Gus Gassmann presented the following explanation :
> On Tuesday, 26 April 2022 at 08:37:20 UTC-3, zelos...@gmail.com wrote:
>> tisdag 26 april 2022 kl. 13:15:57 UTC+2 skrev WM:
>>> zelos...@gmail.com schrieb am Dienstag, 26. April 2022 um 06:50:32 UTC+2:
>>>> måndag 25 april 2022 kl. 12:15:16 UTC+2 skrev WM:
> [...]
>
>>>>> Everyone claiming that all fractions can be enumerated claims that all
>>>>> fractions can be collected in the first column.
>>>> No one is claiming that, what one claim is that there is a function from N
>>>> to Q+, that is a different claim
>>> No, that is precisely this claim. All fractions can be collected in the
>>> first column since the line numbers are the indices of an infinite
>>> sequence.
>> Nope, those are DIFFERENT claims. How is this hard for you to understand?
>> How retarded are you?
>
> It is the same claim, or at least very closely related. The first column of
> the matrix has aleph_0 places. If Q+ is countable, then the positive
> fractions can be arranged to fill (exactly) the places in the first column.
> And the stepwise matrix process is a series of transformations that gets you
> there. It is constructed exactly so that the positive fractions line up in
> the column in the order described by the Cantor sequence. What WM does not
> understand/accept/whatever is that the process is infinite, and at no finite
> step is the process complete. In order to figure out the final process one
> has to take a limit, which is also not very difficult.
>
> [...]

He simply refuses to accept that |N|^2 = |N|

On 4/26/2022 7:27 AM, Gus Gassmann wrote:
> On Tuesday, 26 April 2022 at 08:37:20 UTC-3, zelos...@gmail.com wrote:
>> tisdag 26 april 2022 kl. 13:15:57 UTC+2 skrev WM:
>>> zelos...@gmail.com schrieb am Dienstag, 26. April 2022 um 06:50:32 UTC+2:
>>>> måndag 25 april 2022 kl. 12:15:16 UTC+2 skrev WM:
> [...]
>
>>>>> Everyone claiming that all fractions can be enumerated claims that all fractions can be collected in the first column.
>>>> No one is claiming that, what one claim is that there is a function from N to Q+, that is a different claim
>>> No, that is precisely this claim. All fractions can be collected in the first column since the line numbers are the indices of an infinite sequence.
>> Nope, those are DIFFERENT claims. How is this hard for you to understand? How retarded are you?
>
> It is the same claim, or at least very closely related. The first column of the matrix has aleph_0 places. If Q+ is countable, then the positive fractions can be arranged to fill (exactly) the places in the first column. And the stepwise matrix process is a series of transformations that gets you there. It is constructed exactly so that the positive fractions line up in the column in the order described by the Cantor sequence. What WM does not understand/accept/whatever is that the process is infinite, and at no finite step is the process complete. In order to figure out the final process one has to take a limit, which is also not very difficult.
>
> [...]

Face it, WM is Mathematically Retarded.

Would you trust this guy counting your change, since he made Scrooge McDuck go broke ?

On Tuesday, 26 April 2022 at 11:52:05 UTC-3, sergio wrote:
[...]
> Face it, WM is Mathematically Retarded.
>
> Would you trust this guy counting your change, since he made Scrooge McDuck go broke ?

I wouldn't trust him with the time of day, but that's a different matter.

FromTheRafters schrieb am Dienstag, 26. April 2022 um 16:09:00 UTC+2:

> He simply refuses to accept that |N|^2 = |N|

No I simply disprove it.

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

XXOO...
OOOO...
XOOO...
XOOO...
....

XXOO...
XOOO...
OOOO...
XOOO...
....

XXXO...
XOOO...
OOOO...
OOOO...
....

Regards, WM

On Tuesday, 26 April 2022 at 11:09:00 UTC-3, FromTheRafters wrote:
> Gus Gassmann presented the following explanation :
> > On Tuesday, 26 April 2022 at 08:37:20 UTC-3, zelos...@gmail.com wrote:
> >> tisdag 26 april 2022 kl. 13:15:57 UTC+2 skrev WM:
> >>> zelos...@gmail.com schrieb am Dienstag, 26. April 2022 um 06:50:32 UTC+2:
> >>>> måndag 25 april 2022 kl. 12:15:16 UTC+2 skrev WM:
> > [...]
> >
> >>>>> Everyone claiming that all fractions can be enumerated claims that all
> >>>>> fractions can be collected in the first column.
> >>>> No one is claiming that, what one claim is that there is a function from N
> >>>> to Q+, that is a different claim
> >>> No, that is precisely this claim. All fractions can be collected in the
> >>> first column since the line numbers are the indices of an infinite
> >>> sequence.
> >> Nope, those are DIFFERENT claims. How is this hard for you to understand?
> >> How retarded are you?
> >
> > It is the same claim, or at least very closely related. The first column of
> > the matrix has aleph_0 places. If Q+ is countable, then the positive
> > fractions can be arranged to fill (exactly) the places in the first column.
> > And the stepwise matrix process is a series of transformations that gets you
> > there. It is constructed exactly so that the positive fractions line up in
> > the column in the order described by the Cantor sequence. What WM does not
> > understand/accept/whatever is that the process is infinite, and at no finite
> > step is the process complete. In order to figure out the final process one
> > has to take a limit, which is also not very difficult.
> >
> > [...]
> He simply refuses to accept that |N|^2 = |N|

I think you mean |N^2| = |N|. This is not my area of expertise, but if I understand correctly, you may need the axiom of choice to infer equality.

But that's not really what I responded to in my previous post. WM has various ways to conceptualize for himself that the infinite cannot possibly be real. He is quite creative in his dementia at constructing new and ever more convoluted schemes to delude his own head. (Always brings to mind Bob Dylan's song "License To Kill" with the line "his brain has been mismanaged with great skill".) Whenever I see a new idiocy of his, I always try to figure out exactly where the mistake occurs and how to fix it.

An unsavory Idiot WM drivels:

> FromTheRafters schrieb:
>
>> He simply refuses to accept that |N|^2 = |N|
> No I simply disprove it.

ROFL.
> XOOO...
> XOOO...
> XOOO...
> XOOO...
> ...
>
> XXOO...
> OOOO...
> XOOO...
> XOOO...
> ...
>
> XXOO...
> XOOO...
> OOOO...
> XOOO...
> ...
>
> XXXO...
> XOOO...
> OOOO...
> OOOO...
> ...

ROFL - Ingenious for a clown.

On 4/26/2022 10:25 AM, WM wrote:
> FromTheRafters schrieb am Dienstag, 26. April 2022 um 16:09:00 UTC+2:
>
>> He simply refuses to accept that |N|^2 = |N|
>
> No I simply disprove it.
>
> XOOO...
> XOOO...
> XOOO...
> XOOO...
> ...
>
> XXOO...
> OOOO...
> XOOO...
> XOOO...
> ...
>
> XXOO...
> XOOO...
> OOOO...
> XOOO...
> ...
>
> XXXO...
> XOOO...
> OOOO...
> OOOO...
> ...
>
> Regards, WM

you are doing it all wrong, My turn to disprove it;

XXOO...
OOXO...
XOOO...
XOOO...
....

XXOO...
XOOO...
OOOX...
XOOO...
....
XOOX...
XOOO...
XOXO...
XOOO...
....

Bonus Question:

is
XXXO...
OXOO...
XOXO...
XOOX... ?

On 4/26/2022 10:45 AM, Tom Bola wrote:
> An unsavory Idiot WM drivels:
>
>> FromTheRafters schrieb:
>>
>>> He simply refuses to accept that |N|^2 = |N|
>
>> No I simply disprove it.
>
> ROFL.
>
>> XOOO...
>> XOOO...
>> XOOO...
>> XOOO...
>> ...
>>
>> XXOO...
>> OOOO...
>> XOOO...
>> XOOO...
>> ...
>>
>> XXOO...
>> XOOO...
>> OOOO...
>> XOOO...
>> ...
>>
>> XXXO...
>> XOOO...
>> OOOO...
>> OOOO...
>> ...
>
> ROFL - Ingenious for a clown.

XXOO!! OOXO, and XOOO!

XOOX ?? "XXOX."

On 4/26/2022 7:10 AM, WM wrote:
> Jim Burns schrieb
> am Montag, 25. April 2022 um 20:48:48 UTC+2:
>> On 4/25/2022 1:39 PM, WM wrote:

>>> Is the contents of the first column
>>> an infinite sequence?
>>
>> It is an infinite sequence as "infinite sequence"
>> is usually meant.
>
> So it is. 1/1, 2/1, 3/1, ...
> By values this is same as 1, 2, 3, ...
> Therefore here are all indices which
> Cantor wants to spread over all positive fractions.
>
> But it is obvious that
>

[...]

>> The contents of the first column are
>> totally-ordered such that,
>> there is a first entry but no last entry,
>
> It is the set of indices.

You haven't described an infinite sequence.
You've only given a name, "indices", as though
that name is the answer to the question.

You're trying to hide your dark numbers in vagueness.

But we reject your vagueness,
so you call us "matheologians".

WM pretended :
> FromTheRafters schrieb am Dienstag, 26. April 2022 um 16:09:00 UTC+2:
>
>> He simply refuses to accept that |N|^2 = |N|
>
> No I simply disprove it.

Hugs and kisses are not proof.

Gus Gassmann expressed precisely :
> On Tuesday, 26 April 2022 at 11:09:00 UTC-3, FromTheRafters wrote:
>> Gus Gassmann presented the following explanation :
>>> On Tuesday, 26 April 2022 at 08:37:20 UTC-3, zelos...@gmail.com wrote:
>>>> tisdag 26 april 2022 kl. 13:15:57 UTC+2 skrev WM:
>>>>> zelos...@gmail.com schrieb am Dienstag, 26. April 2022 um 06:50:32 UTC+2:
>>>>>> måndag 25 april 2022 kl. 12:15:16 UTC+2 skrev WM:
>>> [...]
>>>
>>>>>>> Everyone claiming that all fractions can be enumerated claims that all
>>>>>>> fractions can be collected in the first column.
>>>>>> No one is claiming that, what one claim is that there is a function from
>>>>>> N to Q+, that is a different claim
>>>>> No, that is precisely this claim. All fractions can be collected in the
>>>>> first column since the line numbers are the indices of an infinite
>>>>> sequence.
>>>> Nope, those are DIFFERENT claims. How is this hard for you to understand?
>>>> How retarded are you?
>>>
>>> It is the same claim, or at least very closely related. The first column of
>>> the matrix has aleph_0 places. If Q+ is countable, then the positive
>>> fractions can be arranged to fill (exactly) the places in the first column.
>>> And the stepwise matrix process is a series of transformations that gets
>>> you there. It is constructed exactly so that the positive fractions line
>>> up in the column in the order described by the Cantor sequence. What WM
>>> does not understand/accept/whatever is that the process is infinite, and
>>> at no finite step is the process complete. In order to figure out the
>>> final process one has to take a limit, which is also not very difficult.
>>>
>>> [...]
>> He simply refuses to accept that |N|^2 = |N|
>
> I think you mean |N^2| = |N|.

What is N^2 in that equation?

> This is not my area of expertise, but if I
> understand correctly, you may need the axiom of choice to infer equality.

ZFC has AoC, but I refer here to cardinal arithmetic.

The cardinality of the natural numbers times the cardinality of the
natural numbers equals the cardinality of the natural numbers. He won't
accept it because he denies or does not understand cardinal arithmetic.

> But that's not really what I responded to in my previous post. WM has various
> ways to conceptualize for himself that the infinite cannot possibly be real.
> He is quite creative in his dementia at constructing new and ever more
> convoluted schemes to delude his own head. (Always brings to mind Bob Dylan's
> song "License To Kill" with the line "his brain has been mismanaged with
> great skill".) Whenever I see a new idiocy of his, I always try to figure out
> exactly where the mistake occurs and how to fix it.

His mistake is always his ego.

On Tuesday, 26 April 2022 at 15:40:08 UTC-3, FromTheRafters wrote:
> Gus Gassmann expressed precisely :
> > On Tuesday, 26 April 2022 at 11:09:00 UTC-3, FromTheRafters wrote:
> >> Gus Gassmann presented the following explanation :
> >>> On Tuesday, 26 April 2022 at 08:37:20 UTC-3, zelos...@gmail.com wrote:
> >>>> tisdag 26 april 2022 kl. 13:15:57 UTC+2 skrev WM:
> >>>>> zelos...@gmail.com schrieb am Dienstag, 26. April 2022 um 06:50:32 UTC+2:
> >>>>>> måndag 25 april 2022 kl. 12:15:16 UTC+2 skrev WM:
> >>> [...]
> >>>
> >>>>>>> Everyone claiming that all fractions can be enumerated claims that all
> >>>>>>> fractions can be collected in the first column.
> >>>>>> No one is claiming that, what one claim is that there is a function from
> >>>>>> N to Q+, that is a different claim
> >>>>> No, that is precisely this claim. All fractions can be collected in the
> >>>>> first column since the line numbers are the indices of an infinite
> >>>>> sequence.
> >>>> Nope, those are DIFFERENT claims. How is this hard for you to understand?
> >>>> How retarded are you?
> >>>
> >>> It is the same claim, or at least very closely related. The first column of
> >>> the matrix has aleph_0 places. If Q+ is countable, then the positive
> >>> fractions can be arranged to fill (exactly) the places in the first column.
> >>> And the stepwise matrix process is a series of transformations that gets
> >>> you there. It is constructed exactly so that the positive fractions line
> >>> up in the column in the order described by the Cantor sequence. What WM
> >>> does not understand/accept/whatever is that the process is infinite, and
> >>> at no finite step is the process complete. In order to figure out the
> >>> final process one has to take a limit, which is also not very difficult.
> >>>
> >>> [...]
> >> He simply refuses to accept that |N|^2 = |N|
> >
> > I think you mean |N^2| = |N|.
> What is N^2 in that equation?
Very sloppy notation for NxN.

Gus Gassmann wrote on 4/26/2022 :
> On Tuesday, 26 April 2022 at 15:40:08 UTC-3, FromTheRafters wrote:
>> Gus Gassmann expressed precisely :
>>> On Tuesday, 26 April 2022 at 11:09:00 UTC-3, FromTheRafters wrote:
>>>> Gus Gassmann presented the following explanation :
>>>>> On Tuesday, 26 April 2022 at 08:37:20 UTC-3, zelos...@gmail.com wrote:
>>>>>> tisdag 26 april 2022 kl. 13:15:57 UTC+2 skrev WM:
>>>>>>> zelos...@gmail.com schrieb am Dienstag, 26. April 2022 um 06:50:32
>>>>>>> UTC+2:
>>>>>>>> måndag 25 april 2022 kl. 12:15:16 UTC+2 skrev WM:
>>>>> [...]
>>>>>
>>>>>>>>> Everyone claiming that all fractions can be enumerated claims that
>>>>>>>>> all fractions can be collected in the first column.
>>>>>>>> No one is claiming that, what one claim is that there is a function
>>>>>>>> from N to Q+, that is a different claim
>>>>>>> No, that is precisely this claim. All fractions can be collected in the
>>>>>>> first column since the line numbers are the indices of an infinite
>>>>>>> sequence.
>>>>>> Nope, those are DIFFERENT claims. How is this hard for you to
>>>>>> understand? How retarded are you?
>>>>>
>>>>> It is the same claim, or at least very closely related. The first column
>>>>> of the matrix has aleph_0 places. If Q+ is countable, then the positive
>>>>> fractions can be arranged to fill (exactly) the places in the first
>>>>> column. And the stepwise matrix process is a series of transformations
>>>>> that gets you there. It is constructed exactly so that the positive
>>>>> fractions line up in the column in the order described by the Cantor
>>>>> sequence. What WM does not understand/accept/whatever is that the
>>>>> process is infinite, and at no finite step is the process complete. In
>>>>> order to figure out the final process one has to take a limit, which is
>>>>> also not very difficult.
>>>>>
>>>>> [...]
>>>> He simply refuses to accept that |N|^2 = |N|
>>>
>>> I think you mean |N^2| = |N|.
>> What is N^2 in that equation?
> Very sloppy notation for NxN.

Then yes, it sort of describes WM's matrix's dimensions and that the
cardinality of a single row or column can be the same as the
cardinality of the whole thing. It is exactly this which he denies
because it doesn't "feel" right to him.

tisdag 26 april 2022 kl. 17:25:56 UTC+2 skrev WM:
> FromTheRafters schrieb am Dienstag, 26. April 2022 um 16:09:00 UTC+2:
>
> > He simply refuses to accept that |N|^2 = |N|
> No I simply disprove it.
> XOOO...
> XOOO...
> XOOO...
> XOOO...
> ...
> XXOO...
> OOOO...
> XOOO...
> XOOO...
> ...
>
> XXOO...
> XOOO...
> OOOO...
> XOOO...
> ...
>
> XXXO...
> XOOO...
> OOOO...
> OOOO...
> ...
> Regards, WM
You don't disprove it, all you prove is that you are an idiot.

tisdag 26 april 2022 kl. 21:18:45 UTC+2 skrev horand....@gmail.com:
> On Tuesday, 26 April 2022 at 15:40:08 UTC-3, FromTheRafters wrote:
> > Gus Gassmann expressed precisely :
> > > On Tuesday, 26 April 2022 at 11:09:00 UTC-3, FromTheRafters wrote:
> > >> Gus Gassmann presented the following explanation :
> > >>> On Tuesday, 26 April 2022 at 08:37:20 UTC-3, zelos...@gmail.com wrote:
> > >>>> tisdag 26 april 2022 kl. 13:15:57 UTC+2 skrev WM:
> > >>>>> zelos...@gmail.com schrieb am Dienstag, 26. April 2022 um 06:50:32 UTC+2:
> > >>>>>> måndag 25 april 2022 kl. 12:15:16 UTC+2 skrev WM:
> > >>> [...]
> > >>>
> > >>>>>>> Everyone claiming that all fractions can be enumerated claims that all
> > >>>>>>> fractions can be collected in the first column.
> > >>>>>> No one is claiming that, what one claim is that there is a function from
> > >>>>>> N to Q+, that is a different claim
> > >>>>> No, that is precisely this claim. All fractions can be collected in the
> > >>>>> first column since the line numbers are the indices of an infinite
> > >>>>> sequence.
> > >>>> Nope, those are DIFFERENT claims. How is this hard for you to understand?
> > >>>> How retarded are you?
> > >>>
> > >>> It is the same claim, or at least very closely related. The first column of
> > >>> the matrix has aleph_0 places. If Q+ is countable, then the positive
> > >>> fractions can be arranged to fill (exactly) the places in the first column.
> > >>> And the stepwise matrix process is a series of transformations that gets
> > >>> you there. It is constructed exactly so that the positive fractions line
> > >>> up in the column in the order described by the Cantor sequence. What WM
> > >>> does not understand/accept/whatever is that the process is infinite, and
> > >>> at no finite step is the process complete. In order to figure out the
> > >>> final process one has to take a limit, which is also not very difficult.
> > >>>
> > >>> [...]
> > >> He simply refuses to accept that |N|^2 = |N|
> > >
> > > I think you mean |N^2| = |N|.
> > What is N^2 in that equation?
> Very sloppy notation for NxN.
it is not sloppy, it is very standard

tisdag 26 april 2022 kl. 13:15:57 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Dienstag, 26. April 2022 um 06:50:32 UTC+2:
> > måndag 25 april 2022 kl. 12:15:16 UTC+2 skrev WM:
>
> > > > You still haven't defined what "dark" means
> > > Dark natural numbers cannot be used individually.
> > Define that in FOL because "individually" is meaningless.
> > >They can only be used collectively.
> > Define that in FOL
> Why should I use the language FOOL?
> > >They can be removed to isolate omega
> > Omega is an ordinal, it is not part of natural numbers so ti is irrelevant here.
> I use the set {1, 2, 3, ..., omega} which is existing in ZF.
> > > {1, 2, 3, ..., omega} \ {1, 2, 3, ...} = {omega}
> > > Definable natural numbers can be used individually, but omega will never be isolated
> > > ∀n ∈ ℕ_def: {1, 2, 3, ..., omega} \ {1, 2, 3, ..., n} = {n+1, n+2, ..., omega} .
> > And?
> This is a difference.
> > > > > 1/1, 1/2, 1/3, 1/4, ...
> > > > > 2/1, 2/2, 2/3, 2/4, ...
> > > > > 3/1, 3/2, 3/3, 3/4, ...
> > > > > 4/1, 4/2, 4/3, 4/4, ...
> > > > > 5/1, 5/2, 5/3, 5/4, ...
> > > > > ...
> > > > >
> > > > > every attempt to collect all fractions in the first column will fail:
> > > > No one is doing that
> > > Everyone claiming that all fractions can be enumerated claims that all fractions can be collected in the first column.
> > No one is claiming that, what one claim is that there is a function from N to Q+, that is a different claim
> No, that is precisely this claim. All fractions can be collected in the first column since the line numbers are the indices of an infinite sequence.
> > > > > When all definable fractions of Cantor's sequence 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ... will have transferred into the first column, nevertheless all matrix places remain occupied by fractions which are undefinable, because all definable fractions have gone.
> > > > N^2 and N are not the same sets so this is invalid.
> > > According to Cantor N^2 can be linearized.
> > We have a bijection between them,
> that establishs my claim.
>
> Regards, WM
so face it VM, you failed EVERYTHING here

Jim Burns schrieb am Dienstag, 26. April 2022 um 19:51:50 UTC+2:
> On 4/26/2022 7:10 AM, WM wrote:

> > So it is. 1/1, 2/1, 3/1, ...
> > By values this is same as 1, 2, 3, ...

> > It is the set of indices.
> You haven't described an infinite sequence.
> You've only given a name, "indices", as though
> that name is the answer to the question.

Liar.

I have described the first column of the matrix:

1/1, 1/2, 1/3, 1/4, ...
2/1, 2/2, 2/3, 2/4, ...
3/1, 3/2, 3/3, 3/4, ...
4/1, 4/2, 4/3, 4/4, ...
5/1, 5/2, 5/3, 5/4, ...
....

Regards, WM

FromTheRafters schrieb am Dienstag, 26. April 2022 um 22:05:48 UTC+2:

> Then yes, it sort of describes WM's matrix's dimensions and that the
> cardinality of a single row or column can be the same as the
> cardinality of the whole thing. It is exactly this which he denies
> because it

it can be disproved by the fact that every permutation of the X's fails to cover the whole matrix

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

Regards, WM

torsdag 28 april 2022 kl. 14:48:06 UTC+2 skrev WM:
> FromTheRafters schrieb am Dienstag, 26. April 2022 um 22:05:48 UTC+2:
>
> > Then yes, it sort of describes WM's matrix's dimensions and that the
> > cardinality of a single row or column can be the same as the
> > cardinality of the whole thing. It is exactly this which he denies
> > because it
> it can be disproved by the fact that every permutation of the X's fails to cover the whole matrix
> XOOO...
> XOOO...
> XOOO...
> XOOO...
> ...
> Regards, WM

None of this is relevant to you proving your darknumbers.

You couldn't even fucking DEFINE THEM USING FIRST ORDER LOGIC!

You are a failure!

On Thursday, 28 April 2022 at 09:48:06 UTC-3, WM wrote:
> FromTheRafters schrieb am Dienstag, 26. April 2022 um 22:05:48 UTC+2:
>
> > Then yes, it sort of describes WM's matrix's dimensions and that the
> > cardinality of a single row or column can be the same as the
> > cardinality of the whole thing. It is exactly this which he denies
> > because it
> it can be disproved by the fact that every permutation of the X's fails to cover the whole matrix
> XOOO...
> XOOO...
> XOOO...
> XOOO...

More unreflected garbage from you. What the fuck do you think a "permutation of the X's" might look like? And where do the O's fit into your nonthinking? Please get lost.

On 4/28/2022 7:45 AM, WM wrote:
> Jim Burns schrieb am Dienstag, 26. April 2022 um 19:51:50 UTC+2:
>> On 4/26/2022 7:10 AM, WM wrote:
>
>>> So it is. 1/1, 2/1, 3/1, ...
>>> By values this is same as 1, 2, 3, ...
>
>>> It is the set of indices.
>> You haven't described an infinite sequence.
>> You've only given a name, "indices", as though
>> that name is the answer to the question.
>
> Liar.
>
> I have described the first column of the matrix:
>
> 1/1, 1/2, 1/3, 1/4, ...
> 2/1, 2/2, 2/3, 2/4, ...
> 3/1, 3/2, 3/3, 3/4, ...
> 4/1, 4/2, 4/3, 4/4, ...
> 5/1, 5/2, 5/3, 5/4, ...
> ...
>
> Regards, WM

very sloppy math, WM

take your first column, write it as its own series, assuming your last three dots ... means it goes on to infinity, {1/1,2/1,3/1,4/1...}, this is the
set of natural numbers, however it is not in reduced form.

Bonus Question:

what are the indices to this new series ?

On 4/28/2022 7:48 AM, WM wrote:
> FromTheRafters schrieb am Dienstag, 26. April 2022 um 22:05:48 UTC+2:
>
>> Then yes, it sort of describes WM's matrix's dimensions and that the
>> cardinality of a single row or column can be the same as the
>> cardinality of the whole thing. It is exactly this which he denies
>> because it
>
> it can be disproved by the fact that every permutation of the X's fails to cover the whole matrix
>
> XOOO...
> XOOO...
> XOOO...
> XOOO...
> ...
>
> Regards, WM

nope. wrong. try again.

On Thursday, April 21, 2022 at 5:03:43 AM UTC-7, WM wrote:
> zelos...@gmail.com schrieb am Donnerstag, 21. April 2022 um 12:34:25 UTC+2:
> > Hey WM, let's start fresh. You keep claiming there are such things as "dark numbers"
> >
> > Define it in in terms of FOL and then prove that there exists two disjoint non-empty sets that has the union of natural numbers, where one set is your supposed claimed "dark" and the other is not, undark?
> This task is more difficult than the proof that there are dark fractions. If you have understood that it is impossible to enumerate all fractions, because starting from
>
> 1/1, 1/2, 1/3, 1/4, ...
> 2/1, 2/2, 2/3, 2/4, ...
> 3/1, 3/2, 3/3, 3/4, ...
> 4/1, 4/2, 4/3, 4/4, ...
> 5/1, 5/2, 5/3, 5/4, ...
> ...
>
> every attempt to collect all fractions in the first column will fail:
>
> 1/1, 2/1, 1/3, 1/4, ... 1/1, 3/1, 1/3, 1/4, ... 1/1, 3/1, 4/1, 1/4, ... 1/1, 3/1, 4/1, 1/4, ...
> 1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 2/2, 2/3, 2/4, ... 1/2, 5/1, 2/3, 2/4, ...
> 3/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ... 2/1, 3/2, 3/3, 3/4, ...
> 4/1, 4/2, 4/3, 4/4, ... 4/1, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ... 1/3, 4/2, 4/3, 4/4, ...
> 5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 5/1, 5/2, 5/3, 5/4, ... 2/2, 5/2, 5/3, 5/4, ...
> ... ... ... ...
>
> When all definable fractions of Cantor's sequence 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ... will have transferred into the first column, nevertheless all matrix places remain occupied by fractions which are undefinable, because all definable fractions have gone.
>
> If you have understood this, then we can proceed to understand, that even most places in the first column, all of which have been occupied by integer fractions or natural numbers, are undefinable too.
> > No, your proof of
> > An e N: n e [0,n]=F_n
> > Aka, "all natural is in in a finite set" is instantly invalid as that applies to all natural numbers, thus one set is non-empty.
> By induction we prove that every definable natural number, i.e., every natural number which is subject to induction, belongs to a finite set F_n but has ℵo successors which cannot be removed whatever n you consider. That means they cannot be used as individuals.
>
> Regards, WM

The argument that I like to make is that mathematics has an important purpose, which is to provide a conceptual framework that facilitates reasoning about the real world (i.e. mathematics is the language of science). And Cantor's theory of infinite sets is simply irrelevant to that important purpose.

What I'm wondering is, how is your (Mueckenheim) argument relevant to the very important purpose of mathematics? Perhaps more importantly, why should people care about your argument? What's the point?

Need I remind you that any theory of infinity is a fiction? Why is your fiction more important than Cantor's?

WM formulated on Thursday :
> FromTheRafters schrieb am Dienstag, 26. April 2022 um 22:05:48 UTC+2:
>
>> Then yes, it sort of describes WM's matrix's dimensions and that the
>> cardinality of a single row or column can be the same as the
>> cardinality of the whole thing. It is exactly this which he denies
>> because it
>
> it can be disproved by the fact that every permutation of the X's fails to
> cover the whole matrix
>
> XOOO...
> XOOO...
> XOOO...
> XOOO...
> ...

How many permutations are there for an infinite set? Are you sure you
have covered them all?

On 4/28/2022 9:26 AM, sergio wrote:
> On 4/28/2022 7:45 AM, WM wrote:
>> Jim Burns schrieb am Dienstag, 26. April 2022 um 19:51:50 UTC+2:
>>> On 4/26/2022 7:10 AM, WM wrote:
>>
>>>> So it is. 1/1, 2/1, 3/1, ...
>>>> By values this is same as 1, 2, 3, ...
>>
>>>> It is the set of indices.
>>> You haven't described an infinite sequence.
>>> You've only given a name, "indices", as though
>>> that name is the answer to the question.
>>
>> Liar.
>>
>> I have described the first column of the matrix:
>>
>> 1/1, 1/2, 1/3, 1/4, ...
>> 2/1, 2/2, 2/3, 2/4, ...
>> 3/1, 3/2, 3/3, 3/4, ...
>> 4/1, 4/2, 4/3, 4/4, ...
>> 5/1, 5/2, 5/3, 5/4, ...
>> ...
>>
>> Regards, WM
>
>
>
>              very sloppy math, WM
>
> take your first column, write it as its own series, assuming your last three dots ... means it goes on to infinity, {1/1,2/1,3/1,4/1...}, this is the
> set of natural numbers, however it is not in reduced form.
>
>
> Bonus Question:
>
> what are the indices to this new series ?
>
>
>
>
sequence, not series