On 9/12/2022 8:53 AM, WM wrote:
> Fritz Feldhase schrieb am Sonntag, 11. September 2022 um 16:39:31 UTC+2:
>> On Sunday, September 11, 2022 at 3:05:21 PM UTC+2, WM wrote:
>>> Fritz Feldhase schrieb am Samstag, 10. September 2022 um 19:24:35 UTC+2:
>>>> On Friday, September 9, 2022 at 2:05:33 PM UTC+2, WM wrote:
>>>>> Fritz Feldhase schrieb am Donnerstag, 8. September 2022 um 21:31:00 UTC+2:
>>>>>
>>>>>> Now we can distribute them the following way (to fill the first column of a matrix):
>>>>>>
>>>>>> X_1 O O ...
>>>>>> X_2 O O ...
>>>>>> X_3 O O ...
>>>>>> ...
>>>>>>
>>>>>> or we can distribute them the following way (to fill all elements of a matrix):
>>>>>>
>>>>>> X_1 X_2 X_4 ...
>>>>>> X_3 X_5 X_8 ...
>>>>>> X_6 X_9 X_1/3 ...
>>>>>> ...
>>>>> But the first matrix cannot be turned into the second matrix [by a sequence of pairwise exchages of] Xs and Os.
>>>>>
>>>> Right.
>>>>
>>>> But NO ONE -except you- ever suggested that this might or should be possible.
>>>>
>>> Cantor has.
>> No, he hasn't.
>>
>> Mind to present a quote to back up your (false) claim?
>
> "wenn sie sich gegenseitig eindeutig, Element für Element einander zuordnen lassen." [Cantor, p. 167]

bad quote, its simply mapping, no swaparoofesting;

"if they can be clearly assigned to each other, element by element."

>
> Regards, WM

On 9/12/2022 9:54 AM, WM wrote:
> Fritz Feldhase schrieb am Sonntag,
> 11. September 2022 um 16:48:48 UTC+2:
>> On Sunday, September 11, 2022
>> at 3:14:28 PM UTC+2, WM wrote:

>>> Hilbert's hotel adds another room with
>>> no problems.
>>
>> Nonsense. You are just making this up,
>> you silly crank!!!
>> No room is added.
>
> Every person has his own room.

For each room,
for each split of its lower-numbered rooms,
there is a room i last-before the split,
and a room i+1 first-after the split.

> A person is added.

Every guest moves to the next room.
Room 0 is left empty.
The new guest takes room 0.

> Every person has his own room.

For each room,
for each split of its lower-numbered rooms,
there is a room i last-before the split,
and a room i+1 first-after the split.

Infinity is not
a reallyreallyreallyreallyreallyreally
big number.

Jim Burns schrieb am Montag, 12. September 2022 um 19:29:36 UTC+2:
> On 9/12/2022 9:54 AM, WM wrote:
> > Fritz Feldhase schrieb am Sonntag,
> > 11. September 2022 um 16:48:48 UTC+2:
> >> On Sunday, September 11, 2022
> >> at 3:14:28 PM UTC+2, WM wrote:
>
> >>> Hilbert's hotel adds another room with
> >>> no problems.
> > Every person has his own room.
> For each room,
> for each split of its lower-numbered rooms,
> there is a room i last-before the split,
> and a room i+1 first-after the split.
>
> > A person is added.
>
> Every guest moves to the next room.
> Room 0 is left empty.
> The new guest takes room 0.
> > Every person has his own room.
> For each room,
> for each split of its lower-numbered rooms,
> there is a room i last-before the split,
> and a room i+1 first-after the split.
>
>
> Infinity is not
> a reallyreallyreallyreallyreallyreally
> big number.

One fact that you cannot deny: There is one more person after than before and every person has his own room. Therefore there is one more room, contradicting completeness.

Regards, WM

On 9/12/2022 4:50 PM, WM wrote:
> Jim Burns schrieb am Montag,
> 12. September 2022 um 19:29:36 UTC+2:
>> On 9/12/2022 9:54 AM, WM wrote:
>>> Fritz Feldhase schrieb am Sonntag,
>>> 11. September 2022 um 16:48:48 UTC+2:
>>>> On Sunday, September 11, 2022
>>>> at 3:14:28 PM UTC+2, WM wrote:

>>>>> Hilbert's hotel adds another room with
>>>>> no problems.
>>>
>>> Every person has his own room.
>>
>> For each room,
>> for each split of its lower-numbered rooms,
>> there is a room i last-before the split,
>> and a room i+1 first-after the split.
>>
>>> A person is added.
>>
>> Every guest moves to the next room.
>> Room 0 is left empty.
>> The new guest takes room 0.
>>
>>> Every person has his own room.
>>
>> For each room,
>> for each split of its lower-numbered rooms,
>> there is a room i last-before the split,
>> and a room i+1 first-after the split.
>>
>>
>> Infinity is not
>> a reallyreallyreallyreallyreallyreally
>> big number.
>
> One fact that you cannot deny:
> There is one more person after than before
> and every person has his own room.

Another fact:
Nowhere in the problem description are there
instructions to a construction crew.
No "Build another room".

Each room is occupied.
Each current guest moves to an occupied room
There is an empty room for the new guest.

> Therefore there is one more room,
> contradicting completeness.

Before Guest Minus One arrives,
for each room,
for each split of its lower-numbered rooms,
there is a room i last-before the split,
and a room i+1 first-after the split.

After Guest Minus One arrives,
for each room,
for each split of its lower-numbered rooms,
there is a room i last-before the split,
and a room i+1 first-after the split.

On Monday, September 12, 2022 at 3:53:15 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Sonntag, 11. September 2022 um 16:39:31 UTC+2:
> > On Sunday, September 11, 2022 at 3:05:21 PM UTC+2, WM wrote:

You fucking asshole mentioned:

| But the first matrix cannot be turned into the second matrix [by a sequence of pairwise exchages of] Xs and Os.

To which I relied:

| Right.
| But NO ONE -except you- ever suggested that this might or should be possible.

Then you claimed:

| Cantor has.

To which I replied:

| No, he hasn't.
| Mind to present a quote to back up your (false) claim?

Now you write:

> "wenn sie sich gegenseitig eindeutig, Element für Element einander zuordnen lassen." [Cantor, p. 167]

Du bist so verwirrt, Mückenheim, dass man es gar nicht mehr in Worte fassen kann.

WAS BITTE soll dieses Zitat mit Deiner Behauptung zu tun haben, dass CANTOR den Scheißdreck behauptet hätte, den DU ihm offenbar in den Mund legen willst?

Du kannst wirklich nicht mehr klar denken!

Cantor just talks about a BIJEKTION here. Has NOTHING to do with your braindead idea of "swapping matrix element", you silly crank!

Hint: NO ONE -except you- ever suggested that it might or should be possible to turn "the first matrix" into "the second matrix" by a sequence of pairwise exchages of Xs and Os.

Got it now, you psychotic asshole full of shit?

On Monday, September 12, 2022 at 3:54:41 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Sonntag, 11. September 2022 um 16:48:48 UTC+2:
> > On Sunday, September 11, 2022 at 3:14:28 PM UTC+2, WM wrote:
> > >
> > > Hilbert's hotel adds another room with no problems.
> > >
> > Nonsense. You are just making this up, you silly crank!!!
> >
> > No room is added.
> >
> Every person has his own room. A person is added. Every person has his own room.

So what? Still, no room is added, you silly crank.

Hint: "Hilbert's paradox of the Grand Hotel (colloquial: Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive property of infinite sets. It is demonstrated that a fully occupied hotel with infinitely many rooms may still accommodate additional guests." (Wikipedia)

In detail:

"Consider a hypothetical hotel with a countably infinite number of rooms, all of which are occupied. One might be tempted to think that the hotel would not be able to accommodate any newly arriving guests, as would be the case with a finite number of rooms, where the pigeonhole principle would apply..

Suppose a new guest arrives and wishes to be accommodated in the hotel. We can (simultaneously) move the guest currently in room 1 to room 2, the guest currently in room 2 to room 3, and so on, moving every guest from their current room n to room n+1. After this, room 1 is empty and the new guest can be moved into that room." (Wikipedia)

WE SEE: _No room is added_, you fucking asshole full of shit!

Source: https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel

On Monday, September 12, 2022 at 10:50:24 PM UTC+2, WM wrote:

> One fact that you cannot deny: There is one more person after than before and every person has his own room.

We don't deny _that_. :-)

> Therefore there is one more room[.]

Non sequitur.

Hint: "Hilbert's paradox of the Grand Hotel (colloquial: Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive property of infinite sets. It is demonstrated that a fully occupied hotel with infinitely many rooms may still accommodate additional guests." (Wikipedia)

In detail:

"Consider a hypothetical hotel with a countably infinite number of rooms, all of which are occupied. One might be tempted to think that the hotel would not be able to accommodate any newly arriving guests, as would be the case with a finite number of rooms, where the pigeonhole principle would apply..

Suppose a new guest arrives and wishes to be accommodated in the hotel. We can (simultaneously) move the guest currently in room 1 to room 2, the guest currently in room 2 to room 3, and so on, moving every guest from their current room n to room n+1. After this, room 1 is empty and the new guest can be moved into that room." (Wikipedia)

Hint: The hotel does not "grow" (i. e. "gain" or "develop" new rooms) in a magical way, you know. And NO ONE -except you- ever suggested such a nonsensical thing!

Source: https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel

On Monday, 12 September 2022 at 10:50:27 UTC-3, WM wrote:
> Gus Gassmann schrieb am Sonntag, 11. September 2022 um 15:41:29 UTC+2:
> > On Sunday, 11 September 2022 at 10:14:28 UTC-3, WM wrote:
> > [...]
> > > An infinite set according to Cantor is complete. That means nothing can be added. Hilbert's hotel adds another room [...]
> >
> > No room is added
> A person is added.

Yes.

> A room is occupied that before was not occupied.

No. Emphatically NO. You simply have no clue how infinity works.

måndag 12 september 2022 kl. 15:50:27 UTC+2 skrev WM:
> Gus Gassmann schrieb am Sonntag, 11. September 2022 um 15:41:29 UTC+2:
> > On Sunday, 11 September 2022 at 10:14:28 UTC-3, WM wrote:
> > [...]
> > > An infinite set according to Cantor is complete. That means nothing can be added. Hilbert's hotel adds another room [...]
> >
> > No room is added
> A person is added. A room is occupied that before was not occupied.
>
> Regards, WM
You clearly do not understand how it works

Jim Burns schrieb am Montag, 12. September 2022 um 23:42:37 UTC+2:
> On 9/12/2022 4:50 PM, WM wrote:

> > One fact that you cannot deny:
> > There is one more person after than before
> > and every person has his own room.
> Another fact:
> Nowhere in the problem description are there
> instructions to a construction crew.
> No "Build another room".

Irrelevant. X guests have completely occupied all rooms. With a new guest there are X+1 guests, i.e., one more guest.
>
> Each room is occupied.
> Each current guest moves to an occupied room
> There is an empty room for the new guest.

The magic of potentialinfinity! If there was completed infinity, then no room could become empty. I have proved this by the Mona Lisa. The new guest hands the stolen Mona Lisa to the gust moving from room 1 to room 2. He hands the Mona Lisa to the guest moving from room 2 to room 3. And so does every guest. Finally the Mona Lisa has disappeared. That means finally a guest carrying the Mona Lisa has disappeared.

People who believe in Hilbert's hotel haven't a clue of actual infinity.

Regards, WM

Fritz Feldhase schrieb am Dienstag, 13. September 2022 um 00:46:44 UTC+2:

> > Every person has his own room. A person is added. Every person has his own room.
> So what? Still, no room is added, you silly crank.
>
> Hint: "Hilbert's paradox of the Grand Hotel (colloquial: Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive property of infinite sets.

It illustrates that most people have not the faintest idea about actual infinity but it is their boast that they can believe in counter-intuitive results.

> WE SEE: _No room is added

No guest is added?
If one guest is added and the number of rooms is the number of guests, then one room is added.

Regards, WM

Fritz Feldhase schrieb am Dienstag, 13. September 2022 um 00:55:22 UTC+2:
> We can (simultaneously) move the guest currently in room 1 to room 2, the guest currently in room 2 to room 3, and so on,

For every visible guest this can be done without the "simultaneity-cheating". Only counterfeiters need it.

Regards, WM

zelos...@gmail.com schrieb am Dienstag, 13. September 2022 um 07:26:02 UTC+2:
> måndag 12 september 2022 kl. 15:50:27 UTC+2 skrev WM:
> > Gus Gassmann schrieb am Sonntag, 11. September 2022 um 15:41:29 UTC+2:
> > > On Sunday, 11 September 2022 at 10:14:28 UTC-3, WM wrote:
> > > [...]
> > > > An infinite set according to Cantor is complete. That means nothing can be added. Hilbert's hotel adds another room [...]
> > >
> > > No room is added
> > A person is added. A room is occupied that before was not occupied.
> >
> You clearly do not understand how it works

It is very easy to understand the sleight of hand.

Regards, WM

On 9/13/2022 7:37 AM, WM wrote:
> zelos...@gmail.com schrieb am Dienstag, 13. September 2022 um 07:26:02 UTC+2:
>> måndag 12 september 2022 kl. 15:50:27 UTC+2 skrev WM:
>>> Gus Gassmann schrieb am Sonntag, 11. September 2022 um 15:41:29 UTC+2:
>>>> On Sunday, 11 September 2022 at 10:14:28 UTC-3, WM wrote:
>>>> [...]
>>>>> An infinite set according to Cantor is complete. That means nothing can be added. Hilbert's hotel adds another room [...]
>>>>
>>>> No room is added
>>> A person is added. A room is occupied that before was not occupied.
>>>
>> You clearly do not understand how it works
>
> It is very easy to understand the sleight of hand.
>
> Regards, WM

A KEEPER !!

"It is very easy to understand the sleight of hand." -WM

On Tuesday, September 13, 2022 at 2:26:17 PM UTC+2, WM wrote:
> Jim Burns schrieb am Montag, 12. September 2022 um 23:42:37 UTC+2:
> >
> > No "Build another room".
> >
> X guests have completely occupied all rooms. With a new guest there are X+1 guests

Yeah, you blithering idiot, where X = aleph_0 and hence X+1 = X. <facepalm>

> , i.e., [THE SAME NUMBER OF GUEST].

Fuck off, Mückenheim!

On Tuesday, September 13, 2022 at 2:32:06 PM UTC+2, WM wrote

something that shows, that he has

> not the faintest idea about actual infinity.

Yes, Mückenheim. This fact is well known.

On Tuesday, September 13, 2022 at 2:32:06 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Dienstag, 13. September 2022 um 00:46:44 UTC+2:
> >
> > WE SEE: _No room is added_
> >
> No guest is added?

Something wrong with your reading coprehension too?

I WROTE: ____No room is added____, you fucking idiot!

EOD

On 9/13/2022 8:26 AM, WM wrote:
> Jim Burns schrieb am Montag,
> 12. September 2022 um 23:42:37 UTC+2:
>> On 9/12/2022 4:50 PM, WM wrote:

>>> One fact that you cannot deny:
>>> There is one more person after than before
>>> and every person has his own room.
>>
>> Another fact:
>> Nowhere in the problem description are there
>> instructions to a construction crew.
>> No "Build another room".
>
> Irrelevant.
> X guests have completely occupied all rooms.
> With a new guest there are X+1 guests, i.e.,
> one more guest.

....in the same rooms.

Infinity is not
a reallyreallyreallyreallyreallyreally
big number.

>> Each room is occupied.
>> Each current guest moves to an occupied room
>> There is an empty room for the new guest.
>
> The magic of potentialinfinity!

| Any sufficiently advanced technology
| is indistinguishable from magic.
| -- Clarke's Third Law

For you (WM), "sufficiently advanced" is
practically anything.

> If there was completed infinity,
> then no room could become empty.

If there was WM-completed-infinity,
some rooms would not equal themselves.

Fritz Feldhase schrieb am Dienstag, 13. September 2022 um 17:47:40 UTC+2:
> On Tuesday, September 13, 2022 at 2:26:17 PM UTC+2, WM wrote:
> > Jim Burns schrieb am Montag, 12. September 2022 um 23:42:37 UTC+2:
> > >
> > > No "Build another room".
> > >
> > X guests have completely occupied all rooms. With a new guest there are X+1 guests
> Yeah, where X = aleph_0 and hence X+1 = X.

Irrelevant. X+1 is more than X. This is provable by the new guest.
>
> > , i.e., [THE SAME NUMBER OF GUEST].

This "number" is not sharp but only means many. Otherwise it could not be multiplied by 10 and even itself without changing its value. Many times many is many. Not a very helpful "number".

Regards, WM

Fritz Feldhase schrieb am Dienstag, 13. September 2022 um 17:51:49 UTC+2:
> On Tuesday, September 13, 2022 at 2:32:06 PM UTC+2, WM wrote:
> > Fritz Feldhase schrieb am Dienstag, 13. September 2022 um 00:46:44 UTC+2:
> > >
> > > WE SEE: _No room is added_
> > >
> > No guest is added?
>
> I WROTE: ____No room is added

You wrote nonsense, like most matheologians.

Regards, WM

Jim Burns schrieb am Dienstag, 13. September 2022 um 18:55:19 UTC+2:

> If there was WM-completed-infinity,
> some rooms would not equal themselves.

You can distinguish the old set of guests and the present set of guests, can't you?
But you cannot distinguish their rooms. Strange.

Note: ℵ₀ means nothing else but "many". Therefore ℵ₀ + 1 = ℵ₀. But ℕ is fixed such that |ℕ| is a precise number such that |ℕ| + 1 =/= |ℕ|.

Regards, WM

On 9/13/2022 1:36 PM, WM wrote:
> Jim Burns schrieb am Dienstag, 13. September 2022 um 18:55:19 UTC+2:
>
>> If there was WM-completed-infinity,
>> some rooms would not equal themselves.
>
> You can distinguish the old set of guests and the present set of guests, can't you?
> But you cannot distinguish their rooms. Strange.
>
> Note: ℵ₀ means nothing else but "many". Therefore ℵ₀ + 1 = ℵ₀. But ℕ is fixed such that |ℕ| is a precise number such that |ℕ| + 1 =/= |ℕ|.
>
> Regards, WM

so what is the price value of |ℕ| ?

On 9/13/2022 1:37 PM, Sergio wrote:
> On 9/13/2022 1:36 PM, WM wrote:
>> Jim Burns schrieb am Dienstag, 13. September 2022 um 18:55:19 UTC+2:
>>
>>> If there was WM-completed-infinity,
>>> some rooms would not equal themselves.
>>
>> You can distinguish the old set of guests and the present set of guests, can't you?
>> But you cannot distinguish their rooms. Strange.
>>
>> Note: ℵ₀ means nothing else but "many". Therefore ℵ₀ + 1 = ℵ₀. But ℕ is fixed such that |ℕ| is a precise number such that |ℕ| + 1 =/= |ℕ|.
>>
>> Regards, WM
>
> so what is the price value of |ℕ| ?

So what is the precise value of |ℕ| ? and Who fixed it ?

On Tuesday, September 13, 2022 at 8:25:56 PM UTC+2, WM wrote:
> Fritz Feldhase schrieb am Dienstag, 13. September 2022 um 17:47:40 UTC+2:
> > On Tuesday, September 13, 2022 at 2:26:17 PM UTC+2, WM wrote:
> > > Jim Burns schrieb am Montag, 12. September 2022 um 23:42:37 UTC+2:
> > > >
> > > > No "Build another room".
> > > >
> > > X guests have completely occupied all rooms. With a new guest there are X+1 guests
> > >
> > Yeah, where X = aleph_0 and hence X+1 = X.
> >
> X+1 is more than X.

No, you blithering idiot, X+1 is NOT "more than" - read: larger than - X+1, since X+1 = X (and not X+1 > X).

Man, you are dumb like shit!

On Tuesday, September 13, 2022 at 8:36:32 PM UTC+2, WM wrote:
> Jim Burns schrieb am Dienstag, 13. September 2022 um 18:55:19 UTC+2:
>
> ℵ₀ means nothing else but "many".

No, in set theory this is the cardinal number of "countable infinite" sets, you silly asshole!

See: https://en.wikipedia.org/wiki/Aleph_number#Aleph-nought

Hence it means "countably infinitely many".

> ℵ₀ + 1 = ℵ₀.

Right.

Hint: If a !e A and card(A) = ℵ₀, then card(A u {a}) = ℵ₀.

> But ℕ is fixed such that |ℕ| is a precise number

Which number is it? A natural number?

> such that |ℕ| + 1 =/= |ℕ|.

How is "addition" defined for your mysterious numbers? How can we PROVE that |ℕ| + 1 =/= |ℕ|.

You see an application of the axiom "Because I said so" is not good enough in set theory. You have to DEFINE your notions and to PROVE your claims.

Yeah, "[WM’s] conclusions are based on the sloppiness of his notions, his inability of giving precise definitions, his fundamental misunderstanding of elementary mathematical concepts, and sometimes, as the late Dik Winter remarked [...], on nothing at all."