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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	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
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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	William
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	William
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Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	William
Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
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Re: Natural numbers and vases III	WM
Re: Natural numbers and vases III	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, 29 Aug 2022 13:32 UTC

zelos...@gmail.com schrieb am Montag, 29. August 2022 um 12:31:44 UTC+2:
> måndag 29 augusti 2022 kl. 11:26:27 UTC+2 skrev WM:

> > But that is wrong without an empty endsegment, contradicted by
> > (1) a ∈ A
> > (2) b ∈ B
> > (3) a ∉ B
> > (4) b ∉ A.
> > All which fail and are not empty have an element in common.

> you still do not understand how intersections work

If they work, they are working, they are processes. Otherwise they could only *be*.

Regards, WM

Re: Q

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Subject: Re: Q
From: askaske...@gmail.com (WM)
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by: WM - Mon, 29 Aug 2022 13:38 UTC

Fritz Feldhase schrieb am Montag, 29. August 2022 um 13:00:40 UTC+2:
>
> => There is no natural number in INTERSECTION {E(k) : k e IN}.

Then there is no infinite subset in all endsegments.
>
> ALL that is needed for this result is that for each and every n e IN:
>
> ___ Ek e IN: n !e E(k)__.
>

Then an empty endsegment must appear. If the intersection gets empty, then the sequence of endsegments gets empty too = has the limit empty endsegment.

But endsegments can only decrease in steps. And every step removes only one natural number.

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, 29 Aug 2022 13:44 UTC

Jim Burns schrieb am Montag, 29. August 2022 um 13:53:20 UTC+2:
> On 8/29/2022 5:15 AM, WM wrote:

> If 𝐹 is a FISON,
> then 𝐹 is in ___.
> If 𝐹 is in ___,
> then 𝐹 is a FISON,
>
> Is ___ a set?

No.
>
> If ___ is not a set,
> then what can be added?
> Nothing which is a FISON.

A FISON exists only if it can be named individually. Every FISON that can be named has successors. Therefore there is never completeness.

Your letters are not readable.

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, 29 Aug 2022 13:47 UTC

Jim Burns schrieb am Montag, 29. August 2022 um 14:04:19 UTC+2:
> On 8/29/2022 7:53 AM, Jim Burns wrote:
> > On 8/29/2022 5:15 AM, WM wrote:
>
> >> ∩{E(n) | n ∈ ℕ_def} =/= { }.

The collection {E(n) | n ∈ ℕ_def} exists. For instance the first 10^100 endsegments belong to it. You cannot define an endsegment that does not belong to it.

> What I meant to say

You should express that with simple letters.

Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: thenewca...@gmail.com (Eram semper recta)
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by: Eram semper recta - Mon, 29 Aug 2022 13:52 UTC

On Monday, 29 August 2022 at 05:26:27 UTC-4, WM wrote:
> Jim Burns schrieb am Sonntag, 28. August 2022 um 19:32:44 UTC+2:
> > On 8/28/2022 10:24 AM, WM wrote:
>
> > > The conditions (1) to (4) cannot be satisfied
> > > together with non-empty endsegnments.
> > Conditions (1) to (4) don't need to be
> > satisfied for their intersection to be empty.
> >
> > For an empty intersection of all,
> > we only need each element in any end segment
> > to be not-in some other end segment.
> But that is wrong without an empty endsegment, contradicted by
> (1) a ∈ A
> (2) b ∈ B
> (3) a ∉ B
> (4) b ∉ A.
> All which fail and are not empty have an element in common.

It's amusing that in their die-hard attempts to save set theory, set theorists (Jim Burns, etc) tend to overlook the basic details as pointed out, that is, a ∈ A, b ∈ B, a ∉ B, b ∉ A. Tsk, tsk.

You still haven't told me what you think about the proof ∞-∞=0:

https://www.academia.edu/78740399/Georg_Cantor_the_father_of_all_mainstream_mathematical_cranks

>
> 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, 29 Aug 2022 14:02 UTC

> > > On 8/28/2022 10:24 AM, WM wrote:
> It's amusing that in their die-hard attempts to save set theory, set theorists (Jim Burns, etc) tend to overlook the basic details as pointed out, that is, a ∈ A, b ∈ B, a ∉ B, b ∉ A. Tsk, tsk.
>
> You still haven't told me what you think about the proof ∞-∞=0:
>
oo for me means a direction, not a quantity.

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 - Mon, 29 Aug 2022 14:07 UTC

On Monday, August 29, 2022 at 3:27:52 PM UTC+2, WM wrote:

> you are not aware of the fact that dark numbers exist and that your proofs are invalid for dark numbers.

Yeah, I have to admit that I'm indeed not aware of these "facts".

Hint: Your psychosis is connected with delusions.

> > We can prove that for all natural numbers n: n + n = 2*n.
> >
> And we can check that for <bla>

Who cares you psychotic idiot?

And now fuck off!

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 - Mon, 29 Aug 2022 14:19 UTC

On Monday, August 29, 2022 at 4:02:08 PM UTC+2, WM wrote:

> oo for me means a direction, not a quantity.

Fascinating, Mückenheim!

Try to learn some real math, idiot!

https://en.wikipedia.org/wiki/Extended_real_number_line

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 - Mon, 29 Aug 2022 14:33 UTC

On Monday, August 29, 2022 at 3:47:26 PM UTC+2, WM wrote:

∩{E(n) | n ∈ ℕ_def} =/= { }. [with ℕ_def c IN]

> The collection {E(n) | n ∈ ℕ_def} exists. For instance the first 10^100 endsegments belong to it. You cannot define an endsegment that does not belong to it.

Of course, we can, you psychotic asshole.

Hint: If ∩{E(n) | n ∈ ℕ_def} =/= { }, then ℕ_def c IN is finite.*) Hence {E(n) | n ∈ ℕ_def} contains a minimal endsegment, namely ∩{E(n) | n ∈ ℕ_def}, Hence there's a natural number k e IN such that E(k) = ∩{E(n) | n ∈ ℕ_def}. Now let E = E(k+1), then E !e {E(n) | n ∈ ℕ_def} (since E(k+1) c E(k) and hence E(k+1) !e {E(n) | n ∈ ℕ_def}). qed
----------------------------------------------
*) If IN_Def were infinite, then we would have ∩{E(n) | n ∈ ℕ_def} = { }.

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 - Mon, 29 Aug 2022 14:39 UTC

On Monday, August 29, 2022 at 3:47:26 PM UTC+2, WM wrote:

∩{E(n) | n ∈ ℕ_def} =/= { }. [with ℕ_def c IN]

> The collection {E(n) | n ∈ ℕ_def} exists. For instance the first 10^100 endsegments belong to it. You cannot define an endsegment that does not belong to it.

Of course, we can, you psychotic asshole.

Hint: If ∩{E(n) | n ∈ ℕ_def} =/= { }, then ℕ_def c IN is finite.*) Hence {E(n) | n ∈ ℕ_def} contains a minimal endsegment, namely ∩{E(n) | n ∈ ℕ_def}, Let k0 be the natural number such that E(k) = ∩{E(n) | n ∈ ℕ_def}. Now let E = E(k0+1), then E !e {E(n) | n ∈ ℕ_def} (since E(k0+1) c E(k0) and hence E(k0+1) !e {E(n0) | n ∈ ℕ_def}). qed
----------------------------------------------
*) If IN_Def were infinite, then we would have ∩{E(n) | n ∈ ℕ_def} = { }.

Re: Natural numbers and vases III

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 29 Aug 2022 10:48:03 -0400
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by: Jim Burns - Mon, 29 Aug 2022 14:48 UTC

On 8/29/2022 9:30 AM, WM wrote:
> zelos...@gmail.com schrieb am Montag,
> 29. August 2022 um 12:32:41 UTC+2:

>> A sequence is not a stepwise process.
>> It is a function from N to S.
>
> ℕ is a stepwise ordered set.

A FISON can represent a process.
It has a first element.
It has a prescribed relationship
between neighboring elements.
_It has a last element_

For example,
a FISON can index the states a Turing machine
enters during a terminating computation.
A terminating computation enters a last state.

The set of all FISONs contains all
things-that-can-represent-a-process.

Very closely related to the set of all FISONs,
there is the set of all FISON-ends.

In many ways, working with the set of all
FISON-ends is the same as working with
the set of all FISONs.
For each FISON, there is a unique FISON-end.
For each FISON-end, there is a unique FISON.

Just like a FISON, the set of all FISON-ends
has 0 as a first element.

Just like a FISON, the set of all FISON-ends
has the relationship i,i+1 between
neighboring elements.

However,
unlike a FISON, the set of all FISON-ends
does not end anywhere.

The set of all FISON-ends
(the set of all FISONs)
does not represent any one process.

The set of all FISON-ends
represents all processes.

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 - Mon, 29 Aug 2022 14:48 UTC

On Monday, August 29, 2022 at 3:47:26 PM UTC+2, WM wrote:

> ∩{E(n) | n ∈ ℕ_def} =/= { }. [with ℕ_def c IN]
>
> The collection {E(n) | n ∈ ℕ_def} exists. For instance the first 10^100 endsegments belong to it. You cannot define an endsegment that does not belong to it.

Of course, we can, you psychotic asshole.

Hint: If ∩{E(n) | n ∈ ℕ_def} =/= { }, then ℕ_def c IN is finite.*) Hence {E(n) | n ∈ ℕ_def} contains a minimal endsegment, namely ∩{E(n) | n ∈ ℕ_def}, Let k0 be the natural number k such that E(k) = ∩{E(n) | n ∈ ℕ_def}. Now __let E = E(k0+1)__, then E !e {E(n) | n ∈ ℕ_def} (since E(k0+1) c E(k0) and hence E(k0+1) !e {E(n) | n ∈ ℕ_def}). qed
----------------------------------------------
*) If IN_Def were infinite, then we would have ∩{E(n) | n ∈ ℕ_def} = { }.

In other words, __the successor of the smallest endsegent in {E(n) | n ∈ ℕ_def}__ does not belong to ∩{E(n) | n ∈ ℕ_def}.

Hint: If there were no smallest endsegment in {E(n) | n ∈ ℕ_def}, then {E(n) | n ∈ ℕ_def} would be infinite, and hence we would have ∩{E(n) | n ∈ ℕ_def} = { }. But since we don't have ∩{E(n) | n ∈ ℕ_def} = { } (as you claim), {E(n) | n ∈ ℕ_def} contains a smallest endsegment..

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 - Mon, 29 Aug 2022 14:49 UTC

On Monday, 29 August 2022 at 10:30:55 UTC-3, WM wrote:
[...]
> ℕ is a stepwise ordered set.

ℕ is a set that can be ordered, but there is nothing stepwise about the order. Hint: How do you establish that Graham's number is larger than 1? Certainly not by establishing that 2 > 1, 3 > 1, 4 > 1, ..., (Graham's number - 1) > 1, Graham's number > 1.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: Sergio - Mon, 29 Aug 2022 15:07 UTC

On 8/29/2022 8:32 AM, WM wrote:
> zelos...@gmail.com schrieb am Montag, 29. August 2022 um 12:31:44 UTC+2:
>> måndag 29 augusti 2022 kl. 11:26:27 UTC+2 skrev WM:
>
>>> But that is wrong without an empty endsegment, contradicted by
>>> (1) a ∈ A
>>> (2) b ∈ B
>>> (3) a ∉ B
>>> (4) b ∉ A.
>>> All which fail and are not empty have an element in common.
>
>> you still do not understand how intersections work
>
> If they work, they are working, they are processes. Otherwise they could only *be*.

wrong, they are operators on sets.

>
> 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, 29 Aug 2022 15:10 UTC

On Monday, August 29, 2022 at 6:20:57 AM UTC-3, WM wrote:
> William schrieb am Sonntag, 28. August 2022 um 18:27:31 UTC+2:
> > On Sunday, August 28, 2022 at 10:52:02 AM UTC-3, WM wrote:
> > > William schrieb am Samstag, 27. August 2022 um 17:19:36 UTC+2:
> > > > On Saturday, August 27, 2022 at 10:44:04 AM UTC-3, WM wrote:
> > > > > ... you must find an endsegment which contains some elements not in a predecessor.
> > > >
> > > > Nope. No such endsegment is needed in order to get an empty intersection
> > > It is needed if all endsegments are nonempty. The only alternative would be an empty endsegment.
> > Piffle. There is also the alternative that there is no last endsegment.
> All endsegments which are there fail to satisfy
> (1) a ∈ A
> (2) b ∈ B
> (3) a ∉ B
> (4) b ∉ A.

Piffle. No pair of endsengmens satisfies 2 and 4. So what?

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, 29 Aug 2022 15:14 UTC

On Monday, August 29, 2022 at 6:26:27 AM UTC-3, WM wrote:

> (1) a ∈ A
> (2) b ∈ B
> (3) a ∉ B
> (4) b ∉ A.
> All which fail and are not empty have an element in common.

But not the same element. Given and two endsegments A and B there is a common element b(A,B). However, there is no one element b which works for any A and B

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Subject: Re: Natural numbers and vases III
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by: Jim Burns - Mon, 29 Aug 2022 15:32 UTC

On 8/29/2022 10:49 AM, Gus Gassmann wrote:
> On Monday, 29 August 2022 at 10:30:55 UTC-3,
> WM wrote:

>> ℕ is a stepwise ordered set.
>
> ℕ is a set that can be ordered,
> but there is nothing stepwise about the order.

It seems as though that would depend upon what
"stepwise ordered" means.

WM seems to at least passively accept
when I translate
"stepwise ordered"
as
"for each split, a step exists with
a last before and a first after".

It is true of the standard order of ℕ that,
for each split, a step exists with
a last before and a first after.

I would say that makes it a stepwise order.

If not that, what does "stepwise order" mean?

> Hint:
> How do you establish that
> Graham's number is larger than 1?
> Certainly not by establishing that 2
> > 1, 3 > 1, 4 > 1, ...,
> (Graham's number - 1) > 1, Graham's number > 1.

On the other hand,
for each split of the numbers from 1 to
Graham's number, there is a last i before
and a first j after, with j = i+1.

Re: Natural numbers and vases III

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Date: Mon, 29 Aug 2022 11:45:30 -0400
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by: Jim Burns - Mon, 29 Aug 2022 15:45 UTC

On 8/29/2022 9:32 AM, WM wrote:
> zelos...@gmail.com schrieb am Montag,
> 29. August 2022 um 12:31:44 UTC+2:
>> måndag 29 augusti 2022 kl.
>> 11:26:27 UTC+2 skrev WM:

>> you still do not understand how
>> intersections work
>
> If they work, they are working,
> they are processes.

Say instead that you do not understand
_how we work with intersections_

> Otherwise they could only *be*.

You got it.
Intersections *are*

The intersection of a collection of sets
*is* what contains each element which is
in each set in the collection.

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: thenewca...@gmail.com (Eram semper recta)
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by: Eram semper recta - Mon, 29 Aug 2022 16:09 UTC

On Monday, 29 August 2022 at 10:02:08 UTC-4, WM wrote:
> > > > On 8/28/2022 10:24 AM, WM wrote:
> > It's amusing that in their die-hard attempts to save set theory, set theorists (Jim Burns, etc) tend to overlook the basic details as pointed out, that is, a ∈ A, b ∈ B, a ∉ B, b ∉ A. Tsk, tsk.
> >
> > You still haven't told me what you think about the proof ∞-∞=0:
> >
> oo for me means a direction, not a quantity.

Ah, I see you've revised your thoughts.... I think you've taken a turn for the worse here. 😊😊

∞ is not seen as a direction by the mainstream. It is seen as a cardinal number.

Your arguments would not make sense with this revision. Reconsider? Chuckle..

>
> Regards, WM

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
From: thenewca...@gmail.com (Eram semper recta)
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by: Eram semper recta - Mon, 29 Aug 2022 16:12 UTC

On Monday, 29 August 2022 at 12:09:28 UTC-4, Eram semper recta wrote:
> On Monday, 29 August 2022 at 10:02:08 UTC-4, WM wrote:
> > > > > On 8/28/2022 10:24 AM, WM wrote:
> > > It's amusing that in their die-hard attempts to save set theory, set theorists (Jim Burns, etc) tend to overlook the basic details as pointed out, that is, a ∈ A, b ∈ B, a ∉ B, b ∉ A. Tsk, tsk.
> > >
> > > You still haven't told me what you think about the proof ∞-∞=0:
> > >
> > oo for me means a direction, not a quantity.
> Ah, I see you've revised your thoughts.... I think you've taken a turn for the worse here. 😊😊
>
> ∞ is not seen as a direction by the mainstream. It is seen as a cardinal number.

Is ℵ0 not the same thing as ∞ ?

>
> Your arguments would not make sense with this revision. Reconsider? Chuckle.
>
> >
> > Regards, WM

Re: Natural numbers and vases III

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From: horand.g...@gmail.com (Gus Gassmann)
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by: Gus Gassmann - Mon, 29 Aug 2022 16:43 UTC

On Monday, 29 August 2022 at 12:32:41 UTC-3, Jim Burns wrote:
> On 8/29/2022 10:49 AM, Gus Gassmann wrote:
> > On Monday, 29 August 2022 at 10:30:55 UTC-3,
> > WM wrote:
>
> >> ℕ is a stepwise ordered set.
> >
> > ℕ is a set that can be ordered,
> > but there is nothing stepwise about the order.
> It seems as though that would depend upon what
> "stepwise ordered" means.
>
> WM seems to at least passively accept
> when I translate
> "stepwise ordered"
> as
> "for each split, a step exists with
> a last before and a first after".
>
> It is true of the standard order of ℕ that,
> for each split, a step exists with
> a last before and a first after.
> I would say that makes it a stepwise order.

I see. And for the order type {1, 3, 5, ..., 2, 4, 6, ...} (or whatever bracketing is appropriate), there is a split for which this is not the case? But how is that different from a well-order? (Perhaps I am not understanding what you mean by "last before" and "first after". "Last before" what? "First after" what?

> If not that, what does "stepwise order" mean?

Well, to me it was just one of those nonsense terms that WM is so fond of introducing without defining them. I chose to interpret it literally. "One step at a time", that is, in the form I indicated: 5 > 1: 2 > 1, 3 > 1, 3 > 1, 4 > 1, 5 > 1. Separate steps. As an alternative I might have considered the stepwise process 2 > 1, 3 > 2, 4 > 3, 5 > 4. (Remember, this all started when he stated ("because [WM] said so") that "mathematics is nuffin' but steps" --- this could be right from Walt Kelly.)

> > Hint:
> > How do you establish that
> > Graham's number is larger than 1?
> > Certainly not by establishing that 2
> > > 1, 3 > 1, 4 > 1, ...,
> > (Graham's number - 1) > 1, Graham's number > 1.

> On the other hand,
> for each split of the numbers from 1 to
> Graham's number, there is a last i before
> and a first j after, with j = i+1.

Ah, OK. But again, how is that different from a well-order (on |N)?

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: FromTheRafters - Mon, 29 Aug 2022 17:26 UTC

WM wrote on 8/29/2022 :
> FromTheRafters schrieb am Montag, 29. August 2022 um 12:17:14 UTC+2:
>> WM laid this down on his screen :
>>> FromTheRafters schrieb am Sonntag, 28. August 2022 um 18:12:02 UTC+2:
>>>> WM wrote on 8/28/2022 :
>>>
>>>>> Complete does not mean a last element, but all elements are there, none
>>>>> can be added.
>>>> Then what is a set?
>>>
>>> As I said: All elements are there, none can be added.
>> That's a property of a set, what does complete mean again?
>
> Just that.

Just that some sets are growing sets in muckymath?

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From: inva...@invalid.com (Sergio)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 29 Aug 2022 12:38:19 -0500
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by: Sergio - Mon, 29 Aug 2022 17:38 UTC

On 8/29/2022 8:28 AM, WM wrote:
> FromTheRafters schrieb am Montag, 29. August 2022 um 12:17:14 UTC+2:
>> WM laid this down on his screen :
>>> FromTheRafters schrieb am Sonntag, 28. August 2022 um 18:12:02 UTC+2:
>>>> WM wrote on 8/28/2022 :
>>>
>>>>> Complete does not mean a last element, but all elements are there, none can
>>>>> be added.
>>>> Then what is a set?
>>>
>>> As I said: All elements are there, none can be added.
>> That's a property of a set, what does complete mean again?
>
> Just that.
>
> Regards, WM

how do you know it is complete ?

can one verify it is complete ?

How does one know that no elements can be added to the set ?

Which element was the last one put into the set ?

Re: Natural numbers and vases III

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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Mon, 29 Aug 2022 14:28:14 -0400
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by: Jim Burns - Mon, 29 Aug 2022 18:28 UTC

On 8/29/2022 12:43 PM, Gus Gassmann wrote:
> On Monday, 29 August 2022
> at 12:32:41 UTC-3, Jim Burns wrote:

>> WM seems to at least passively accept
>> when I translate
>> "stepwise ordered"
>> as
>> "for each split, a step exists with
>> a last before and a first after".
>>
>> It is true of the standard order of ℕ that,
>> for each split, a step exists with
>> a last before and a first after.
>> I would say that makes it a stepwise order.
>
> I see. And for the order type
> {1, 3, 5, ..., 2, 4, 6, ...}
> (or whatever bracketing is appropriate),
> there is a split for which this is not the case?
> But how is that different from a well-order?
> (Perhaps I am not understanding what
> you mean by "last before" and "first after".
> "Last before" what? "First after" what?

Sorry.
Shorter is not always better.

Last before the split,
first after the split.

I assume a total order.

A split is a two-piece partition,
both non-empty,
with each of one before each of the other.

A step from (last) before the split to
(first) after the split is required to exist.

If we add that there is a first and a last of
the whole collection, we've described a finite set
-- as defined by Paul Stäckel, well-ordered
in both directions.

I like how this approach appeals to our intuitions.
If we can only advance step-by-step, for each
split of the collection, there must be
a step across that split, or "you can't get
there from here". I think that it draws near
to an explanation of what's so special
about finite set. You _can_ get there from
here, from anywhere in the set to anywhere else
in the set.

What I call a _counting-order_ is a stepwise
order in which the required step is
an arithmetic successor, i,i+1

For the movement of an O, swapping with
X's in WM's matrix, the required step p/q,n/1
uses Cantor's formula n = (p+1-1)(p+q-2)/2+p

> I see. And for the order type
> {1, 3, 5, ..., 2, 4, 6, ...}
> (or whatever bracketing is appropriate),
> there is a split for which this is not the case?

Yes, this is an essential point.
For some orders, we can't always
"get there from here".
We can get from any odd number to any other
(odd number) (allowing back steps), and
we can get from any even number to any other
even number. We can't get from odd numbers
to even numbers or vice versa.

We can prove we can't get there, even if
we don't know what is on the other side of
the split-without-a-step (dark numbers),
because each step which starts before it
does not end after it.

My pride and joy:
a solid proof,
not so much that dark numbers don't exist,
who could say that for something so vague,
but that dark numbers don't appear in
any of the "paradoxes" that WM presents.

This, despite a near-complete absence of
information about dark numbers.

>> On the other hand,
>> for each split of the numbers from 1 to
>> Graham's number, there is a last i before
>> and a first j after, with j = i+1.
>
> Ah, OK.
> But again, how is that different from
> a well-order (on |N)?

You give a good example, {odds then evens}
You can't get from the odds to the evens,
step-by-step.

But {odds then evens} is a well-order.

_For the standard-ordered natural numbers_
you can always get from here to there,
step-by-step.

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: Mon, 29 Aug 2022 14:17:15 -0500
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by: Sergio - Mon, 29 Aug 2022 19:17 UTC

On 8/29/2022 4:20 AM, WM wrote:
> William schrieb am Sonntag, 28. August 2022 um 18:27:31 UTC+2:
>> On Sunday, August 28, 2022 at 10:52:02 AM UTC-3, WM wrote:
>>> William schrieb am Samstag, 27. August 2022 um 17:19:36 UTC+2:
>>>> On Saturday, August 27, 2022 at 10:44:04 AM UTC-3, WM wrote:
>>>>> ... you must find an endsegment which contains some elements not in a predecessor.
>>>>
>>>> Nope. No such endsegment is needed in order to get an empty intersection
>>> It is needed if all endsegments are nonempty. The only alternative would be an empty endsegment.
>> Piffle. There is also the alternative that there is no last endsegment.
>
> All endsegments which are there fail to satisfy
> (1) a ∈ A
> (2) b ∈ B
> (3) a ∉ B
> (4) b ∉ A.
> It is irrelevant whether there is a last one if all fail. All which fail have an element in common.

then prove it using math, dude. is it too hard for you ?

>
> Regards, WM

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

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