On 12/30/2023 8:11 AM, Richard Damon wrote:
> On 12/30/23 6:21 AM, WM wrote:
>> Le 28/12/2023 à 19:34, Richard Damon a écrit :
>>> On 12/28/23 11:28 AM, WM wrote:
[...]
> Someone who thinks there must be a highest Natural Number (or smallest
> unit fraction) has already failed.

Right! Big time.

Fritz Feldhase schrieb am Sonntag, 31. Dezember 2023 um 22:01:00 UTC+1:
> On Saturday, December 30, 2023 at 5:44:39 PM UTC+1, WM wrote:
>
> > the matrix
> >
> > X O O O...
> > X O O O...
> > X O O O...
> > X O O O...
> > ...
> > will never be covered by X.
> Das hat vor allem etwas damit zu tun, dass sich eine "gegebene"
Matrix nicht verändert,

But the covering X change their positions.

> Nun kann man aber auch eine Matrix A = (a_n,m)_(n,m e IN) definieren,
die statt Xen z. B. die natürlichen Zahlen 1, 2, 3, ... in der ersten
Spalte enthält (und sonst überall 0):
>
> 1 0 0 ...
> 2 0 0 ...
> 3 0 0 ...
> ...
>
> ODER aber auch eine Matrix B = (b_n,m)_(n,m e IN) , die die Zahlen 1,
2, 3, 4, ... VERTEILT über sämtliche "Positionen" der Matrix enthält,
und zwar gemäß der Definition b_n.m = <1000-mal gepostet>.
>
> 1 2 4 ...
> 3 5 8 ...
> 6 9 13 ...
> ...
>
If both matrices were of same size, then the covering would be possible.
What should hinder it? However it is impossible. That falsifies your claim.

Regards, WM

On 1/1/2024 7:08 AM, WM wrote:
> Fritz Feldhase schrieb am Sonntag, 31. Dezember 2023 um 22:01:00 UTC+1:
> > On Saturday, December 30, 2023 at 5:44:39 PM UTC+1, WM wrote:
> >
> > > the matrix
> > >
> > > X O O O...
> > > X O O O...
> > > X O O O...
> > > X O O O...
> > > ...
> > > will never be covered by X.
> > Das hat vor allem etwas damit zu tun, dass sich eine "gegebene"
> Matrix nicht verändert,
>
> But the covering X change their positions.
>
> > Nun kann man aber auch eine Matrix A = (a_n,m)_(n,m e IN) definieren,
> die statt Xen z. B. die natürlichen Zahlen 1, 2, 3, ... in der ersten
> Spalte enthält (und sonst überall 0):
> >
> > 1 0 0 ...
> > 2 0 0 ...
> > 3 0 0 ...
> > ...
> >
> > ODER aber auch eine Matrix B = (b_n,m)_(n,m e IN) , die die Zahlen 1,
> 2, 3, 4, ... VERTEILT über sämtliche "Positionen" der Matrix enthält,
> und zwar gemäß der Definition b_n.m = <1000-mal gepostet>.
> >
> > 1 2 4 ...
> > 3 5 8 ...
> > 6 9 13 ...
> > ...
> >
> If both matrices were of same size, then the covering would be possible.
> What should hinder it? However it is impossible. That falsifies your claim.

Are you a massive idiot, or just pretty much a moron?

Fritz Feldhase schrieb am Montag, 1. Januar 2024 um 16:36:14 UTC+1:

> Btw. Since these two matrices are of the same size, we may (for example) ADD
> them. Getting A + B:
>
> 2 2 4 ...
> 5 5 8 ...
> 9 9 13 ...
> ...

Richtig, so weit das Auge reicht. Da B genau so viele Elemente hat wie die
erste Spalte von A und eine Umstellung daran nichts ändert, zeugt der
erste matheologische Glaubenssatz von völliger mathematischer
Inkompetenz.

Gruß, WM

On 1/3/2024 8:35 AM, WM wrote:
> Fritz Feldhase schrieb am Montag, 1. Januar 2024 um 16:36:14 UTC+1:
>
>> Btw. Since these two matrices are of the same size, we may (for
>> example) ADD them. Getting A + B:
>> 2 2 4 ... 5 5 8 ... 9 9 13 ... ...
>
> Richtig, so weit das Auge reicht. Da B genau so viele Elemente hat wie
> die erste Spalte von A und eine Umstellung daran nichts ändert, zeugt
> der erste matheologische Glaubenssatz von völliger mathematischer
> Inkompetenz.

Ahhh, you are in a new category! Well done. A new type of hyper massive
idiotic moron. WOW!

Fritz Feldhase schrieb am Mittwoch, 3. Januar 2024 um 18:21:54 UTC+1:
> On Wednesday, January 3, 2024 at 5:35:49 PM UTC+1, WM wrote:

> > Richtig [...]. Da B genau so viele Elemente hat wie die erste Spalte von A
>
> Im Zusammenhang mit unendlichen Mengen/Gesamtheiten spricht man besser mit
> Cantor von Mächtigkeit(en).

Das ist ein sinnloser Begriff, weil er nur die potentiell unendlichen
Anfangsbschnitte aktual unendlicher Mengen verwendet.
>
> Ja, die Mächtigkeit der Menge der Terme der Matrix B ist gleich der
> Mächtigkeit der Menge der Terme in der ersten Spalte der Matrix A, nämlich
> gleich aleph_0.

Genauer: Die Anzahlen sind gleich.
>
> (Hier ist es hilfreich anzumerken, dass aleph_0 * aleph_0 = aleph_0 ist, aber
> das nur am Rande.)

Hier wird bewiesen, dass diese Behauptung falsch ist:

XOOO...
XOOO...
XOOO...
XOOO...
...

Es ist unmöglich, die Matrix mit X zu überdecken, da die Menge der nicht
überdeckten Positionen, gekennzeichnet durch O, konstant bleibt. Das wird
allgemein anerkannt, zum Beispiel: "In einem Punkt hat er natürlich
recht: kein Term seiner 'Matrizenfolge' wird je O-frei sein" (FF). Und
anschließend geschieht nichts mehr.

Aber wer das nicht begreifen will oder kann, mag sich mit matheologischen
Unsinn verlustieren. Es gibt dazu nichts weiter zu sagen als EOD.

Gruß, WM

On Saturday, December 30, 2023 at 12:44:39 PM UTC-4, WM wrote:

> > Your game does not provide a definition for the putative A
> That is because
I.e the putative A is not defined. Yet you continue to use the properties of this non existent thing

On 04.01.2024 17:19, William wrote:
> On Saturday, December 30, 2023 at 12:44:39 PM UTC-4, WM wrote:
>
>>> Your game does not provide a definition for the putative A
>> That is because
> I.e the putative A is not defined. Yet you continue to use the properties of this non existent thing

This matrix is of same size:
XOOO...
XOOO...
XOOO...
XOOO...
....
Its size does not change when reordering the X. The not indexed places,
indicated by O, will be reordered too, but will never be indexed. Only
that is of interest.

Regards, WM

On 1/5/24 5:14 AM, WM wrote:
> On 04.01.2024 17:19, William wrote:
>> On Saturday, December 30, 2023 at 12:44:39 PM UTC-4, WM wrote:
>>
>>>> Your game does not provide a definition for the putative A
>>> That is because
>> I.e the putative A is not defined.  Yet you continue to  use the
>> properties of this non existent thing
>
> This matrix is of same size:
> XOOO...
> XOOO...
> XOOO...
> XOOO...
> ...
> Its size does not change when reordering the X. The not indexed places,
> indicated by O, will be reordered too, but will never be indexed. Only
> that is of interest.
>
> Regards, WM

In other words, you don't understand Cantor's proof and are just trying
to use "common sense" on things that are actually known to defy "common
sense" because infinity introduces some "strangeness"

Note, if you do it right, you can actually make the O's "disappear",
because you can swap them out to an unbounded distance from the start,
and pull in the unbounded number of x's on that first column into the
part of the matrix that we can see.

Yes, the Os are "still there" but have disappered.

Remember, one property of infinite sets is that a proper subset of an
infinte set may still have exactly the same size as the original set itself.

Thus, the original set of all cells with X or O, can be (and in this
case is) the exact same size as both the set of Xs and the set of Os and
those sets are also exactly the same size.

If your mind and logic can't handle that fact, then it is just
insufficient to handle this.

A simple proof of this fact is look at the Natural Numbers and the Even
Numbers. Clearly the Even Numbers are a Proper Subset of the Natural
Numbers, as one way to make that set is to remove all the odd numbers,
which should leave us with a set that is one-half the size.

But another way to build the set of even numbers is to transform the
elements of the set of Natural Numbers by doubling each element. A set
built by transforming every element to a new unique element can't be of
different size as the original set.

Thus, we have shown that for sets of infinite size, the Natural Numbers,
the subset of it , The Even Natural Numbers, is both a proper subset,
and of the same size.

On 1/5/2024 9:04 AM, Richard Damon wrote:
> On 1/5/24 5:14 AM, WM wrote:
>> On 04.01.2024 17:19, William wrote:
>>> On Saturday, December 30, 2023 at 12:44:39 PM UTC-4, WM wrote:
>>>
>>>>> Your game does not provide a definition for the putative A
>>>> That is because
>>> I.e the putative A is not defined.  Yet you continue to  use the
>>> properties of this non existent thing
>>
>> This matrix is of same size:
>> XOOO...
>> XOOO...
>> XOOO...
>> XOOO...
>> ...
>> Its size does not change when reordering the X. The not indexed
>> places, indicated by O, will be reordered too, but will never be
>> indexed. Only that is of interest.
>>
>> Regards, WM
>
> In other words, you don't understand Cantor's proof and are just trying
> to use "common sense" on things that are actually known to defy "common
> sense" because infinity introduces some "strangeness"
>
> Note, if you do it right, you can actually make the O's "disappear",
> because you can swap them out to an unbounded distance from the start,
> and pull in the unbounded number of x's on that first column into the
> part of the matrix that we can see.
>
> Yes, the Os are "still there" but have disappered.
>
> Remember, one property of infinite sets is that a proper subset of an
> infinte set may still have exactly the same size as the original set
> itself.
>
> Thus, the original set of all cells with X or O, can be (and in this
> case is) the exact same size as both the set of Xs and the set of Os and
> those sets are also exactly the same size.
>
> If your mind and logic can't handle that fact, then it is just
> insufficient to handle this.
>
> A simple proof of this fact is look at the Natural Numbers and the Even
> Numbers. Clearly the Even Numbers are a Proper Subset of the Natural
> Numbers, as one way to make that set is to remove all the odd numbers,
> which should leave us with a set that is one-half the size.
>
> But another way to build the set of even numbers is to transform the
> elements of the set of Natural Numbers by doubling each element. A set
> built by transforming every element to a new unique element can't be of
> different size as the original set.
>
> Thus, we have shown that for sets of infinite size, the Natural Numbers,
> the subset of it , The Even Natural Numbers, is both a proper subset,
> and of the same size.
>
>

*Does the directly executed D(D) halt?*

--
Copyright 2023 Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer

On Friday, January 5, 2024 at 6:14:17 AM UTC-4, WM wrote:
> On 04.01.2024 17:19, William wrote:
> > On Saturday, December 30, 2023 at 12:44:39 PM UTC-4, WM wrote:
> >
> >>> Your game does not provide a definition for the putative A
> >> That is because
> > I.e the putative A is not defined. Yet you continue to use the properties of this non existent thing
> This matrix

A does not exist, There is no "the matrix".

On 1/5/24 1:27 PM, olcott wrote:
>
> *Does the directly executed D(D) halt?*

So, you are just showing your total stupidity, as this was posted in
reply to a message and thread that had nothing to do with a program D or
Halting in general, but on counting infinite sets which is a totally
different field of logic and mathematics.

I guess someone is off their medication.

William schrieb am Freitag, 5. Januar 2024 um 19:38:07 UTC+1:
> On Friday, January 5, 2024 at 6:14:17 AM UTC-4, WM wrote:
> > On 04.01.2024 17:19, William wrote:
> > > On Saturday, December 30, 2023 at 12:44:39 PM UTC-4, WM wrote:
> > >
> > >>> Your game does not provide a definition for the putative A
> > >> That is because
> > > I.e the putative A is not defined. Yet you continue to use the properties of
> this non existent thing
> > This matrix
> A does not exist, There is no "the matrix".

If actual infinity exists, then the matrix A(0) =
1, 1/2, 1/3, 1/4, ...
2, 2/2, 2/3, 2/4, ...
3, 3/2, 3/3, 3/4, ...
4, 4/2, 4/3, 4/4, ...
5, 5/2, 5/3, 5/4, ...
...
exists, and every reordering of the X by exchanging X and O does not
remove any O. Hence not all fractions can get indexed.

Regards, WM

Le 05/01/2024 à 16:04, Richard Damon a écrit :
> On 1/5/24 5:14 AM, WM wrote:
>> On 04.01.2024 17:19, William wrote:
>>> On Saturday, December 30, 2023 at 12:44:39 PM UTC-4, WM wrote:
>>>
>>>>> Your game does not provide a definition for the putative A
>>>> That is because
>>> I.e the putative A is not defined.  Yet you continue to  use the
>>> properties of this non existent thing
>>
>> This matrix is of same size:
>> XOOO...
>> XOOO...
>> XOOO...
>> XOOO...
>> ...
>> Its size does not change when reordering the X. The not indexed places,
>> indicated by O, will be reordered too, but will never be indexed. Only
>> that is of interest.

> In other words, you don't

believe in nonsense

> and are just trying
> to use "common sense" on things that are actually known to defy "common
> sense" because infinity introduces some "strangeness"

Only when the religion of matheology is concerned.
>
> Note, if you do it right, you can actually make the O's "disappear",
> because you can swap them out to an unbounded distance from the start,

Yes, they disappear but they cannot leave the matrix by exchange with x.
Simplest logic.
>
> Yes, the Os are "still there" but have disappered.

That means, they have settled at dark places.
>
> Remember, one property of infinite sets is that a proper subset of an
> infinte set may still have exactly the same size as the original set itself.

That is shown to be the belief of cranks by just the present argument. It
cannot be used as an argument to corrupt logic.

Regards, WM

On 1/8/24 5:20 AM, WM wrote:
> Le 05/01/2024 à 16:04, Richard Damon a écrit :
>> On 1/5/24 5:14 AM, WM wrote:
>>> On 04.01.2024 17:19, William wrote:
>>>> On Saturday, December 30, 2023 at 12:44:39 PM UTC-4, WM wrote:
>>>>
>>>>>> Your game does not provide a definition for the putative A
>>>>> That is because
>>>> I.e the putative A is not defined.  Yet you continue to  use the
>>>> properties of this non existent thing
>>>
>>> This matrix is of same size:
>>> XOOO...
>>> XOOO...
>>> XOOO...
>>> XOOO...
>>> ...
>>> Its size does not change when reordering the X. The not indexed
>>> places, indicated by O, will be reordered too, but will never be
>>> indexed. Only that is of interest.
>
>> In other words, you don't
>
> believe in nonsense
>
>> and are just trying to use "common sense" on things that are actually
>> known to defy "common sense" because infinity introduces some
>> "strangeness"
>
> Only when the religion of matheology is concerned.
>>
>> Note, if you do it right, you can actually make the O's "disappear",
>> because you can swap them out to an unbounded distance from the start,
>
> Yes, they disappear but they cannot leave the matrix by exchange with x.
> Simplest logic.
>>
>> Yes, the Os are "still there" but have disappered.
>
> That means, they have settled at dark places.
>>
>> Remember, one property of infinite sets is that a proper subset of an
>> infinte set may still have exactly the same size as the original set
>> itself.
>
> That is shown to be the belief of cranks by just the present argument.
> It cannot be used as an argument to corrupt logic.
>
> Regards, WM
>

In other words, you admit that your whole system is based on things you
can't prove so you rely on just worthless hand waving.

You are just too stupid to understand mathematics.

On 1/8/24 5:15 AM, WM wrote:
> William schrieb am Freitag, 5. Januar 2024 um 19:38:07 UTC+1:
>> On Friday, January 5, 2024 at 6:14:17 AM UTC-4, WM wrote: > On
>> 04.01.2024 17:19, William wrote: > > On Saturday, December 30, 2023 at
>> 12:44:39 PM UTC-4, WM wrote: > > > >>> Your game does not provide a
>> definition for the putative A > >> That is because > > I.e the
>> putative A is not defined. Yet you continue to use the properties of
>> this non existent thing > This matrix
>> A does not exist, There is no "the matrix".
>
> If actual infinity exists, then the matrix A(0) =
> 1, 1/2, 1/3, 1/4, ...
> 2, 2/2, 2/3, 2/4, ...
> 3, 3/2, 3/3, 3/4, ...
> 4, 4/2, 4/3, 4/4, ...
> 5, 5/2, 5/3, 5/4, ...
> ..
> exists, and every reordering of the X by exchanging X and O does not
> remove any O. Hence not all fractions can get indexed.
>
> Regards, WM
>

Right, "exchanging" can't get rid of anything, so something based on
exchanging can't show two things are of the same length as you always
will have xs and os.

You are just too stupid to understand where you are wrong.

Le 08/01/2024 à 13:21, Richard Damon a écrit :
> On 1/8/24 5:15 AM, WM wrote:

>> If actual infinity exists, then the matrix A(0) =
>> 1, 1/2, 1/3, 1/4, ...
>> 2, 2/2, 2/3, 2/4, ...
>> 3, 3/2, 3/3, 3/4, ...
>> 4, 4/2, 4/3, 4/4, ...
>> 5, 5/2, 5/3, 5/4, ...
>> ..
>> exists, and every reordering of the X by exchanging X and O does not
>> remove any O. Hence not all fractions can get indexed.
>>
> Right, "exchanging" can't get rid of anything,

Please inform Jim Burns of this invaluable recognition.

> so something based on
> exchanging can't show two things are of the same length as you always
> will have xs and os.
>
But if the indexing should be done by integer fractions, or if the
replacement of integer fractions by integers is allowed, then Cantor's
"bijection" is "completed" by exchanging. Today I have taught my students
of this argument. No-one has contradicted.

> You are just too stupid to understand where you are wrong.

But you know it? Where? Is the bijection n <--> 1/n impossible? Everything
else happens just as Cantor did it.

Regards, WM

On 1/9/24 11:57 AM, WM wrote:
> Le 08/01/2024 à 13:21, Richard Damon a écrit :
>> On 1/8/24 5:15 AM, WM wrote:
>
>>> If actual infinity exists, then the matrix A(0) =
>>> 1, 1/2, 1/3, 1/4, ...
>>> 2, 2/2, 2/3, 2/4, ...
>>> 3, 3/2, 3/3, 3/4, ...
>>> 4, 4/2, 4/3, 4/4, ...
>>> 5, 5/2, 5/3, 5/4, ...
>>> ..
>>> exists, and every reordering of the X by exchanging X and O does not
>>> remove any O. Hence not all fractions can get indexed.
>>>
>> Right, "exchanging" can't get rid of anything,
>
> Please inform Jim Burns of this invaluable recognition.

WHy, because it just shows that you are doing the wrong thing.

>
>> so something based on exchanging can't show two things are of the same
>> length as you always will have xs and os.
>>
> But if the indexing should be done by integer fractions, or if the
> replacement of integer fractions by integers is allowed, then Cantor's
> "bijection" is "completed" by exchanging. Today I have taught my
> students of this argument. No-one has contradicted.

Who is "indexing" by integer fractions.

You are again pointing the gun the wrong way.

THe indexing is a mapping of the Natural Numbers, to the elements of the
FULL matrix.

>
>> You are just too stupid to understand where you are wrong.
>
> But you know it? Where? Is the bijection n <--> 1/n impossible?
> Everything else happens just as Cantor did it.
>
> Regards, WM

No, we can biject n <--> 1/n, just as we can biject n <--> m/n with a
different pattern.

Le 10/01/2024 à 03:58, Richard Damon a écrit :
> On 1/9/24 11:57 AM, WM wrote:

>> But you know it? Where? Is the bijection n <--> 1/n impossible?
>> Everything else happens just as Cantor did it.
>>
>> Regards, WM
>
> No, we can biject n <--> 1/n, just as we can biject n <--> m/n with a
> different pattern.

Meant was to biject n and n/1 which is possible because n = n/1.

But to cover the matrix
XOOO...
XOOO...
XOOO...
XOOO...
...
by reordering the X is impossible. If you can't see it you are better
suited for the H4O debate, EOD.

Regards, WM

On Monday, January 8, 2024 at 6:15:16 AM UTC-4, WM wrote:

>the matrix A(0)

Is not the putative matrix A. There is no matrix A

William schrieb am Donnerstag, 11. Januar 2024 um 04:05:51 UTC+1:
> On Monday, January 8, 2024 at 6:15:16 AM UTC-4, WM wrote:
>
> >the matrix A(0)
>
> Is not the putative matrix A. There is no matrix A

But all existing matrices A(n) have all O's from the beginning.

Regards, WM