"It never happens that the (always finite number of) pathbunches split into 2^ℵo pathbunches. However, if we posit a time after an infinite number of steps, we can say that the split happened. This 'it never happens but it happened' is unique to processes with no last step. For a process with no last step, you cannot conclude something cannot have happened, because there is no step where it happens."

"You are apparently trying to appeal to a theorem that says that if a_n < A for all n then lim a_n =< A. This statement is false in the context;"

"At every level we have more lamettas than nodes in the binary tree. But through each of these nodes pass infinitely many paths. Maybe you can not distinguish them just by looking at the nodes but they do exist."

"Unfortunately you have not provided a way of moving this from 'true for all finite' to 'true for infinite n', and induction won't take you from 'all finite n' to 'infinite n'."

"If all nodes of a path have been deleted, that does not mean you ever deleted the path!!! You could delete all and only the finite paths from the tree, and that would delete all the nodes, yet you would never have deleted any infinite path, and they would all still exist in any case, regardless of what had been deleted!"

Gruß, WM

Y A schrieb am Sonntag, 8. Januar 2023 um 09:58:51 UTC+1:
> Write to black paper with a white pencil.

Dark numbers can only be written with black ink to black paper or with white ink to white paper.

Regards, WM

posting link to earlier thread

Newsgroups: sci.math
Date: Sun, 8 Jan 2023 00:57:17 -0800 (PST)
Message-ID: <d09971d9-6cfa-4668-9bb1-77ccabe1c86bn@googlegroups.com>
Subject: Re: Question on Hilbert's Hotel.
From: WM <monteuffl@t-online.de>
Injection-Date: Sun, 08 Jan 2023 08:57:18 +0000
Content-Type: text/plain; charset="UTF-8"
Content-Transfer-Encoding: quoted-printable
Lines: 31
Xref: reader01.eternal-september.org sci.math:600306

William schrieb am Sonntag, 8. Januar 2023 um 00:12:07 UTC+1:
> On Saturday, January 7, 2023 at 5:37:18 PM UTC-4, WM wrote:
>> William schrieb am Samstag, 7. Januar 2023 um 20:34:15 UTC+1:
>>> On Saturday, January 7, 2023 at 3:23:21 PM UTC-4, WM wrote:
>>> .
>>>>>>> There is always a set of Peano elements of cardinality ℵo
"outside"
>>>>>> There are always Peano elements outside.
>>>>> Consider step n There is always at least one Peano element
outside. Call it p(n) (note it can and does change)
>>>>> Then the set S_n={p(n), sp(n), ssp(n), sssp(n) ...} of
cardinality ℵo. is outside
>>>> Not of cardinality ℵo .
>>>
>>> Yes of cardinality ℵo. S_n is clearly a Peano set with cardinality ℵo.
>> This 'it never happens but it happened' is unique to processes
> What process?

For every definable n there is a process leading to it.

> S_n is a set, something that does not change. There is no process
involved in determining the cardinality.,

There is no process possible for cardinality ℵo of infinite sets.

This thread has become too long and too slow a process. Please continue
here: Who recognizes these true pioneers of dark
numbers?https://groups.google.com/g/sci.math/c/x7hGpSOF-co

Regards, WM

Jim Burns schrieb am Sonntag, 8. Januar 2023 um 11:41:12 UTC+1:
> posting link to earlier thread
>
> William schrieb am Sonntag, 8. Januar 2023 um 00:12:07 UTC+1:
> > On Saturday, January 7, 2023 at 5:37:18 PM UTC-4, WM wrote:
> >> William schrieb am Samstag, 7. Januar 2023 um 20:34:15 UTC+1:

Congratulations! First identity is solved.
(The original source of this statement was [William Hughes in "Can that be?", sci.math (19 Jun 2019)])

Regards, WM

On 1/8/2023 2:35 AM, WM wrote:
> "It never happens that the (always finite number of) pathbunches split into 2^ℵo pathbunches. However, if we posit a time after an infinite number of steps, we can say that the split happened. This 'it never happens but it happened' is unique to processes with no last step. For a process with no last step, you cannot conclude something cannot have happened, because there is no step where it happens."
>
> "You are apparently trying to appeal to a theorem that says that if a_n < A for all n then lim a_n =< A. This statement is false in the context;"
>
> "At every level we have more lamettas than nodes in the binary tree. But through each of these nodes pass infinitely many paths. Maybe you can not distinguish them just by looking at the nodes but they do exist."
>
> "Unfortunately you have not provided a way of moving this from 'true for all finite' to 'true for infinite n', and induction won't take you from 'all finite n' to 'infinite n'."
>
> "If all nodes of a path have been deleted, that does not mean you ever deleted the path!!! You could delete all and only the finite paths from the tree, and that would delete all the nodes, yet you would never have deleted any infinite path, and they would all still exist in any case, regardless of what had been deleted!"
>
> Gruß, WM

NONE of those statement have anything to do with your imagined "DARK NUMBERS"!

you are psychotic and delusional.

On 1/8/2023 4:28 AM, WM wrote:
> Y A schrieb am Sonntag, 8. Januar 2023 um 09:58:51 UTC+1:
>> Write to black paper with a white pencil.
>
> Dark numbers can only be written with black ink to black paper or with white ink to white paper.

WRONG, since you can write it, you know the number, it cannot be dark anymore.

you are psychotic and delusional.

>
> Regards, WM

you are correct, with WM there is no logic, just his imagination

On 1/8/2023 6:24 AM, Y A wrote:
> I don't recognize any logic in the previous.
>
>
> On Sunday, January 8, 2023 at 12:28:41 PM UTC+2, WM wrote:
>> Y A schrieb am Sonntag, 8. Januar 2023 um 09:58:51 UTC+1:
>>> Write to black paper with a white pencil.
>> Dark numbers can only be written with black ink to black paper or with white ink to white paper.
>>
>> Regards, WM

On Sunday, January 8, 2023 at 4:13:16 PM UTC+1, Sergi o wrote:
> On 1/8/2023 4:28 AM, WM wrote:
> > Y A schrieb am Sonntag, 8. Januar 2023 um 09:58:51 UTC+1:
> >> Write to black paper with a white pencil.
> >
> > Dark numbers can only be written with black ink to black paper or with white ink to white paper.
> WRONG, since you can write it, you know the number, it cannot be dark anymore.
> you are psychotic and delusional.

When Mücke writes it will still be dark. What made you
think that Mücke knows what he is writing?

WM: There are always Peano elements outside.
WH: If there is at least on Peano element outside the are an infinite number of Peano elements outside.

No process mentioned or used.

William schrieb am Sonntag, 8. Januar 2023 um 17:44:10 UTC+1:
> WM: There are always Peano elements outside.

That is the nature of potential infinity. I cannot change it.

> WH: If there is at least on Peano element outside the are an infinite number of Peano elements outside.

Yes, that is true, but not ℵo.
>
> No process mentioned or used.

Collecting Peano elements is a never ending process, if you use the same time for every step. If you use always half the time, the process comes to an end in tim. But you will not be able to identify the collected numbers till the end. Before the end, there will be a cloud of dark elements.

Remember: 'it never happens but it happened' is unique to processes with no last step.

The author wanted to tell us that it is impossible to observe the complete process of collecting numbers. But after the end it turns out that all numbers have been collected - in a not observable way. Don't you think so?

Regards, WM

On Sunday, January 8, 2023 at 1:21:10 PM UTC-4, WM wrote:
> William schrieb am Sonntag, 8. Januar 2023 um 17:44:10 UTC+1:
> > WM: There are always Peano elements outside.
> That is the nature of potential infinity.
Nothing to do with "potential infinity". A Peano set does not change.

WM wrote:
> William schrieb am Sonntag,
> 8. Januar 2023 um 00:12:07 UTC+1:

>> S_n is a set, something that does not change.
>> There is no process involved
>> in determining the cardinality.,

> For every definable n
> there is a process leading to it.

> There is no process possible
> for cardinality ℵo of infinite sets.

No,
there is a process.

However,
it is not the process you're imagining.
It is not a count-to-infinity process.

Instead, it is a
check-a-finite-sequence-of-claims-for-
-all-not-first-possibly-false-hood
process.

A sequence of claims either
has a _first_ possibly-false claim or
doesn't have any possibly-false claim.

Therefore,
a sequence which
doesn't have a _first_ possibly-false claim
doesn't have a possibly-false claim.

For a finite sequence of claims,
there is a process of checking whether
each claim is either
known to be not-possibly-false
for reasons outside the sequence, or
known to be not-first-possibly-false
for reasons visible inside the sequence.

A reason outside the sequence could be
that it's a claim in some other
all-not-first-possibly-false sequence
(which is to say, that it's a theorem).

A reason outside the sequence could be
that it's a claim true of each one of
whatever we're reasoning about
(hence, not-possibly-false about those)

For example,
if we're reasoning about elements n of
the sequence 1 2 3 ... with i last-before,
i⁺⁺ first-after for each split,
then it's a not-possibly-false claim about
what we're reasoning about that it's an
element of 1 2 3 ... with i last-before,
i⁺⁺ first-after for each split,
even though it's a possibly-false claim about
other, not-being-reasoned-about things.

A reason visible inside a sequence that
claim 𝓆 is not-first-possibly-false
could be that 𝓅 and 𝓅⇒𝓆 precede 𝓆 in
the sequence.

If that were the case, either
𝓅 or 𝓅⇒𝓆 is possibly-false
and 𝓆 can't be _first_ or
both 𝓅 and 𝓅⇒𝓆 are not-possibly-false
and 𝓆 can't be _possibly-false_
I'll write that as 𝓅,𝓅⇒𝓆 ⊢ 𝓆

There only needs to be a very few rules
like 𝓅,𝓅⇒𝓆 ⊢ 𝓆 for
visible not-first-possibly-false-hood.
Without them,
we would be left with repeating over and
over things we already knew were
not-possibly-false.

> There is no process possible
> for cardinality ℵo of infinite sets.

No,
there is a process, a
check-a-finite-sequence-of-claims-for-
-all-not-first-possibly-false-hood
process.

On Sunday, January 8, 2023 at 11:26:18 AM UTC-8, Jim Burns wrote:
> WM wrote:
> > William schrieb am Sonntag,
> > 8. Januar 2023 um 00:12:07 UTC+1:
> >> S_n is a set, something that does not change.
> >> There is no process involved
> >> in determining the cardinality.,
>
> > For every definable n
> > there is a process leading to it.
>
> > There is no process possible
> > for cardinality ℵo of infinite sets.
> No,
> there is a process.
>
> However,
> it is not the process you're imagining.
> It is not a count-to-infinity process.
>
> Instead, it is a
> check-a-finite-sequence-of-claims-for-
> -all-not-first-possibly-false-hood
> process.
>
> A sequence of claims either
> has a _first_ possibly-false claim or
> doesn't have any possibly-false claim.
>
> Therefore,
> a sequence which
> doesn't have a _first_ possibly-false claim
> doesn't have a possibly-false claim.
>
> For a finite sequence of claims,
> there is a process of checking whether
> each claim is either
> known to be not-possibly-false
> for reasons outside the sequence, or
> known to be not-first-possibly-false
> for reasons visible inside the sequence.
>
> A reason outside the sequence could be
> that it's a claim in some other
> all-not-first-possibly-false sequence
> (which is to say, that it's a theorem).
>
> A reason outside the sequence could be
> that it's a claim true of each one of
> whatever we're reasoning about
> (hence, not-possibly-false about those)
>
> For example,
> if we're reasoning about elements n of
> the sequence 1 2 3 ... with i last-before,
> i⁺⁺ first-after for each split,
> then it's a not-possibly-false claim about
> what we're reasoning about that it's an
> element of 1 2 3 ... with i last-before,
> i⁺⁺ first-after for each split,
> even though it's a possibly-false claim about
> other, not-being-reasoned-about things.
>
> A reason visible inside a sequence that
> claim 𝓆 is not-first-possibly-false
> could be that 𝓅 and 𝓅⇒𝓆 precede 𝓆 in
> the sequence.
>
> If that were the case, either
> 𝓅 or 𝓅⇒𝓆 is possibly-false
> and 𝓆 can't be _first_ or
> both 𝓅 and 𝓅⇒𝓆 are not-possibly-false
> and 𝓆 can't be _possibly-false_
> I'll write that as 𝓅,𝓅⇒𝓆 ⊢ 𝓆
>
> There only needs to be a very few rules
> like 𝓅,𝓅⇒𝓆 ⊢ 𝓆 for
> visible not-first-possibly-false-hood.
> Without them,
> we would be left with repeating over and
> over things we already knew were
> not-possibly-false.
> > There is no process possible
> > for cardinality ℵo of infinite sets.
> No,
> there is a process, a
> check-a-finite-sequence-of-claims-for-
> -all-not-first-possibly-false-hood
> process.

Should not sub finite and.. the no quantity at all.. be the dark?
Zero is absolute dark... the unlimited small has a relative dark.

On 1/8/2023 6:39 AM, WM wrote:
> Jim Burns schrieb am Sonntag,
> 8. Januar 2023 um 11:41:12 UTC+1:
>> posting link to earlier thread

> Congratulations! First identity is solved.

A sequence of claims either
has a _first_ possibly-false claim or
doesn't have any possibly-false claim.

There is a _process_ to check whether
a finite sequence of claims is
all-not-first-possibly-false.

If the finite sequence passes the check,
each claim in the sequence is
not-possibly-false, which is necessarily-true.

Even if the claims are about one of infinitely-
-many individuals, and we don't know which one,

but the sequence is all-not-first-possibly-false
then each of its claims is necessarily-true.

On 1/8/2023 2:32 PM, mitchr...@gmail.com wrote:
> On Sunday, January 8, 2023
> at 11:26:18 AM UTC-8, Jim Burns wrote:
>> WM wrote:

>>> There is no process possible
>>> for cardinality ℵo of infinite sets.
>>
>> No,
>> there is a process, a
>> check-a-finite-sequence-of-claims-for-
>> -all-not-first-possibly-false-hood
>> process.
>
> Should not sub finite and..
> the no quantity at all..
> be the dark?
> Zero is absolute dark...
> the unlimited small has a relative dark.

The dark is not my baby, it is WM's.

However,
my understanding is that "the dark" is
about being beyond unknown, unknowable.

There are many questions for which
zero is known to be the answer.
That would make zero not-dark, I think.

My anti-dark argument is that
we can know something true of infinitely-many
individuals without performing infinitely-many
actions.

The agreed-upon fact that
there are infinitely-many individuals
is not a good argument for dark things.

Moscow & Tehran ██۞██ Moscow electric blackouts██۞██ Jim Burns are the scopes Oval or Ellipse??
Re: Wolfgang Mueckenheim fuck my ass!
Sergi_o,Anja Karliczek,Metin Tolin,Susanne Schneider,Steffen Schumann,Cynthia A. Volkert are they
Jan 7


2
Re: _Should Marc Tessier-Lavigne, Wolfgang Mueckenheim, Ben Bacarisse, William, FromTheRafters, Chris Thomasson, John Gabriel go to prison for their science corruption with their "fake pictures" science and brainwashing innocent students?
Jan 7

zelos...@gmail.com's profile photo
zelos...@gmail.com
, …

17
Re: Gonna cum in my mouth?
Ben Bacarisse,Susanne Schneider,Metin Tolan,Anja Karliczek,,Prof. Dr. Steffen Schumann,Prof. Cynthia
Jan 7

Chris M. Thomasson's profile photo
Chris M. Thomasson
, …
Archimedes Plutonium
16
For WM...
Ben Bacarisse ██۞██ Moscow electric blackouts██۞██ Ben Bacarisse are the scopes Oval or Ellipse?? Ben
Jan 7

mitchr...@gmail.com's profile photo
mitchr...@gmail.com
,
Y A
2

On Sunday, January 8, 2023 at 2:35:15 AM UTC-6, WM wrote:
> "It never happens that the (always finite number of) pathbunches split

WM,Susanne Schneider,Metin Tolan,Anja Karliczek,Susanne Schneider,Steffen Schumann, Cynthia A. Volkert are they forever going to be mindless idiots of math especially geometry.

And here you can plainly see the side EC is smaller than CF, while a ellipse requires them to be equal
......../\E
....../ c.\
F / .......\

entrance E of planar cut, and "c" the center axis, and F the exit of planar cut, cF is far larger than Ec.

Are they trying to turn sci.math into a gay pick up bar rather than legitimate math with endless day after day spam?

Jim Burns 17 "Who...dark numbers"
Sergi_o 68, "Questions on...."
Wolfgang Mueckenheim 324 "Three proofs of dark numbers..."
of the fine Bacarisse cheese
Ben Bacarisse 323 "Three proofs of dark numbers..."
FromTheRafters (more like gutters) 221 "Two similar..."
Sergi_o 161 "Two similar..."
Ben Bacarisse 133, "Two similar properties..."

WM turning Gottingen Germany into geometry failures.
Kibo chasing corpses in WM gay pick up bar, for Kibo sure does not know the difference between Oval and ellipse as seen in his latest stupidity-- a revolving axis as Kibo the moron and BWR describes it--

Let's try again with your little diagram, fixed.
> > >>> .......A
> > >>> ....../.\E
> > >>> ...../.C.\
> > >>> ..../B....\
> > >>> .../.......\
> > >>> .F/....G....\
> >
> > You chose point C to be the intersection of line segment EF and the axis
> > of the cone AG. As you say segment EC is smaller than CF. Not in
> > dispute. But that doesn't show that the intersecting curve isn't
> > symmetric around EF. C is not the center of EF. To see if the
> > intersection figure is symmetric around EF, you obviously have to start
> > at the center, the halfway point of EF. Here I called it B, and the
> > length BE = length BF. Now you need to show that the curve is or is not
> > symmetric around B. That the width at B+d is or is not = the width at
> > B-d, as bwr stated. Not quite as simple.
>

On Monday, December 5, 2022 at 1:48:16 PM UTC-6, Michael Moroney wrote:
> On 12/5/2022 12:22 AM, Chris M. Thomasson wrote:
> > On 12/4/2022 8:19 PM, Michael Moroney wrote:
> >> On 12/4/2022 7:43 PM, Mathin3D wrote:
> >>> Serious Question:

Kibo Parry M on Harvard's Dr. Hau.
Kibo on > I want to fuck her corpse
On Sunday, September 11, 2022 at 12:07:15 AM UTC-5, Michael Moroney wrote:
> I want to fuck her corpse
Why Kibo??? Because she refuses to finish her experiment and see all the light vanishes simultaneously, or is it because she can not admit slant cut of cone is Oval, never ellipse???

On Wednesday, November 2, 2022 at 12:21:30 AM UTC-5, Michael Moroney wrote:
>"Imp of Math"
On Monday, January 18, 2021 at 2:06:24 PM UTC-6, Michael Moroney wrote:
> fails at math and science:

Re: Drs.Larry Summers, Sheldon Glashow, Lisa Randall of Harvard, teach percentages correctly??-- Moroney//never realizing the Real Electron = muon, proton=840MeV, .5MeV = Dirac's monopole (1)
By Michael Moroney 1/23/18, 44 posts 461 views

On Sunday, September 11, 2022 at 12:07:15 AM UTC-5, Michael Moroney wrote:
> I want to fuck her corpse
Kibo Parry Moroney in 1997 blows his CIA cover-- to the entire world, mind you---
Re: Archimedes Vanadium, America's most beloved poster
>> In article <5nefan$i06$9...@news.thecia.net> kibo greps <ki...@shell.thecia.net> writes:
> >

On Tuesday, November 1, 2022 at 9:13:14 AM UTC-5, Michael Moroney wrote:
>"Court Jester of Math"

Kibo,is Ruth Charney of AMS the model in your book, for she cannot admit the slant cut of cone is Oval, never the ellipse as proven by AP in 2016? I know it falls on deaf ears of Kibo with his 938 is 12% short of 945. And Ruth, would the AMS publish Kibo's 938 is 12% short of 945, because the AMS certainly will not publish AP's conic proof? Maybe that is all the AMS publishes-- fake math.

On Sunday, September 11, 2022 at 12:07:15 AM UTC-5, Michael Moroney wrote:
> I want to fuck her corpse
On Monday, September 19, 2022 at 3:21:37 PM UTC-5, Michael Moroney wrote:
> fails at math and science:

On Sunday, September 18, 2022 at 12:43:52 AM UTC-5, Michael Moroney wrote:
>"bozo"
> fails at math and science:
>"psychoceramic"

On Tuesday, September 13, 2022 at 10:40:13 AM UTC-5, Michael Moroney wrote:
>"physics hater"
> tarded:
> Drag Queen of Science, especially Physics

AP no longer tolerates 30 year nonstop stalker shitheads like Kibo Parry M.
> No wonder Dr.Tao is a failed mathematician who cannot see that |/\| planar cut simultaneously through cylinder and cone has to yield a Oval in cone, a ellipse in cylinder. Tao fails fails fails math, and no wonder the nitwit cannot do a geometry proof of Fundamental Theorem of Calculus.
>
> On Sunday, December 4, 2022 at 6:19:00 PM UTC-6, Michael Moroney wrote:
> > On 12/4/2022 5:52 PM, bwr fml wrote:
> > > On Sunday, December 4, 2022 at 2:39:25 PM UTC-8, Archimedes Plutonium wrote:
> > >>> And here you can plainly see the side EC is smaller than CF, while a ellipse requires them to be equal
> > >>> ......./\E
> > >>> ...../ c.\
> > >>> F / .......\
> > >
> > > If you are thinking your cone is symmetric around the z axis and the point c is on the z axis
> > > then you claim that Ec is less than cF is true.
> > > And that means absolutely nothing about whether the intersection of the cone and plane is an ellipse.
> > >
> > > The fundamental crank mistake you made a decade ago is thinking that the point c on the z axis
> > > has ANYTHING to do with whether the intersection is an ellipse or not..
> > >
> > > As I clearly showed a couple of days ago, the algebra CLEARLY shows that your point c needs to be
> > > exactly half way between the point E and the point F. Then the distances Ec and cF are equal.
> > > BUT, far more important, all the widths of the intersection in that plane for any distance d to the left
> > > and the distance d to the right of that point c are then precisely equal and that is the definition
> > > of a plane of symmetry and the intersection is an ellipse.
> > >
> > > But you have screeched your false claim out your crank hole for long enough and you DESPERATELY
> > > need to imagine that you are right and everyone else in the history of the world is wrong... that you
> > > probably can't ever admit that you made this mistake and just keep screeching it.
> > >
> > > Go out in your yard and scream it loud and proud:
> > > RETARDED, RETARDED, ARCHIE IS RETARDED
> > > and keep crank screaming that until they call the cops on you.
> > bwr is correct, Archie. Let's try again with your little diagram, fixed..
> > >>> .......A
> > >>> ....../.\E
> > >>> ...../.C.\
> > >>> ..../B....\
> > >>> .../.......\
> > >>> .F/....G....\
> >
> > You chose point C to be the intersection of line segment EF and the axis
> > of the cone AG. As you say segment EC is smaller than CF. Not in
> > dispute. But that doesn't show that the intersecting curve isn't
> > symmetric around EF. C is not the center of EF. To see if the
> > intersection figure is symmetric around EF, you obviously have to start
> > at the center, the halfway point of EF. Here I called it B, and the
> > length BE = length BF. Now you need to show that the curve is or is not
> > symmetric around B. That the width at B+d is or is not = the width at
> > B-d, as bwr stated. Not quite as simple.
>
> AP comments: so look at the moron Moroney (Kibo Parry) being a spokesperson for failed Dr. Tao with his "move around axis of the cone-- say Kibo and Tao is there a witch flying around on a broomstick in that cone also???

William schrieb am Sonntag, 8. Januar 2023 um 18:33:33 UTC+1:
> On Sunday, January 8, 2023 at 1:21:10 PM UTC-4, WM wrote:
> > William schrieb am Sonntag, 8. Januar 2023 um 17:44:10 UTC+1:
> > > WM: There are always Peano elements outside.
> > That is the nature of potential infinity.
> Nothing to do with "potential infinity". A Peano set does not change.

What you erroneously call Peano set is Cantor's set ℕ.
That ℕ is not a Peano set is proved by the fact that you will never have collected its elements completely.

There is a dark interval between what you can do and completeness.
Remember: 'it never happens but it happened' is unique to processes with no last step.

The author wanted to tell us that it is impossible to observe the complete process of collecting numbers. But after the end it turns out that all numbers have been collected - in a not observable way. Don't you think so?

Regards, WM

Jim Burns schrieb am Sonntag, 8. Januar 2023 um 20:26:18 UTC+1:
> WM wrote:
> > William schrieb am Sonntag,
> > 8. Januar 2023 um 00:12:07 UTC+1:
> >> S_n is a set, something that does not change.
> >> There is no process involved
> >> in determining the cardinality.,
>
> > For every definable n
> > there is a process leading to it.
>
> > There is no process possible
> > for cardinality ℵo of infinite sets.

> No,
> there is a process.
>
> However,
> it is not the process you're imagining.
> It is not a count-to-infinity process.
>
> Instead, it is a
> check-a-finite-sequence-of-claims-for-
> -all-not-first-possibly-false-hood
> process.

Maybe. Writing and checking claims is a process. But the process of individual treatment requires individual treatment. That is not possible for Cantor's set ℕ. Always amost all ℵo elments remain outside / uncounted.
>
> A sequence of claims either
> has a _first_ possibly-false claim or
> doesn't have any possibly-false claim.

This sequence has no first false claim:
After collecting n ∈ ℕ almost all ℵo elements remain uncollected.
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
>
> > There is no process possible
> > for cardinality ℵo of infinite sets.
> No,
> there is a process, a
> check-a-finite-sequence-of-claims-for-
> -all-not-first-possibly-false-hood
> process.

This is not what I call a process. In fact there is no process required to check
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
Only a counterexample. But there is none.

Regards, WM

On 1/9/2023 2:46 AM, WM wrote:
> Jim Burns schrieb am Sonntag, 8. Januar 2023 um 20:26:18 UTC+1:
>> WM wrote:
>>> William schrieb am Sonntag,
>>> 8. Januar 2023 um 00:12:07 UTC+1:
>>>> S_n is a set, something that does not change.
>>>> There is no process involved
>>>> in determining the cardinality.,
>>
>>> For every definable n
>>> there is a process leading to it.
>>
>>> There is no process possible
>>> for cardinality ℵo of infinite sets.
>
>> No,
>> there is a process.
>>
>> However,
>> it is not the process you're imagining.
>> It is not a count-to-infinity process.
>>
>> Instead, it is a
>> check-a-finite-sequence-of-claims-for-
>> -all-not-first-possibly-false-hood
>> process.
>
> Maybe. Writing and checking claims is a process. But the process of individual treatment requires individual treatment. That is not possible for Cantor's set ℕ. >Always amost all ℵo elments remain outside / uncounted.

*What a load of bullshit*.

*You get an F for FAIL in Math*, as you cannot and refuse to understand a formal Math Proof.

that is why you are still counting, one by one, step by step your sheeps or rocks.

>>
>> A sequence of claims either
>> has a _first_ possibly-false claim or
>> doesn't have any possibly-false claim.
>
> This sequence has no first false claim:
> After collecting n ∈ ℕ almost all ℵo elements remain uncollected.
> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo

where you stopped at n. you have a FISON, and an Endsegment, did you forget those again ?

>>
>>> There is no process possible
>>> for cardinality ℵo of infinite sets.
>> No,
>> there is a process, a
>> check-a-finite-sequence-of-claims-for-
>> -all-not-first-possibly-false-hood
>> process.
>
> This is not what I call a process. In fact there is no process required to check
> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo.
> Only a counterexample. But there is none.

no "checking" is required if it has been Proven, but you dont even understand these simple math terms.

>
> Regards, WM

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How do You rate this on 1....10 scale ?
On Sunday, January 8, 2023 at 10:02:33 PM UTC+2, Jim Burns wrote:
> On 1/8/2023 2:32 PM, mitchr...@gmail.com wrote:
> > On Sunday, January 8, 2023
> > at 11:26:18 AM UTC-8, Jim Burns wrote:
> >> WM wrote:
>
> >>> There is no process possible
> >>> for cardinality ℵo of infinite sets.
> >>
> >> No,
> >> there is a process, a
> >> check-a-finite-sequence-of-claims-for-
> >> -all-not-first-possibly-false-hood
> >> process.
> >
> > Should not sub finite and..
> > the no quantity at all..
> > be the dark?
> > Zero is absolute dark...
> > the unlimited small has a relative dark.
> The dark is not my baby, it is WM's.
>
> However,
> my understanding is that "the dark" is
> about being beyond unknown, unknowable.
>
> There are many questions for which
> zero is known to be the answer.
> That would make zero not-dark, I think.
>
>
> My anti-dark argument is that
> we can know something true of infinitely-many
> individuals without performing infinitely-many
> actions.
>
> The agreed-upon fact that
> there are infinitely-many individuals
> is not a good argument for dark things.

On Monday, January 9, 2023 at 9:46:18 AM UTC+1, WM wrote:

> That is not possible for Cantor's set ℕ. Always amost all ℵo elements remain outside / uncounted.

Nonsense. All natural numbers are in IN, by definition.

Hint: x is a natural number <-> x e IN.

Got that you silly crank?

Moreover, Chuck Norris counted all (infinitely many) elements in IN - twice..

On Monday, January 9, 2023 at 4:37:30 AM UTC-4, WM wrote:
> That ℕ is not a Peano set is proved by the fact that you will never have collected its elements completely.

Nope. At no step will you have collected every element of a Peano set. At every step there is a set, S_n={p(n), sp(n), ssp(n), ....}, with cardinality aleph_0 uncollected (For different n, S_n can be different). Note, a Peano set cannot have "dark" elements.

|N satisfies the Peano axioms, thus |N is a Peano set.

On 1/9/2023 2:37 AM, WM wrote:
> William schrieb am Sonntag, 8. Januar 2023 um 18:33:33 UTC+1:
>> On Sunday, January 8, 2023 at 1:21:10 PM UTC-4, WM wrote:
>>> William schrieb am Sonntag, 8. Januar 2023 um 17:44:10 UTC+1:
>>>> WM: There are always Peano elements outside.
>>> That is the nature of potential infinity.
>> Nothing to do with "potential infinity". A Peano set does not change.
>
> What you erroneously call Peano set is Cantor's set ℕ.

QUACK!!

> That ℕ is not a Peano set is proved by the fact that you will never have collected QUACK!!

> its elements completely.
>
> There is a dark interval between what you can do and completeness.

QuaCK!! there is a dark interval between WM and Math.

> Remember: 'it never happens but it happened' is unique to processes with no last step.

QUACK!!! "WM never proves anything, but says its proved"

>

> But after the end it turns out that all numbers have been collected - in a not observable way. Don't you think so?

you insist on seeing each number, so go do it. report back later when you are done, and not before!

>
> Regards, WM

William schrieb am Montag, 9. Januar 2023 um 15:58:03 UTC+1:
> On Monday, January 9, 2023 at 4:37:30 AM UTC-4, WM wrote:
>
> > That ℕ is not a Peano set is proved by the fact that you will never have collected its elements completely.
> Nope. At no step will you have collected every element of a Peano set. At every step there is a set, S_n={p(n), sp(n), ssp(n), ....}, with cardinality aleph_0 uncollected (For different n, S_n can be different).

But collectively, i.e., without applying an order, you can collect all such that none remains.

> Note, a Peano set cannot have "dark" elements.

Agreed. At no step you have all.
>
> |N satisfies the Peano axioms, thus |N is a Peano set.

Not that |N that can be collected only collectively.

Regards,WM

On 1/9/2023 1:26 PM, WM wrote:
> William schrieb am Montag, 9. Januar 2023 um 15:58:03 UTC+1:
>> On Monday, January 9, 2023 at 4:37:30 AM UTC-4, WM wrote:
>>
>>> That ℕ is not a Peano set is proved by the fact that you will never have collected its elements completely.
>> Nope. At no step will you have collected every element of a Peano set. At every step there is a set, S_n={p(n), sp(n), ssp(n), ....}, with cardinality aleph_0 uncollected (For different n, S_n can be different).
>
> But collectively, i.e., without applying an order, you can collect all such that none remains.
>
>> Note, a Peano set cannot have "dark" elements.
>
> Agreed. At no step you have all.
>>
>> |N satisfies the Peano axioms, thus |N is a Peano set.
>
> Not that |N that can be collected only collectively.
>
> Regards,WM

so you are talking about a subset of |N, of your collected elements, and not the entire set |N.