On 5/7/2022 1:38 PM, WM wrote:
> Jim Burns schrieb am Samstag, 7. Mai 2022 um 17:57:54 UTC+2:
>> On 5/7/2022 10:16 AM, WM wrote:
>
>> Why should I listen to you about Cantor?
>
> Because I know his writings better than most and in particular better than you.

No. You don't understand Cantor.

You try to challenge his simple and correct Enumeration with silly non math kisses and hugs X+O, and disconnected swaparoos tiles in a mutulated matrix.

>
> Regards, WM

You use Cantors name to lend importance to your posts, but your posts stink on their own, like a dead defined fish on the beach of imagination.

William schrieb am Samstag, 7. Mai 2022 um 22:13:39 UTC+2:
> On Saturday, May 7, 2022 at 8:33:00 AM UTC-3, WM wrote:
> > William schrieb am Freitag, 6. Mai 2022 um 23:28:16 UTC+2:
>
> >> There is no element of N_p between the set N_p and omega.
> > You can claim this nonsense,
> Piffle. It is not nonsense. How could an element of N_p be between the set N_p and omega?

There are infinitely many dark natnumbers between the set N_p and omega.

It would have to be between itself and omega. Recall, N_p is a Peano set and thus has no "dark elements".

Then the dark elements are between it and omega.

> Whatever, if anything, is between the set N_p and omega it is not an element of N_p

It is dark.

Regards, WM

Jim Burns schrieb am Samstag, 7. Mai 2022 um 23:00:11 UTC+2:
> On 5/7/2022 2:38 PM, WM wrote:
> > Jim Burns schrieb
> > am Samstag, 7. Mai 2022 um 17:57:54 UTC+2:
> >> On 5/7/2022 10:16 AM, WM wrote:
>
> >> Why should I listen to you about Cantor?
> >
> > Because I know his writings better than most
> > and in particular better than you.
> I won't accept your reading of Cantor.

Read him.
> You can't get what I write correct.

You write a lot of nonsense.

> Why should I listen to you about Cantor?
> For example, *here*
> What I mean is:
> why should I *trust* you about Cantor?
> You got it wrong.
>
> Practically everything that can be misinterpreted
> you (WM) misinterpret.

Then find the right interpretation here:

If all positive fractions can be enumerated, then the natural numbers of 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, ...
....

can be shuffled such that they cover the whole matrix. In short, there is a permutation such that the X of the first column

XOOOO...
XOOOO...
XOOOO...
XOOOO...
XOOOO...
....

cover all matrix positions. This is obviously impossible.
If the fractions m/n are enumerated by the natural numbers k according to Cantor's function
k = (m + n - 1)(m + n - 2)/2 + m
then the fractions of the sequence
1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...
are indexed (or covered by X's) but the number of not indexed fractions (the O's) will remain the same forever.

Regards, WM

On 5/8/2022 7:40 AM, WM wrote:
> William schrieb am Samstag, 7. Mai 2022 um 22:13:39 UTC+2:
>> On Saturday, May 7, 2022 at 8:33:00 AM UTC-3, WM wrote:
>>> William schrieb am Freitag, 6. Mai 2022 um 23:28:16 UTC+2:
>>
>>>> There is no element of N_p between the set N_p and omega.
>>> You can claim this nonsense,
>> Piffle. It is not nonsense. How could an element of N_p be between the set N_p and omega?
>
> There are infinitely many dark natnumbers between the set N_p and omega.
>
> It would have to be between itself and omega. Recall, N_p is a Peano set and thus has no "dark elements".
>
> Then the dark elements are between it and omega.
>
>> Whatever, if anything, is between the set N_p and omega it is not an element of N_p
>
> It is dark.
>
> Regards, WM

So far, you have been unable to prove anything at all about dark numbers or dark elements.

All of your attempts have major flaws.

Above you state your ideas about the dark things, but they are not based upon facts.

Use Math, specifically equations, to formally prove your idea, and you will find great acceptance.

On 5/8/2022 7:42 AM, WM wrote:
> Jim Burns schrieb am Samstag, 7. Mai 2022 um 23:00:11 UTC+2:
>> On 5/7/2022 2:38 PM, WM wrote:
>>> Jim Burns schrieb
>>> am Samstag, 7. Mai 2022 um 17:57:54 UTC+2:
>>>> On 5/7/2022 10:16 AM, WM wrote:
>>
>>>> Why should I listen to you about Cantor?
>>>
>>> Because I know his writings better than most
>>> and in particular better than you.
>> I won't accept your reading of Cantor.
>
> Read him.
>
>> You can't get what I write correct.
>
> You write a lot of nonsense.
>
>> Why should I listen to you about Cantor?
>> For example, *here*
>> What I mean is:
>> why should I *trust* you about Cantor?
>> You got it wrong.
>>
>> Practically everything that can be misinterpreted
>> you (WM) misinterpret.
>
> Then find the right interpretation here:
>

<snip crap>

> If the fractions m/n are enumerated by the natural numbers k according to Cantor's function
> k = (m + n - 1)(m + n - 2)/2 + m
> then the fractions of the sequence
> 1/1, 1/2, 2/1, 1/3, 2/2, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ...

are enumerated.

<snip last line of bs>

>
> Regards, WM

On 5/8/2022 8:42 AM, WM wrote:
> Jim Burns schrieb
> am Samstag, 7. Mai 2022 um 23:00:11 UTC+2:
>> On 5/7/2022 2:38 PM, WM wrote:
>>> Jim Burns schrieb
>>> am Samstag, 7. Mai 2022 um 17:57:54 UTC+2:
>>>> On 5/7/2022 10:16 AM, WM wrote:

>>>> Why should I listen to you about Cantor?
>>>
>>> Because I know his writings better than most
>>> and in particular better than you.
>>
>> I won't accept your reading of Cantor.
>
> Read him.
>
>> You can't get what I write correct.
>
> You write a lot of nonsense.

And, in your mind, that justifies misinterpreting me.

What do you say about Cantor?

That he writes a lot of nonsense.

And, in your mind, that justifies misinterpreting him.

Why should I listen to you about Cantor?

On 5/8/2022 8:42 AM, WM wrote:
> Jim Burns schrieb
> am Samstag, 7. Mai 2022 um 23:00:11 UTC+2:

>> Practically everything that can be misinterpreted
>> you (WM) misinterpret.
>
> Then find the right interpretation here:
>
> If all positive fractions can be enumerated,

As they can be. For example, by
j = p+(p+q-1)*(p+q-2)/2

> then the natural numbers of 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, ...
> ...
>
> can be shuffled such that they cover the whole matrix.
> In short, there is a permutation such that the X of
> the first column
>
> XOOOO...
> XOOOO...
> XOOOO...
> XOOOO...
> XOOOO...
> ...
>
> cover all matrix positions.
>
> This is obviously impossible.

You are wrong.
j = p+(p+q-1)*(p+q-2)/2

> If the fractions m/n

such that
each collection =< m and each collection =< n
contains a first and a last