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Ahead warp factor one, Mr. Sulu.

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	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	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
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	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	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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From: james.g....@att.net (Jim Burns)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 29 Jul 2022 14:28:32 -0400
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by: Jim Burns - Fri, 29 Jul 2022 18:28 UTC

On 7/29/2022 10:00 AM, WM wrote:

> We accept that the final state exists.
> But it cannot be reached by definable steps.

Whatever cannot be reached by definable steps
cannot be reached by dark steps.

If i+1 is _out of_ the definables,
then i cannot be _in_ the definables.
The only i,i+1 pairs with i definable
also have i+1 definable.

But, in order to reach after all definables,
some single step somewhere must be be from
definables to less-than-perfectly-definables.

There is no single step from a definable
to anything that isn't a definable.

Therefore,
there cannot be reachable post-definables.

It doesn't matter what their nature is,
these mysterious "dark" numbers.
This is about the nature of the definables,
and their sharp borders-between requiring
(hypothetically) a single step from before
to after.

> If there is a completion
> then it is consisting of dark elements.

If
everything can match itself,
then
each superset of a WM-incomplete set is
also WM-incomplete
and
there is no WM-completion.

No WM-completion.
However,
suppose a natural number is
a thing we can count to, a thing in a FISON.

To claim "k is in some FISON"
uses k as a _complete reference_ over all
the natural numbers.

Reasoning from "k is in a FISON" brings us
to more claims we know are true of _all_
natural numbers.

What we want are claims we know are true of _all_
natural numbers.
That's what we have,
and we have it without things which cannot
match themselves.

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, 29 Jul 2022 18:47 UTC

On Friday, 29 July 2022 at 15:24:11 UTC-3, FromTheRafters wrote:
> Fritz Feldhase submitted this idea :
> > On Friday, July 29, 2022 at 6:11:09 PM UTC+2, FromTheRafters wrote:
> >> WM wrote on 7/29/2022 :
> >>> FromTheRafters schrieb am Freitag, 29. Juli 2022 um 16:37:55 UTC+2:
> >>>> WM laid this down on his screen :
> >>>
> >>> In ZFC everything is a set.
> >>>
> >> Everything in ZFC is a set.
> >
> > In ZFC: Everything is a set.
> Dark Numbers are not a set in ZFC.
>
> In ZFC: Dark Numbers are not.

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, 29 Jul 2022 18:48 UTC

On Friday, 29 July 2022 at 15:24:11 UTC-3, FromTheRafters wrote:
[...]
> In ZFC: Dark Numbers are not.

In ZFC every dark number is an element of the empty set, and the set of dark numbers is a subset of the empty set...

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, 29 Jul 2022 20:14 UTC

On Friday, July 29, 2022 at 8:24:11 PM UTC+2, FromTheRafters wrote:
> Fritz Feldhase submitted this idea :
> > On Friday, July 29, 2022 at 6:11:09 PM UTC+2, FromTheRafters wrote:
> >> WM wrote on 7/29/2022 :
> >>> FromTheRafters schrieb am Freitag, 29. Juli 2022 um 16:37:55 UTC+2:
> >>>> WM laid this down on his screen :
> >>>
> >>> In ZFC everything is a set.
> >>>
> >> Everything in ZFC is a set.
> >
> > In ZFC: Everything is a set.
> >
> Dark Numbers are not a set in ZFC.
>
> In ZFC: Dark Numbers are not.

In WM's wahnsystem: There are Dark Numbers.

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, 29 Jul 2022 20:19 UTC

On Friday, July 29, 2022 at 8:48:51 PM UTC+2, Gus Gassmann wrote:
> On Friday, 29 July 2022 at 15:24:11 UTC-3, FromTheRafters wrote:
> >
> > In ZFC: Dark Numbers are not.
> >
> In ZFC every dark number is an element of the empty set, and the set of dark numbers is a subset of the empty set...

On the other hand, how would you know. :-P

Do have a proof for your claim? :-)

Re: Natural numbers and vases III

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From: nom...@afraid.org (FromTheRafters)
Newsgroups: sci.math
Subject: Re: Natural numbers and vases III
Date: Fri, 29 Jul 2022 18:04:33 -0400
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by: FromTheRafters - Fri, 29 Jul 2022 22:04 UTC

Fritz Feldhase used his keyboard to write :
> On Friday, July 29, 2022 at 8:24:11 PM UTC+2, FromTheRafters wrote:
>> Fritz Feldhase submitted this idea :
>>> On Friday, July 29, 2022 at 6:11:09 PM UTC+2, FromTheRafters wrote:
>>>> WM wrote on 7/29/2022 :
>>>>> FromTheRafters schrieb am Freitag, 29. Juli 2022 um 16:37:55 UTC+2:
>>>>>> WM laid this down on his screen :
>>>>>
>>>>> In ZFC everything is a set.
>>>>>
>>>> Everything in ZFC is a set.
>>>
>>> In ZFC: Everything is a set.
>>>
>> Dark Numbers are not a set in ZFC.
>>
>> In ZFC: Dark Numbers are not.
>
> In WM's wahnsystem: There are Dark Numbers.

And a single axiom.

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, 29 Jul 2022 22:59 UTC

On Saturday, July 30, 2022 at 12:04:57 AM UTC+2, FromTheRafters wrote:
> Fritz Feldhase used his keyboard to write :
> > On Friday, July 29, 2022 at 8:24:11 PM UTC+2, FromTheRafters wrote:
> >> Fritz Feldhase submitted this idea :
> >>> On Friday, July 29, 2022 at 6:11:09 PM UTC+2, FromTheRafters wrote:
> >>>> WM wrote on 7/29/2022 :
> >>>>> FromTheRafters schrieb am Freitag, 29. Juli 2022 um 16:37:55 UTC+2:
> >>>>>> WM laid this down on his screen :
> >>>>>
> >>>>> In ZFC everything is a set.
> >>>>>
> >>>> Everything in ZFC is a set.
> >>>
> >>> In ZFC: Everything is a set.
> >>>
> >> Dark Numbers are not a set in ZFC.
> >>
> >> In ZFC: Dark Numbers are not.
> >
> > In WM's wahnsystem: There are Dark Numbers.
> >
> And a single axiom.

I guess, you mean the powerful axiom "Because I said so", right?

Yes, of course. :-)

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: Fri, 29 Jul 2022 20:19:01 -0400
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by: Jim Burns - Sat, 30 Jul 2022 00:19 UTC

On 7/29/2022 4:19 PM, Fritz Feldhase wrote:
> On Friday, July 29, 2022 at 8:48:51 PM UTC+2,
> Gus Gassmann wrote:
>> On Friday, 29 July 2022 at 15:24:11 UTC-3,
>> FromTheRafters wrote:

>>> In ZFC: Dark Numbers are not.
>>
>> In ZFC every dark number is
>> an element of the empty set,
>> and the set of dark numbers is
>> a subset of the empty set...
>
> On the other hand, how would you know. :-P

We are told very little about dark numbers.
Very little, but not nothing.

Dark numbers are assigned the task of
WM-completing a WM-incomplete set.
This is not an assignment that can be done.
Any set with a WM-incomplete subset
is itself a WM-incomplete subset.

The things which can WM-complete a
WM-incomplete set are elements of the empty set.
The set of things which can WM-complete
a WM-incomplete set is the empty set.

> Do have a proof for your claim? :-)

I have.
I've shown the proof to WM.
He considers it too long.

----
To be fair,
I do not use WM's notion of "infinite" in my proof.

I use a correct notion, and WM treats omega
as though it means "reallyreallyreallyreallyreally
large number" and dark numbers are between
omega and the beepable, tappable, flashable numbers
we use to count sheep in the pasture or
stars in the sky.

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 - Sat, 30 Jul 2022 01:08 UTC

On Friday, 29 July 2022 at 17:19:23 UTC-3, Fritz Feldhase wrote:
> On Friday, July 29, 2022 at 8:48:51 PM UTC+2, Gus Gassmann wrote:
> > On Friday, 29 July 2022 at 15:24:11 UTC-3, FromTheRafters wrote:
> > >
> > > In ZFC: Dark Numbers are not.
> > >
> > In ZFC every dark number is an element of the empty set, and the set of dark numbers is a subset of the empty set...
> On the other hand, how would you know. :-P
>
> Do have a proof for your claim? :-)

It follows directly from Muckenheim's axiom. Because I said so.

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 - Sat, 30 Jul 2022 01:20 UTC

On Saturday, July 30, 2022 at 3:08:59 AM UTC+2, Gus Gassmann wrote:
> On Friday, 29 July 2022 at 17:19:23 UTC-3, Fritz Feldhase wrote:
> > On Friday, July 29, 2022 at 8:48:51 PM UTC+2, Gus Gassmann wrote:
> > > On Friday, 29 July 2022 at 15:24:11 UTC-3, FromTheRafters wrote:
> > > >
> > > > In ZFC: Dark Numbers are not.
> > > >
> > > In ZFC every dark number is an element of the empty set, and the set of dark numbers is a subset of the empty set...
> > >
> > On the other hand, how would you know? :-P
> >
> > Do have a proof for your claim? :-)
> >
> It follows directly from Muckenheim's axiom. Because I said so.

Point taken. I'll accept your proof.

Though someone mentioned that Mückenheim's axiom is not just "Because I said so", but "Because I -Mückenheim- said so". See?

After all, Mückenheim is the GRÖMAZ (GREAMOAT, Greates Mathematician of all Times).

Re: Natural numbers and vases III

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Subject: Re: Natural numbers and vases III
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by: Sergio - Sat, 30 Jul 2022 02:12 UTC

On 7/29/2022 8:20 PM, Fritz Feldhase wrote:
> On Saturday, July 30, 2022 at 3:08:59 AM UTC+2, Gus Gassmann wrote:
>> On Friday, 29 July 2022 at 17:19:23 UTC-3, Fritz Feldhase wrote:
>>> On Friday, July 29, 2022 at 8:48:51 PM UTC+2, Gus Gassmann wrote:
>>>> On Friday, 29 July 2022 at 15:24:11 UTC-3, FromTheRafters wrote:
>>>>>
>>>>> In ZFC: Dark Numbers are not.
>>>>>
>>>> In ZFC every dark number is an element of the empty set, and the set of dark numbers is a subset of the empty set...
>>>>
>>> On the other hand, how would you know? :-P
>>>
>>> Do have a proof for your claim? :-)
>>>
>> It follows directly from Muckenheim's axiom. Because I said so.
>
> Point taken. I'll accept your proof.
>
> Though someone mentioned that Mückenheim's axiom is not just "Because I said so", but "Because I -Mückenheim- said so". See?
>
> After all, Mückenheim is the GRÖMAZ (GREAMOAT, Greates Mathematician of all Times).
>

Großer Furz Mückenheim (?)

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by: FromTheRafters - Sat, 30 Jul 2022 11:40 UTC

Fritz Feldhase has brought this to us :
> On Saturday, July 30, 2022 at 12:04:57 AM UTC+2, FromTheRafters wrote:
>> Fritz Feldhase used his keyboard to write :
>>> On Friday, July 29, 2022 at 8:24:11 PM UTC+2, FromTheRafters wrote:
>>>> Fritz Feldhase submitted this idea :
>>>>> On Friday, July 29, 2022 at 6:11:09 PM UTC+2, FromTheRafters wrote:
>>>>>> WM wrote on 7/29/2022 :
>>>>>>> FromTheRafters schrieb am Freitag, 29. Juli 2022 um 16:37:55 UTC+2:
>>>>>>>> WM laid this down on his screen :
>>>>>>>
>>>>>>> In ZFC everything is a set.
>>>>>>>
>>>>>> Everything in ZFC is a set.
>>>>>
>>>>> In ZFC: Everything is a set.
>>>>>
>>>> Dark Numbers are not a set in ZFC.
>>>>
>>>> In ZFC: Dark Numbers are not.
>>>
>>> In WM's wahnsystem: There are Dark Numbers.
>>>
>> And a single axiom.
>
> I guess, you mean the powerful axiom "Because I said so", right?
>
> Yes, of course. :-)

Yes, all other methods for proving the existence of dark numbers having
been exhausted, he relies upon the axiom.

All of his attempts to show dark numbers have natural numbers being
'undefined' or 'undefinable' just because they can't be conveyed
without unlimited resources. Not enough chalk to write them down or not
enough time, or not enough scratch space.

Maybe he forgets that sets are a collection of 'well defined' elements
not ill-defined fuzzballs.

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Subject: Re: Natural numbers and vases III
From: askaske...@gmail.com (WM)
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by: WM - Sat, 30 Jul 2022 12:14 UTC

Fritz Feldhase schrieb am Freitag, 29. Juli 2022 um 17:49:01 UTC+2:
> On Friday, July 29, 2022 at 5:17:19 PM UTC+2, WM wrote:
> > FromTheRafters schrieb am Freitag, 29. Juli 2022 um 16:37:55 UTC+2:
> > > WM laid this down on his screen :
> > > > Fritz Feldhase schrieb am Donnerstag, 28. Juli 2022 um 23:53:43 UTC+2:
> > > > > On Thursday, July 28, 2022 at 11:38:38 PM UTC+2, William wrote:
> > > > > >
> > > > > > We still have that a "final state" exists [...]
> > > > > >
> > > > > You are talking nonsense. And you know it, asshole!
> > > > >
> > > > > The limit of a sequence is not a "final state" (of what?!).
> > > > >
> > > > The completion of a set is the final state.
> > > >
> > > A set is not a process, though it can be a function.
> > >
> > In ZFC everything is a set. Processes can be decribed by mathematics. Mathematics is based on ZFC. Conclusion: Processes [can be] described as sets.
>
> Did ANYONE claim otherwise, Mückenheim? :-)

Some fools claim that infinite processes, so-called supertasks, do not belong to set theory although its main advantage is the description of the actions of infinite sets and of super tasks, for instance enumerating the farctions.

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 - Sat, 30 Jul 2022 12:16 UTC

Fritz Feldhase schrieb am Freitag, 29. Juli 2022 um 17:54:29 UTC+2:
> On Friday, July 29, 2022 at 5:30:53 PM UTC+2, WM wrote:
>
> > Philosophers who reject their possibility tend not to reject them on grounds such as Thomson's but because they have qualms with the notion of infinity itself.
> >
> > We do not.
> We? Huh?!
>
> So you are claiming that you don't have qualms with the notion of actual infinity?

Yes, I have managed to explain it by dark numbers.

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 - Sat, 30 Jul 2022 12:19 UTC

William schrieb am Freitag, 29. Juli 2022 um 18:37:31 UTC+2:
> On Friday, July 29, 2022 at 11:00:09 AM UTC-3, WM wrote:
>
> >If there is a completion then it is consisting of dark elements.
> Piffle. A "final state" cannot be reached by a stepwise process not because a "final state" contains "dark elements" but because the state changes at every step and there is no last step.

The final state like omega does not change in actual infinity. It canot be reached because its predecessors are dark.

Regards, WM

Re: Natural numbers and vases III

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by: WM - Sat, 30 Jul 2022 12:20 UTC

FromTheRafters schrieb am Freitag, 29. Juli 2022 um 20:24:11 UTC+2:
> Fritz Feldhase submitted this idea :
> > On Friday, July 29, 2022 at 6:11:09 PM UTC+2, FromTheRafters wrote:
> >> WM wrote on 7/29/2022 :
> >>> FromTheRafters schrieb am Freitag, 29. Juli 2022 um 16:37:55 UTC+2:
> >>>> WM laid this down on his screen :
> >>>
> >>> In ZFC everything is a set.
> >>>
> >> Everything in ZFC is a set.
> >
> > In ZFC: Everything is a set.
> Dark Numbers are not a set in ZFC.
>
> In ZFC: Dark Numbers are not.

Without dark numbers ZFC is not.

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 - Sat, 30 Jul 2022 12:25 UTC

FromTheRafters schrieb am Samstag, 30. Juli 2022 um 13:41:06 UTC+2:

> Yes, all other methods for proving the existence of dark numbers having
> been exhausted, he relies upon the axiom.

There are many methods. Alas they require some intelligence - more than most readers can summon up.
>
> All of his attempts to show dark numbers have natural numbers being
> 'undefined' or 'undefinable' just because they can't be conveyed
> without unlimited resources.

No. Proof by endsegments. All endsegments which together have an infinite intersection have together an infinite intersection. Do you agree?
Try to define an additional endsegment using unlimited ressources. Fail.

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 - Sat, 30 Jul 2022 12:31 UTC

Jim Burns schrieb am Freitag, 29. Juli 2022 um 18:55:08 UTC+2:

> WM-dark numbers, end segments, fractions
> can be hypothetically added to a WM-incomplete
> subset to produce a WM-complete set.

Very good!
>
> the dark remainder can match itself,

No.

> WM-completeness requires elements which
> _cannot_ match themselves.

Yes.

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 - Sat, 30 Jul 2022 12:38 UTC

Jim Burns schrieb am Freitag, 29. Juli 2022 um 20:28:41 UTC+2:
> On 7/29/2022 10:00 AM, WM wrote:
>
> > We accept that the final state exists.
> > But it cannot be reached by definable steps.
> Whatever cannot be reached by definable steps
> cannot be reached by dark steps.

Dark natnumbers are not suitable for steps. They are just the stuff between definable numbers and omega, which partially can get defined and then used for steps.
>
> If i+1 is _out of_ the definables,
> then i cannot be _in_ the definables.
> The only i,i+1 pairs with i definable
> also have i+1 definable.

Very good!
>
> There is no single step from a definable
> to anything that isn't a definable.
>
So it is.

> What we want are claims we know are true of _all_
> natural numbers.
> That's what we have,
> and we have it without things which cannot
> match themselves.

No. Proof by endsegments. All endsegments which can match themselves have together an infinite intersection. Do you agree?
Try to define an additional endsegment. Fail.
(You can define more than you have defined yet - but you cannot define an endsegment which would reduce the intersection to less than infinity.)

Regards, WM

Re: Natural numbers and vases III

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From: nom...@afraid.org (FromTheRafters)
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by: FromTheRafters - Sat, 30 Jul 2022 13:24 UTC

WM brought next idea :
> Fritz Feldhase schrieb am Freitag, 29. Juli 2022 um 17:49:01 UTC+2:
>> On Friday, July 29, 2022 at 5:17:19 PM UTC+2, WM wrote:
>>> FromTheRafters schrieb am Freitag, 29. Juli 2022 um 16:37:55 UTC+2:
>>>> WM laid this down on his screen :
>>>>> Fritz Feldhase schrieb am Donnerstag, 28. Juli 2022 um 23:53:43 UTC+2:
>>>>>> On Thursday, July 28, 2022 at 11:38:38 PM UTC+2, William wrote:
>>>>>>>
>>>>>>> We still have that a "final state" exists [...]
>>>>>>>
>>>>>> You are talking nonsense. And you know it, asshole!
>>>>>>
>>>>>> The limit of a sequence is not a "final state" (of what?!).
>>>>>>
>>>>> The completion of a set is the final state.
>>>>>
>>>> A set is not a process, though it can be a function.
>>>>
>>> In ZFC everything is a set. Processes can be decribed by mathematics.
>>> Mathematics is based on ZFC. Conclusion: Processes [can be] described as
>>> sets.
>>
>> Did ANYONE claim otherwise, Mückenheim? :-)
>
> Some fools claim that infinite processes, so-called supertasks, do not belong
> to set theory although its main advantage is the description of the actions
> of infinite sets and of super tasks, for instance enumerating the farctions.

If you want time and steps to be part of your mathematics, you must
include them. A bijection takes no time at all, and there are no steps
or supertasks involved.

Re: Natural numbers and vases III

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by: FromTheRafters - Sat, 30 Jul 2022 13:28 UTC

WM has brought this to us :
> FromTheRafters schrieb am Samstag, 30. Juli 2022 um 13:41:06 UTC+2:
>
>> Yes, all other methods for proving the existence of dark numbers having
>> been exhausted, he relies upon the axiom.
>
> There are many methods. Alas they require some intelligence - more than most
> readers can summon up.

Sets have well-defined elements. You define your elements as 'not
defined' or even 'not definable' and then you blame others for not
understanding your system?

I think that they understand it just fine.

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by: Sergio - Sat, 30 Jul 2022 13:29 UTC

On 7/30/2022 7:25 AM, WM wrote:
> FromTheRafters schrieb am Samstag, 30. Juli 2022 um 13:41:06 UTC+2:
>
>> Yes, all other methods for proving the existence of dark numbers having
>> been exhausted, he relies upon the axiom.
>
> There are many methods. Alas they require some intelligence - more than most readers can summon up.
>>
>> All of his attempts to show dark numbers have natural numbers being
>> 'undefined' or 'undefinable' just because they can't be conveyed
>> without unlimited resources.
>
> No. Proof by endsegments. All endsegments which together have an infinite intersection have together an infinite intersection. Do you agree?
> Try to define an additional endsegment using unlimited ressources. Fail.
>
> Regards, WM
>

Straw Grasping 101

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: Sat, 30 Jul 2022 08:32:14 -0500
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by: Sergio - Sat, 30 Jul 2022 13:32 UTC

On 7/30/2022 7:19 AM, WM wrote:
> William schrieb am Freitag, 29. Juli 2022 um 18:37:31 UTC+2:
>> On Friday, July 29, 2022 at 11:00:09 AM UTC-3, WM wrote:
>>
>>> If there is a completion then it is consisting of dark elements.
>> Piffle. A "final state" cannot be reached by a stepwise process not because a "final state" contains "dark elements" but because the state changes at every step and there is no last step.
>
> The final state like omega does not change in actual infinity.

You mean a Limit ?

> It canot be reached because its predecessors are dark.

that is your perception, others use Limits, Induction, and no darkies are needed

>
> Regards, 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: Sat, 30 Jul 2022 08:37:22 -0500
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by: Sergio - Sat, 30 Jul 2022 13:37 UTC

On 7/30/2022 7:38 AM, WM wrote:
> Jim Burns schrieb am Freitag, 29. Juli 2022 um 20:28:41 UTC+2:
>> On 7/29/2022 10:00 AM, WM wrote:
>>
>>> We accept that the final state exists.
>>> But it cannot be reached by definable steps.
>> Whatever cannot be reached by definable steps
>> cannot be reached by dark steps.
>
> Dark natnumbers are not suitable for steps. They are just the stuff between definable numbers and omega,

they are called "Endsegments".

> which partially can get defined and then used for steps.

no, as your rules, "defined" they are not dark.

>>
>> If i+1 is _out of_ the definables,
>> then i cannot be _in_ the definables.
>> The only i,i+1 pairs with i definable
>> also have i+1 definable.
>
> Very good!

no, "definable" is WMs joke

>>
>> There is no single step from a definable
>> to anything that isn't a definable.
>>
> So it is.
>
>> What we want are claims we know are true of _all_
>> natural numbers.
>> That's what we have,
>> and we have it without things which cannot
>> match themselves.
>

> 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 - Sat, 30 Jul 2022 14:50 UTC

On Saturday, July 30, 2022 at 9:19:32 AM UTC-3, WM wrote:

> The final state like omega does not change in actual infinity. It canot be reached

By "can be reached " you mean "is an element or subset of the state at a step of a stepwise process". So what? As you note, a "final state" exists.

> because its predecessors are dark.

Piffle. |N is a Peano set and does not contain "dark elements". The reason a "final state cannot" be reached by a stepwise process is that the state changes at every step and there is no last step, The reason has nothing to do with "dark elements". Note, the fact that each *element* of |N has the property "can be reached" does not mean the *set* |N has the property "can be reached".

--
William Hughes

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

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