On Thursday, November 2, 2023 at 6:50:50 PM UTC-3, WM wrote:
> William schrieb am Donnerstag, 2. November 2023 um 20:30:56 UTC+1:
> > On Thursday, November 2, 2023 at 12:34:23 PM UTC-3, WM wrote:
> > > William schrieb am Donnerstag, 2. November 2023 um 12:33:16 UTC+1:
> > > > On Thursday, November 2, 2023 at 7:39:17 AM UTC-3, WM wrote:
> > > > > William schrieb am Donnerstag, 2. November 2023 um 02:35:41 UTC+1:
> > > > > > On Wednesday, November 1, 2023 at 6:16:19 PM UTC-3, WM wrote:
> > > > > > > William schrieb am Mittwoch, 1. November 2023 um 18:56:02 UTC+1:
> > > > > > > > On Wednesday, November 1, 2023 at 7:12:47 AM UTC-3, WM wrote:
> > > > > > > >
> > > > > > > > > > At each step n your game of billiards produces A(n). There is no step which produces A, i.e.your game of billiards never produces A.
> > > > > > > > > Then never all indices have been applied in my game.
> > > > > > Correct. There is no last step in your game of billiards. At no step have all indices been applied.
> > > > > But all steps are defined by the definition of the game,
> > > > Correct. And, according to this definition, at no step have all indices been applied.
> > > At no step, yes, but what about: when all steps have been done?
> > This is not part of your billiard game.
> My billiard game.
never reaches "when all steps have been done"

Fritz Feldhase schrieb am Donnerstag, 2. November 2023 um 17:51:33 UTC+1:
> On Thursday, November 2, 2023 at 4:31:43 PM UTC+1, WM wrote:
>
> > Cantor's bijections are supertasks
> You don't know what you are talking about,

I know that there is no deviation between Cantor's counting and a supertask..

Regards, WM

Jim Burns schrieb am Donnerstag, 2. November 2023 um 22:04:48 UTC+1:
> On 11/2/2023 11:31 AM, WM wrote:
> > Jim Burns schrieb am Donnerstag,
> > 2. November 2023 um 03:49:29 UTC+1:
> >> [...]
> >
> > [...] that Cantor's bijections are supertasks
>
> If Georg Cantor had googled "bijection",
He did not know yet that his theory had to be defended by defrauders.
He simply counted all natural numbers. That is a supertask.
"we can talk about the nth algebraic number where not a single one of this epitome () has been forgotten."

Regards, WM

On Thursday, November 2, 2023 at 2:50:50 PM UTC-7, WM wrote:
> William schrieb am Donnerstag, 2. November 2023 um 20:30:56 UTC+1:
> > On Thursday, November 2, 2023 at 12:34:23 PM UTC-3, WM wrote:
> > > William schrieb am Donnerstag, 2. November 2023 um 12:33:16 UTC+1:
> > > > On Thursday, November 2, 2023 at 7:39:17 AM UTC-3, WM wrote:
> > > > > William schrieb am Donnerstag, 2. November 2023 um 02:35:41 UTC+1:
> > > > > > On Wednesday, November 1, 2023 at 6:16:19 PM UTC-3, WM wrote:
> > > > > > > William schrieb am Mittwoch, 1. November 2023 um 18:56:02 UTC+1:
> > > > > > > > On Wednesday, November 1, 2023 at 7:12:47 AM UTC-3, WM wrote:
> > > > > > > >
> > > > > > > > > > At each step n your game of billiards produces A(n). There is no step which produces A, i.e.your game of billiards never produces A.
> > > > > > > > > Then never all indices have been applied in my game.
> > > > > > Correct. There is no last step in your game of billiards. At no step have all indices been applied.
> > > > > But all steps are defined by the definition of the game,
> > > > Correct. And, according to this definition, at no step have all indices been applied.
> > > At no step, yes, but what about: when all steps have been done?
> > This is not part of your billiard game.
>
> My billiard game mimics Cantor's bijection.

No, it doesn't, because you don't have the second principle of generation of whole real numbers.

William schrieb am Donnerstag, 2. November 2023 um 22:57:01 UTC+1:
> On Thursday, November 2, 2023 at 6:50:50 PM UTC-3, WM wrote:

> > My billiard game.
> never reaches "when all steps have been done"
According to Cantor we can talk about the nth step number where not a single step has been forgotten.

Regards, WM

FredJeffries schrieb am Donnerstag, 2. November 2023 um 23:10:29 UTC+1:
> On Thursday, November 2, 2023 at 2:50:50 PM UTC-7, WM wrote:
> > William schrieb am Donnerstag, 2. November 2023 um 20:30:56 UTC+1:
> > > On Thursday, November 2, 2023 at 12:34:23 PM UTC-3, WM wrote:
> > > > William schrieb am Donnerstag, 2. November 2023 um 12:33:16 UTC+1:
> > > > > On Thursday, November 2, 2023 at 7:39:17 AM UTC-3, WM wrote:
> > > > > > William schrieb am Donnerstag, 2. November 2023 um 02:35:41 UTC+1:
> > > > > > > On Wednesday, November 1, 2023 at 6:16:19 PM UTC-3, WM wrote:
> > > > > > > > William schrieb am Mittwoch, 1. November 2023 um 18:56:02 UTC+1:
> > > > > > > > > On Wednesday, November 1, 2023 at 7:12:47 AM UTC-3, WM wrote:
> > > > > > > > >
> > > > > > > > > > > At each step n your game of billiards produces A(n). There is no step which produces A, i.e.your game of billiards never produces A.
> > > > > > > > > > Then never all indices have been applied in my game.
> > > > > > > Correct. There is no last step in your game of billiards. At no step have all indices been applied.
> > > > > > But all steps are defined by the definition of the game,
> > > > > Correct. And, according to this definition, at no step have all indices been applied.
> > > > At no step, yes, but what about: when all steps have been done?
> > > This is not part of your billiard game.
> >
> > My billiard game mimics Cantor's bijection.
> No, it doesn't, because you don't have the second principle of generation of whole real numbers.

I do exactly the same as Cantor.

Regards, WM

On Thursday, November 2, 2023 at 7:10:46 PM UTC-3, WM wrote:
> William schrieb am Donnerstag, 2. November 2023 um 22:57:01 UTC+1:
> > On Thursday, November 2, 2023 at 6:50:50 PM UTC-3, WM wrote:
>
> > > My billiard game.
> > never reaches "when all steps have been done"
> According to Cantor we can talk about the nth step number where not a single step has been forgotten.
False and irrelevant. Your billiard game does not have an nth step "where not a single step has been forgotten". There is no matrix A in you billiard game.

On Thursday, November 2, 2023 at 11:05:36 PM UTC+1, WM wrote:

> He [Cantor] simply counted all natural numbers. That is a supertask.

Mückenheim, Du verwechselst Cantor mit Chuck Norris.*)

Ganz offensichtlich bist Du dabei, in einem Rekordtempo zu verblöden.

________________________________________

*) Chuck Norris counted to infinity - twice!

On Thursday, November 2, 2023 at 3:11:48 PM UTC-7, WM wrote:
> FredJeffries schrieb am Donnerstag, 2. November 2023 um 23:10:29 UTC+1:
> > On Thursday, November 2, 2023 at 2:50:50 PM UTC-7, WM wrote:
> > > William schrieb am Donnerstag, 2. November 2023 um 20:30:56 UTC+1:
> > > > On Thursday, November 2, 2023 at 12:34:23 PM UTC-3, WM wrote:
> > > > > William schrieb am Donnerstag, 2. November 2023 um 12:33:16 UTC+1:
> > > > > > On Thursday, November 2, 2023 at 7:39:17 AM UTC-3, WM wrote:
> > > > > > > William schrieb am Donnerstag, 2. November 2023 um 02:35:41 UTC+1:
> > > > > > > > On Wednesday, November 1, 2023 at 6:16:19 PM UTC-3, WM wrote:
> > > > > > > > > William schrieb am Mittwoch, 1. November 2023 um 18:56:02 UTC+1:
> > > > > > > > > > On Wednesday, November 1, 2023 at 7:12:47 AM UTC-3, WM wrote:
> > > > > > > > > >
> > > > > > > > > > > > At each step n your game of billiards produces A(n).. There is no step which produces A, i.e.your game of billiards never produces A.
> > > > > > > > > > > Then never all indices have been applied in my game.
> > > > > > > > Correct. There is no last step in your game of billiards. At no step have all indices been applied.
> > > > > > > But all steps are defined by the definition of the game,
> > > > > > Correct. And, according to this definition, at no step have all indices been applied.
> > > > > At no step, yes, but what about: when all steps have been done?
> > > > This is not part of your billiard game.
> > >
> > > My billiard game mimics Cantor's bijection.
> >
> > No, it doesn't, because you don't have the second principle of generation of whole real numbers.
>
> I do exactly the same as Cantor.

In that case, you can show us where you use he second principle of generation of whole real numbers.

On 11/2/2023 6:05 PM, WM wrote:
> Jim Burns schrieb am Donnerstag,
> 2. November 2023 um 22:04:48 UTC+1:
>> On 11/2/2023 11:31 AM, WM wrote:

>>> [...] that
>>> Cantor's bijections are supertasks
>>
>> If Georg Cantor had googled "bijection",

B ⊆ U×V:
∀u ∈ U: ∃!⟨u,vᵤ⟩ ∈ B ∧
∀v ∈ V: ∃!⟨uᵥ,v⟩ ∈ B

> He did not know yet that his theory
> had to be defended by defrauders.

∀⟨1,…,n⟩ ⊆ ℕ = ⋂{S⊆ℕ| ∀⟨1,…,n⟩ ⊆ S }

U := ℕ×ℕ
V := ℕ×{1}
B := {⟨⟨i,j⟩,⟨k,1⟩⟩|k=i+(i+j-1)(i+j-2)/2}

B ⊆ U×V:
∀u ∈ U: ∃!⟨u,vᵤ⟩ ∈ B ∧
∀v ∈ V: ∃!⟨uᵥ,v⟩ ∈ B

Also, U ⊃≠ V

> He simply counted all natural numbers.
> That is a supertask.

No,
Georg Cantor didn't count to infinity.
You are thinking of Chuck Norris.

> "we can talk about the nth algebraic number
> where not a single one of this epitome ()
> has been forgotten."

On Thursday, November 2, 2023 at 11:05:36 PM UTC+1, WM wrote:

> He [Cantor] simply counted all natural numbers.

Certainly not, you psychotic asshole full of shit.

Hint: "/Counting/ is the process of determining the number of elements of a finite set of objects; that is, determining the size of a [finite] set." (Wikipedia)

Only Chuck Norris ever counted to infinity (even twice).

On Thursday, November 2, 2023 at 3:58:55 PM UTC-7, Jim Burns wrote:
> On 11/2/2023 6:05 PM, WM wrote:

> > He simply counted all natural numbers.

He did no such thing. He enumerated the SET of natural numbers.

> > That is a supertask.

He was humble enough to realize that he would never count 'all natural numbers'. (He clearly distinguishes his transfinites from the metaphysical, mystical, theological,... 'absolute infinite')

He did something else. He invented the concept of the second principle of generation of whole real numbers and was thus able to enumerate the set of natural numbers.

Not the same as performing your demanded 'supertask'. But something that could actually be achieved.

But since you don't understand the second principle of generation of whole real numbers -- nay, you refuse to acknowledge it's existence -- you will never understand what Cantor (and set theory) accomplishes.

on 11/2/2023, WM supposed :
> Fritz Feldhase schrieb am Donnerstag, 2. November 2023 um 17:51:33 UTC+1:
>> On Thursday, November 2, 2023 at 4:31:43 PM UTC+1, WM wrote:
>>
>>> Cantor's bijections are supertasks
>> You don't know what you are talking about,
>
> I know that there is no deviation between Cantor's counting and a supertask.

You 'know' this because you can't envision things being 'built' or
demonstrated in other than step-by-step fashion. This is your
shortcoming, not anybody else's.

WM explained :
> Jim Burns schrieb am Donnerstag, 2. November 2023 um 22:04:48 UTC+1:
>> On 11/2/2023 11:31 AM, WM wrote:
>>> Jim Burns schrieb am Donnerstag,
>>> 2. November 2023 um 03:49:29 UTC+1:
>>>> [...]
>>>
>>> [...] that Cantor's bijections are supertasks
>>
>> If Georg Cantor had googled "bijection",
> He did not know yet that his theory had to be defended by defrauders.

You are a fraud.

> He simply counted all natural numbers.

No, he showed that there is a bijection between these countable sets.

> That is a supertask.

Only if you insist upon treating the set as a step-by-step project
instead of a mathematically described object.

> "we can talk about the nth algebraic number where not a single one of this
> epitome () has been forgotten."

So what? It still doesn't mean what you want it to.

On 11/2/2023 6:05 PM, WM wrote:
> Jim Burns schrieb am Donnerstag,
> 2. November 2023 um 22:04:48 UTC+1:

>> [...]

> [Cantor] simply counted all natural numbers.
> That is a supertask.
> "we can talk about
> the nth algebraic number where
> not a single one of this epitome ()
> has been forgotten."

_Talking about_ infinitely-many numbers by
making finitely-many finite-length claims
is not a super-task.

Even finitely talking about a super-task
is not itself a super-task.

Describe an algebraic number ==
Make a claims true of each algebraic number
and not all true of anything else,
not forgetting any of them.
Not a super-task.

Augment those claims with only
not-first-false claims,
finite-length, finitely-many.
For those of us not Chuck Norris,
necessarily not a super-task.

It is _because_ it is not a super-task
that we know that the augmenting is true.

In a _finite_ sequence of claims,
there can't be a false claim without
a first-false claim.

Some finite sequences of claims have only
not-first-false claims.
Those sequences have only not-false claims.
_Because_ the sequence is finite.

Some claims are visibly not-first-false,
because they are after certain other claims.
There is no super-task-verifying involved
in seeing what claims they're after.

For example,
∀y∃x:P(x,y) is not-first false in
⟨... ∃x∀y:P(x,y) ∀y∃x:P(x,y) ...⟩

∀y∃x:P(x,y) can be false, but
it can't be false with ∃x∀y:P(x,y) true.
∀y∃x:P(x,y) can't be _first_ false.

We know that just by looking at
⟨... ∃x∀y:P(x,y) ∀y∃x:P(x,y) ...⟩

In contrast,
we aren't able to make a similar claim about
⟨... ∀y∃x:P(x,y) ∃x∀y:P(x,y) ...⟩

There are instances with both
∀y∃x:P(x,y) true and ∃x∀y:P(x,y) false,
and ∃x∀y:P(x,y) possibly first-false.

∃x∀y:P(x,y) could be true anyway, but
we can't tell that just by looking at
⟨... ∀y∃x:P(x,y) ∃x∀y:P(x,y) ...⟩
the way in which we can for
⟨... ∃x∀y:P(x,y) ∀y∃x:P(x,y) ...⟩
Not-first-false sequences are limited in scope,
but, where they reach, they can't be wrong.

> [Cantor] simply counted all natural numbers.
> That is a supertask.

We can talk about each of infinitely-many
natural numbers, and know
_what we say about infinitely-many_ is true,
without performing super-tasks.

William schrieb am Donnerstag, 2. November 2023 um 23:26:07 UTC+1:
> On Thursday, November 2, 2023 at 7:10:46 PM UTC-3, WM wrote:
> > William schrieb am Donnerstag, 2. November 2023 um 22:57:01 UTC+1:
> > > On Thursday, November 2, 2023 at 6:50:50 PM UTC-3, WM wrote:
> >
> > > > My billiard game.
> > > never reaches "when all steps have been done"
> > According to Cantor we can talk about the nth step number where not a single step has been forgotten.
> False and irrelevant.

Cantor.

>Your billiard game does not have an nth step "where not a single step has been forgotten".

Could you name anything of Cantor's that is missing in my game?

> There is no matrix A in you billiard game.

Could you name any natnumber that is not used as an index? - and that is used by Cantor? Instead of claiming a difference show it please.

Regards, WM

FredJeffries schrieb am Donnerstag, 2. November 2023 um 23:44:52 UTC+1:
> On Thursday, November 2, 2023 at 3:11:48 PM UTC-7, WM wrote:

> > > > My billiard game mimics Cantor's bijection.
> > >
> > > No, it doesn't, because you don't have the second principle of generation of whole real numbers.
> >
> > I do exactly the same as Cantor.
> In that case, you can show us where you use he second principle of generation of whole real numbers.

Cantor does not use it in his counting argument. When dealing with Cantor's mappings between infinite sets, it is argued usually that these mappings require a "limit" or "second principle of generation of whole real numbers" to be completed or that they cannot be completed. Such arguing has to be rejected flatly. For this reason some of Cantor's statements are quoted below..

"If we think the numbers p/q in such an order [...] then every number p/q comes at an absolutely fixed position of a simple infinite sequence" [E. Zermelo: "Georg Cantor – Gesammelte Abhandlungen mathematischen und philosophischen Inhalts", Springer, Berlin (1932) p. 126]

"The infinite sequence thus defined has the peculiar property to contain the positive rational numbers completely, and each of them only once at a determined place." [G. Cantor, letter to R. Lipschitz (19 Nov 1883)]

Find a natural number that is applied by Cantor but not by me.

Regards, WM

Hello,

So it is my last post here , so you have to know that i am not a spammer ,
it is just that i have grouped my thoughts of my philosophy and of my thoughts about artificial intelligence and i have posted them here in my previous post, so it is my last post here.

Thank you,
Amine Moulay Ramdane.

Fritz Feldhase schrieb am Freitag, 3. November 2023 um 01:03:41 UTC+1:
> On Thursday, November 2, 2023 at 11:05:36 PM UTC+1, WM wrote:
> > He [Cantor] simply counted all natural numbers.

> Hint: "/Counting/ is the process of determining the number of elements of a finite set of objects; that is, determining the size of a [finite] set." (Wikipedia)
>
Countability = Abzählbarkeit, so daß alle singulären Puncte sich in der Form einer Reihe setzen lassen.
festgesetzten Rangordnung ihrer Elemente gegenseitig eindeutig aufeinander abbilden, oder wie man sich gewöhnlich ausdrückt, aufeinander *abzählen* lassen.
Find a natnumber applied by Cantor but not by me.

Regards, WM

On Friday, November 3, 2023 at 8:21:23 AM UTC-7, Amine Moulay Ramdane wrote:
> Hello,
>
>
> So it is my last post here , so you have to know that i am not a spammer ,
> it is just that i have grouped my thoughts of my philosophy and of my thoughts about artificial intelligence and i have posted them here in my previous post, so it is my last post here.
>
> Thank you,
> Amine Moulay Ramdane.

Que sera sera - if you post again you will.

Any will.

"What will be will be", que sera sera,
but that's the future, and the future is not yet written.

FromTheRafters schrieb am Freitag, 3. November 2023 um 10:11:08 UTC+1:
> on 11/2/2023, WM supposed :
> > Fritz Feldhase schrieb am Donnerstag, 2. November 2023 um 17:51:33 UTC+1:
> >> On Thursday, November 2, 2023 at 4:31:43 PM UTC+1, WM wrote:
> >>
> >>> Cantor's bijections are supertasks
> >> You don't know what you are talking about,
> >
> > I know that there is no deviation between Cantor's counting and a supertask.
> You 'know' this because you can't envision things being 'built' or
> demonstrated in other than step-by-step fashion.

Counting is done in step-by-step fashion. Find a deciation between Cantor's indices and mine.

Regards, WM

on 11/3/2023, Wolfgang supposed :
> William schrieb am Donnerstag, 2. November 2023 um 23:26:07 UTC+1:
>> On Thursday, November 2, 2023 at 7:10:46 PM UTC-3, WM wrote:
>>> William schrieb am Donnerstag, 2. November 2023 um 22:57:01 UTC+1:
>>>> On Thursday, November 2, 2023 at 6:50:50 PM UTC-3, WM wrote:
>>>>> My billiard game.
>>>> never reaches "when all steps have been done"
>>> According to Cantor we can talk about the nth step number where not a
>>> single step has been forgotten.
>> False and irrelevant.
>
> Cantor.
>
>> Your billiard game does not have an nth step "where not a single step has
>> been forgotten".
>
> Could you name anything of Cantor's that is missing in my game?

Sanity, which is really something considering his unfortunate history.
Your game only demonstrates your misunderstanding of things infinite.

Amine Moulay Ramdane Sep 28, 2022, 7:50:43 AM
It was my last post about my thoughts that are not about math,
from now on i will post just about math if i want to post here.

Amine Moulay Ramdane Aug 18, 2023, 10:42:11 AM
Don't worry, i have just posted two posts about generative AI and about my proverbs and
it is my last post here in this newsgroup.

Amine Moulay Ramdane Sep 7, 2023, 11:50:08 AM
i invite you to read my new following thoughts and all my below thoughts, and of course
it is my last post here:

Amine Moulay Ramdane 8:21 AM (1 hour ago)
So it is my last post here , so you have to know that i am not a spammer , it is just
that i have grouped my thoughts of my philosophy and of my thoughts about artificial
intelligence and i have posted them here in my previous post,
so it is my last post here.

Do you want to bet on that?

Searching sci.math for amine moulay ramdane philosophy
returns over 1800 posts dating back to August 2022
and before that you posted about your philosophy
with the name Wisdom91 and before that Wisdom90
and Horizon68 and Sky89 and computer45 and inteli2
and ram18 and Ramine dating back to 2/3/2017.
I'm fairly confident there are even more posts about your
philosophy and your love poems and your corrections
of your previous posts that my simple search did not find.

On Friday, November 3, 2023 at 4:19:51 PM UTC+1, Wolfgang wrote:

> When dealing with Cantor's mappings between infinite sets, it is argued usually that these mappings require a "limit" or

Das ist lediglich eine Deiner Wahnideen, Du Spinner.

On Friday, November 3, 2023 at 4:44:06 PM UTC+1, FromTheRafters wrote:
> on 11/3/2023, Wolfgang supposed :
> >
> > Could you name anything of Cantor's that is missing in my game?
> >
> Sanity, which is really something considering his unfortunate history.
> Your game only demonstrates your misunderstanding of things infinite.

Oh, I'd say it shows MUCH more...