a subset exists.

Do all definable endsegments have infinite intersections together? Try to define more. Fail. But you claim that there are more endsegments. Or should the same endsegments have another intersection if you utter the spell "infinite"? Then all nonsense would defeat logic.

> |N is infinite |N does not contain "dark elements".

Refuted above.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Mon, 1 Aug 2022 11:25 UTC

Fritz Feldhase schrieb am Sonntag, 31. Juli 2022 um 18:08:26 UTC+2:
> On Sunday, July 31, 2022 at 2:08:42 PM UTC+2, WM wrote:
>
> > There are many dark numbers before omega, alas they cannot be put in order.
> Then they aren't natural numbers, since the set of natural numbers is totally orderd by the usual order on IN.

That is the collection of definable natnumbers. It is not a set.
>
> This means, that for any two natural numbers WM and WM', either WM' < WM, WM' = WM, or WM < WM'.

Then there are no endsegments because there is no actual infinity.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Mon, 1 Aug 2022 11:28 UTC

Fritz Feldhase schrieb am Sonntag, 31. Juli 2022 um 18:14:53 UTC+2:
> On Sunday, July 31, 2022 at 2:17:48 PM UTC+2, WM wrote:
> > Jim Burns schrieb am Sonntag, 31. Juli 2022 um 03:22:06 UTC+2:
> >
> > Take the intersection of all endsegments which together have an infinite intersection.
> I'd like to take the set "of all endsegments which together have an infinite intersection" first.

There is nosuch set.
>
> Can you define that set using the usual symbolic language of set theory?

The collection is {E(k) | k ∈ ℕ_def /\ ∩{E(1), E(2), ..., E(k) = E(k) /\ |E(k)| = ℵ₀}

Regards, WM

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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 - Mon, 1 Aug 2022 11:38 UTC

On Monday, 1 August 2022 at 08:16:27 UTC-3, WM wrote:
> William schrieb am Sonntag, 31. Juli 2022 um 17:03:35 UTC+2:
> > On Sunday, July 31, 2022 at 8:20:01 AM UTC-3, WM wrote:
> >
> > indeed "all endsegments is {E(k) : k ∈ ℕ} but ∩{E(k) : k ∈ ℕ} is not the state of a stepwise process
> > > you agree: all and nothing else. If there are all in a linear process or sequence,
> > >but no last exists or can be determined,
> > indeed, each element has a successor, so no element is the last.
> But for most elements the successor cannot be named.

For every natural number n, the successor can be identified by the successor operation S(n). Hell, you clearly are too demented to know where you can dump your shit. Next time use a bathroom, if you still know how.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Mon, 1 Aug 2022 12:21 UTC

Jim Burns schrieb am Sonntag, 31. Juli 2022 um 22:10:17 UTC+2:
> On 7/31/2022 8:17 AM, WM wrote:

> Dark means that they can WM-complete
> a WM-incomplete collection.

I have neither found the actually infinite nor the potentially infinite.
>
> Things which can WM-complete a WM-incomplete set
> are not things the rest of us are talking about.

Then you must deny to talk about endsegments. The intersection of all endsegments which together have an infinite intersection does not exist either. You cannot define other endsegments.

> > But you claim that all natural numbers are
> > definable
> I claim that natural numbers are things in FISONs.
> It's a definition.

Then you have to abolish actual infinity.
>
> > Take the intersection of all endsegments which
> > together have an infinite intersection.

> The intersection of _all_ end segments
> has nothing in it.

Therefore you should only take those endsegments which have infinitely many elements in common.

> > You cannot define other endsegments.
> > But you claim that there are more,
> > namely enough to yield an empty intersection.
> _These_ end segments by themselves
> have an empty intersection.

Not any of them which you can define individually.
> It is _all_ of _these_ end segments
> which have an empty intersection.

Not those which have an infinite intersection together. Such are existing:
∀k ∈ ℕ_def: ∩{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = ℵ₀ .

Regards, WM

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by: WM - Mon, 1 Aug 2022 12:26 UTC

Jim Burns schrieb am Sonntag, 31. Juli 2022 um 23:24:25 UTC+2:

> > The intersection of _all_ end segments
> > has nothing in it.
> This, I meant to say.

Agreed. But there are subcollections the intersections of which have something in it. And all endsegments which you can define individually belong to these collections.

Regards, WM

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Subject: Re: Natural numbers and vases III
From: zelos.ma...@gmail.com (zelos...@gmail.com)
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by: zelos...@gmail.com - Mon, 1 Aug 2022 12:33 UTC

måndag 1 augusti 2022 kl. 13:25:12 UTC+2 skrev WM:
> Fritz Feldhase schrieb am Sonntag, 31. Juli 2022 um 18:08:26 UTC+2:
> > On Sunday, July 31, 2022 at 2:08:42 PM UTC+2, WM wrote:
> >
> > > There are many dark numbers before omega, alas they cannot be put in order.
> > Then they aren't natural numbers, since the set of natural numbers is totally orderd by the usual order on IN.
> That is the collection of definable natnumbers. It is not a set.
> >
> > This means, that for any two natural numbers WM and WM', either WM' < WM, WM' = WM, or WM < WM'.
> Then there are no endsegments because there is no actual infinity.
> For proof take the intersection of all endsegments which together have an infinite intersection. You cannot define other endsegments. But you claim that there are more, namely enough to yield an empty intersection.
> Regards, WM
there is infinity, get over it already you crank

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: zelos...@gmail.com - Mon, 1 Aug 2022 12:34 UTC

måndag 1 augusti 2022 kl. 13:28:50 UTC+2 skrev WM:
> Fritz Feldhase schrieb am Sonntag, 31. Juli 2022 um 18:14:53 UTC+2:
> > On Sunday, July 31, 2022 at 2:17:48 PM UTC+2, WM wrote:
> > > Jim Burns schrieb am Sonntag, 31. Juli 2022 um 03:22:06 UTC+2:
> > >
> > > Take the intersection of all endsegments which together have an infinite intersection.
> > I'd like to take the set "of all endsegments which together have an infinite intersection" first.
> There is nosuch set.

Correct, because it si horseshit.

> >
> > Can you define that set using the usual symbolic language of set theory?
> The collection is {E(k) | k ∈ ℕ_def /\ ∩{E(1), E(2), ..., E(k) = E(k) /\ |E(k)| = ℵ₀}
>
> Regards, WM

your N_def = N so you have said nothing

Re: Natural numbers and vases III

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From: inva...@invalid.com (Sergio)
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Subject: Re: Natural numbers and vases III
Date: Mon, 1 Aug 2022 08:39:43 -0500
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by: Sergio - Mon, 1 Aug 2022 13:39 UTC

On 8/1/2022 6:28 AM, WM wrote:
> Fritz Feldhase schrieb am Sonntag, 31. Juli 2022 um 18:14:53 UTC+2:
>> On Sunday, July 31, 2022 at 2:17:48 PM UTC+2, WM wrote:
>>> Jim Burns schrieb am Sonntag, 31. Juli 2022 um 03:22:06 UTC+2:
>>>
>>> Take the intersection of all endsegments which together have an infinite intersection.
>> I'd like to take the set "of all endsegments which together have an infinite intersection" first.
>
> There is nosuch set.
>>
>> Can you define that set using the usual symbolic language of set theory?
>
> The collection is {E(k) | k ∈ ℕ_def /\ ∩{E(1), E(2), ..., E(k) = E(k) /\ |E(k)| = ℵ₀}

wrong, try again, without using your bogus "_def" . Fail

>
> Regards, WM

Re: Natural numbers and vases III

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by: Sergio - Mon, 1 Aug 2022 13:40 UTC

On 8/1/2022 7:26 AM, WM wrote:
> Jim Burns schrieb am Sonntag, 31. Juli 2022 um 23:24:25 UTC+2:
>
>
>>> The intersection of _all_ end segments
>>> has nothing in it.
>> This, I meant to say.
>
> Agreed. But there are subcollections the intersections of which have something in it. And all endsegments which you can define individually belong to these collections.

wrong on its face, too general. Try again.

>
> Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
Date: Mon, 1 Aug 2022 08:45:57 -0500
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by: Sergio - Mon, 1 Aug 2022 13:45 UTC

On 8/1/2022 7:21 AM, WM wrote:
> Jim Burns schrieb am Sonntag, 31. Juli 2022 um 22:10:17 UTC+2:
>> On 7/31/2022 8:17 AM, WM wrote:
>
>> Dark means that they can WM-complete
>> a WM-incomplete collection.
>
> I have neither found the actually infinite nor the potentially infinite.
>>
>> Things which can WM-complete a WM-incomplete set
>> are not things the rest of us are talking about.
>
> Then you must deny to talk about endsegments. The intersection of all endsegments which together have an infinite intersection does not exist either. You cannot define other endsegments.
>
>>> But you claim that all natural numbers are
>>> definable
>> I claim that natural numbers are things in FISONs.
>> It's a definition.
>
> Then you have to abolish actual infinity.

not at all. each natural number is in a FISON. The set of natural numbers is infinite.

you generalize too much.

>>
>>> Take the intersection of all endsegments which
>>> together have an infinite intersection.
>
>> The intersection of _all_ end segments
>> has nothing in it.
>
> Therefore you should only take those endsegments which have infinitely many elements in common.

Why ? for what reason ?

>
>>> You cannot define other endsegments.
>>> But you claim that there are more,
>>> namely enough to yield an empty intersection.
>> _These_ end segments by themselves
>> have an empty intersection.
>
> Not any of them which you can define individually.

again, your "defined" using beeps, raps, taps is Quackers.

you do realize that your daffynition makes raps, beeps, flashes, equivelent to FISONs, right ?

>
>> It is _all_ of _these_ end segments
>> which have an empty intersection.
>
> Not those which have an infinite intersection together. Such are existing:
> ∀k ∈ ℕ_def: ∩{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = ℵ₀ .

∀k ∈ ℕ: ∩{E(1), E(2), ..., E(k)} = E(k) /\ |E(k)| = ℵ₀ .

is trivial.

>
> Regards, WM

Re: Natural numbers and vases III

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by: Sergio - Mon, 1 Aug 2022 13:55 UTC

On 8/1/2022 6:16 AM, WM wrote:
> William schrieb am Sonntag, 31. Juli 2022 um 17:03:35 UTC+2:
>> On Sunday, July 31, 2022 at 8:20:01 AM UTC-3, WM wrote:
>>
>> indeed "all endsegments is {E(k) : k ∈ ℕ} but ∩{E(k) : k ∈ ℕ} is not the state of a stepwise process
>>> you agree: all and nothing else. If there are all in a linear process or sequence,
>>> but no last exists or can be determined,
>> indeed, each element has a successor, so no element is the last.
>
> But for most elements the successor cannot be named.

only if you deny induction.

>
>>> then there is a subset of elements which cannot be ordered or distinguished.
>> No. Does not follow and is not True.
>
> For proof take the intersection of all endsegments which together have an infinite intersection.

Wrong. and you have no proof at all, because it is wrong.

> You cannot define other endsegments.

sure thy can, E(17), there you go.

> But you claim that there are more, namely enough to yield an empty intersection. Dark endsegments.

no, that is Dark bullshit.

>
> The fact that something does not exist does not mean a subset exists.

Another Keeper!!

>
> Do all definable endsegments have infinite intersections together? Try to define more. Fail. But you claim that there are more endsegments. Or should the same endsegments have another intersection if you utter the spell "infinite"? Then all nonsense would defeat logic.

all you nonsense is a bogus on its face, you are lost in your own BS.

>
>> |N is infinite |N does not contain "dark elements".
>
> Refuted above.

bogus.

>
> Regards, WM

Re: Natural numbers and vases III

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Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 1 Aug 2022 08:57:53 -0500
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by: Sergio - Mon, 1 Aug 2022 13:57 UTC

On 8/1/2022 6:11 AM, WM wrote:
> Gus Gassmann schrieb am Sonntag, 31. Juli 2022 um 15:44:23 UTC+2:
>> On Sunday, 31 July 2022 at 09:08:42 UTC-3, WM wrote:
>> [...]
>>> That is the impression of blind lookers. There are many dark numbers before omega, alas they cannot be put in order. Their order cannot be discerned.
>> And still none of them is the last,
>
> As I said, they cannot be put in order.

wrong. there is no "they",

there are no dark numbers, they do not exist, they are unknown.

>
> Proof: Take the intersection of all endsegments which together have an infinite intersection. You cannot define other endsegments. But you claim that there are more, namely enough to yield an empty intersection. Dark endsegments.

that is Spoof, not a proof. You do have a vomitorium in all your classes, right ?

>
> 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 - Mon, 1 Aug 2022 14:34 UTC

On Monday, August 1, 2022 at 8:16:27 AM UTC-3, WM wrote:

> Do all definable endsegments have infinite intersections together?

Yes. So what? Each "definable" endsegment has a first element with the property that it can be written down. There are endsegments for which the first element does not have the property that it can be written down.

--
William Hughes

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, 2 Aug 2022 15:29 UTC

William schrieb am Montag, 1. August 2022 um 16:34:17 UTC+2:
> On Monday, August 1, 2022 at 8:16:27 AM UTC-3, WM wrote:
>
> > Do all definable endsegments have infinite intersections together?
> Yes. So what? Each "definable" endsegment has a first element with the property that it can be written down

and that the intersection is infinite: |∩{E(1), E(2), ..., E(k)}| = ℵ₀

>There are endsegments for which the first element does not have the property that it can be written down.

Only those can reduce the infinite intersection to the empty set.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Tue, 2 Aug 2022 15:31 UTC

zelos...@gmail.com schrieb am Montag, 1. August 2022 um 14:34:41 UTC+2:
> måndag 1 augusti 2022 kl. 13:28:50 UTC+2 skrev WM:

> > > Can you define that set using the usual symbolic language of set theory?
> > The collection is {E(k) | k ∈ ℕ_def /\ ∩{E(1), E(2), ..., E(k) = E(k) /\ |E(k)| = ℵ₀}
> >
> your N_def = N so you have said nothing

If you claim that the intersection of all definable endsegments is empty, then define individually endsegments reducing the infinite intersection to the empty set.

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, 2 Aug 2022 16:10 UTC

On Tuesday, August 2, 2022 at 5:31:40 PM UTC+2, WM wrote:
> zelos...@gmail.com schrieb am Montag, 1. August 2022 um 14:34:41 UTC+2:
> >
> > Your N_def = N so you have said nothing.
> >
> If you claim that the intersection of all [...] endsegments is empty, then define [specific] endsegments reducing the infinite intersection to the empty set.

There are no such endsegments, you silly crank.

Hint: INTERSECTION {E(1), E(3), E(5), ...} = INTERSECTION {E(2), E(4), E(6), ...} = { }.

In general: If M is an arbitrary (proper subset of the) set of endsegments, then INTERSECTION ({E(1), E(2), E(3), ...} \ M) = { } iff {E(1), E(2), E(3), ...} \ M is infinite.

It's the NUMBER of endsegments which counts, dumbo: If the number of endsegments in S is infinite, then INTERSECTION S = { }, if the number of endsegments in S is finite (but not zero), then INTERSECTION S is infinite.

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, 2 Aug 2022 16:46 UTC

On Tuesday, August 2, 2022 at 12:29:36 PM UTC-3, WM wrote:
> William schrieb am Montag, 1. August 2022 um 16:34:17 UTC+2:

> >There are endsegments for which the first element does not have the property that it can be written down.
> Only those can reduce the infinite intersection to the empty set.

So what? They do reduce the infinite intersection to the empty set.

--
William Hughes

Re: Natural numbers and vases III

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by: Sergio - Tue, 2 Aug 2022 17:16 UTC

On 8/2/2022 10:31 AM, WM wrote:
> zelos...@gmail.com schrieb am Montag, 1. August 2022 um 14:34:41 UTC+2:
>> måndag 1 augusti 2022 kl. 13:28:50 UTC+2 skrev WM:
>
>>>> Can you define that set using the usual symbolic language of set theory?
>>> The collection is {E(k) | k ∈ ℕ_def /\ ∩{E(1), E(2), ..., E(k) = E(k) /\ |E(k)| = ℵ₀}
>>>
>> your N_def = N so you have said nothing
>
> If you claim that the intersection of all definable endsegments is empty, then define individually endsegments reducing the infinite intersection to the empty set.
nope. Try again. Try without using your ill "defined", it is your crutch, and it makes your math bogus.

> Regards, WM

Re: Natural numbers and vases III

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by: Sergio - Tue, 2 Aug 2022 17:17 UTC

On 8/2/2022 11:46 AM, William wrote:
> On Tuesday, August 2, 2022 at 12:29:36 PM UTC-3, WM wrote:
>> William schrieb am Montag, 1. August 2022 um 16:34:17 UTC+2:
>
>>> There are endsegments for which the first element does not have the property that it can be written down.
>> Only those can reduce the infinite intersection to the empty set.
>
> So what? They do reduce the infinite intersection to the empty set.
>
> --
> William Hughes

WM does not know what an operator is.

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Tue, 2 Aug 2022 20:36 UTC

Fritz Feldhase schrieb am Dienstag, 2. August 2022 um 18:10:39 UTC+2:
> On Tuesday, August 2, 2022 at 5:31:40 PM UTC+2, WM wrote:
> > zelos...@gmail.com schrieb am Montag, 1. August 2022 um 14:34:41 UTC+2:
> > >
> > > Your N_def = N so you have said nothing.
> > >
> > If you claim that the intersection of all [...] endsegments is empty, then define [specific] endsegments reducing the infinite intersection to the empty set.
>
> There are no such endsegments,

There are.

Proof 1: All definabl,e endsegments which are specified by
∀k ∈ ℕ_def: |∩{E(1), E(2), ..., E(k)}| = ℵ₀
cannot have an empty intersection because their position is irrelevant.

Proof 2: All definable endsegments can be subtracted from the set of endsegments with no change of the resulting empty intersection
∩{E(k) : k ∈ ℕ} = { } = ∩{E(k) : k > n ∈ ℕ_def}

> It's the NUMBER of endsegments which counts,

That appears so, caused by the fact that there are ℵ₀-infinitely many dark endsegments but only potentially infinitely many definable endsegments with
|∩{E(k) : k ∈ ℕ_def}| = ℵ₀

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Tue, 2 Aug 2022 20:38 UTC

William schrieb am Dienstag, 2. August 2022 um 18:46:56 UTC+2:
> On Tuesday, August 2, 2022 at 12:29:36 PM UTC-3, WM wrote:
> > William schrieb am Montag, 1. August 2022 um 16:34:17 UTC+2:
>
> > >There are endsegments for which the first element does not have the property that it can be written down.
> > Only those can reduce the infinite intersection to the empty set.
> So what? They do reduce the infinite intersection to the empty set.

Great. Finally we have reached agreement.

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, 2 Aug 2022 20:53 UTC

On Tuesday, August 2, 2022 at 5:38:06 PM UTC-3, WM wrote:

> Great. Finally we have reached agreement.

WM : The intersection of the endsegments is the empty set.

WM: The intersection of the "defined" (i.e. the first element has the property that it can be written down) endsegments is an infinite set.

This is a triviality.

--
WIlliam Hughes

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: franz.fr...@gmail.com (Fritz Feldhase)
Injection-Date: Tue, 02 Aug 2022 21:15:22 +0000
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by: Fritz Feldhase - Tue, 2 Aug 2022 21:15 UTC

On Tuesday, August 2, 2022 at 10:36:29 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Dienstag, 2. August 2022 um 18:10:39 UTC+2:
> > On Tuesday, August 2, 2022 at 5:31:40 PM UTC+2, WM wrote:
> > > zelos...@gmail.com schrieb am Montag, 1. August 2022 um 14:34:41 UTC+2:
> > > >
> > > > Your N_def = N so you have said nothing.
> > > >
> > > If you claim that the intersection of all [...] endsegments is empty, then define [specific] endsegments reducing the infinite intersection to the empty set.
> >
> > There are no such endsegments,
> >
> There are.

No, there aren't. Hint: INTERSECTION {E(1), E(3), E(5), ...} = INTERSECTION {E(2), E(4), E(6), ...} = { }.

In general: If M is an arbitrary (proper subset of the) set of endsegments, then INTERSECTION ({E(1), E(2), E(3), ...} \ M) = { } iff {E(1), E(2), E(3), ...} \ M is infinite.

> > It's ONLY the NUMBER of endsegments which counts, dumbo.
> >
> That <bla>

Hint: Let S b a nonempty set of endsegments. If the number of endsegments in S is infinite, then INTERSECTION S = { }, if the number of endsegments in S is finite (but not zero), then INTERSECTION S is infinite.

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

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