On Monday, September 5, 2022 at 4:43:57 PM UTC+2, Python wrote:

> What's THAT wrong with Hochschule Augsburg?

Well... you see... from 2003 till 2007 he was the dean of the /faculty of general sciences/ of that "Hochschule".

(Source: https://de.wikipedia.org/wiki/Wolfgang_M%C3%BCckenheim)

It's a shame!

On Monday, September 5, 2022 at 2:15:10 PM UTC+2, Jim Burns wrote:
> On 9/5/2022 6:24 AM, Ben Bacarisse wrote:
> > Fritz Feldhase writes:
> >> On Sunday, September 4, 2022 at 11:25:27 PM UTC+2, Ben Bacarisse wrote:
> >>>
> >>> in WMaths (specifically for some
> >>> potentially infinite sets) it is possible
> >>> to have both e ∈ S and S \ {e} = S.
> >> >
> >> From S \ {e} = S we get that ~(e ∈ S),
> >> since ~(e ∈ S \ {e}) by definition of "\".
> >> So in WMaths we have (for some e and some S)
> >> e ∈ S and ~(e ∈ S). A contradiction.
> >
> > I pointed out something similar, of course,
> > based on the entirely conventional definitions
> > of set membership, equality and difference
> > from his textbook. His line is the these
> > were "simplified" (i.e. wrong) to help students
> > with the basics. That's what led to my pressing
> > for the "real" definitions, and his admission
> > that he could not give them.
> >>
> >> What a surprise!
> >> Now a REASONABLE person would (at least)
> >> question some of his or her "existence
> >> assumptions" concerning "potentially
> >> infinite sets".
> >>
> > For a long time I though WM was just
> > playing a game. A sort of mathematical
> > keepy-uppie where he knew he was talking
> > nonsense but was having fun seeing how long
> > he could keep any particular line of nonsense
> > going. But now, I think he may actually
> > believe what he says.
> >
> >> But WM is no REASONABLE person. Actually,
> >> even this devastating result will not have
> >> any effect on him.
> >
> > If WM believes himself, there's no
> > contradiction, just a massive hole where
> > the WMaths definitions of the basic set
> > operations should be. Perhaps the latter
> > is easier to reconcile internally?
> >
> > I often wonder what it would be like to
> > meet a Usenet maths crank in real life.
> > Would it be obvious? How would a
> > mathematical discussion go without the
> > opportunities for deflection and ignoring
> > or awkward points that Usenet facilitates?
> >
> Maybe like this?
>
> | So what mental artillery have we picked up
> | over the last 100 years? Alexander Luria
> | studied neuropsychology in the early half of
> | the century, and he found that people were
> | resistent to classification, to deducing the
> | hypothetical. His subjects simply couldn’t
> | think about anything abstract. Consider
> | this exchange:
> |
> | Luria: What do crows and fish have
> | in common?
> | Subject: Absolutely nothing. A fish swims,
> | and a crow flies.
> | Luria: Are they not both animals?
> | Subject: Of course not, a fish is a fish,
> | and a crow is a bird.
> |
> | The man could only think of the objects as
> | how he might use them, not as abstract
> | objects part of a classification system.
> |
> | Luria told another subject: “There are no
> | camels in Germany. Hamburg is in Germany.
> | Are there camels in Hamburg?” The subject
> | replied, “If it’s big enough, perhaps it
> | has camels.” Luria prompted him again to
> | listen to the conditions, and again he
> | replied that perhaps Hamburg had camels.
> | He was used to camels, and he was unable to
> | imagine that there weren’t any in Hamburg.
>
> https://blog.ted.com/are-we-getting-more-intelligent-jim-flynn-at-ted2013/

BB: In WMaths [for a potentially infinite set S] it is possible to have both e ∈ S and S \ {e} = S.

WM: Yes.

FF From S \ {e} = S we get that ~(e ∈ S), since ~(e ∈ S \ {e}) by definition of '\'. So in WMaths we have (for some e and some S) e ∈ S and ~(e ∈ S). A contradiction.

WM: No, to be an element and to be not an element is not simultaneously possible.

Well...

On 9/5/2022 10:16 AM, Fritz Feldhase wrote:
> On Monday, September 5, 2022 at 4:43:57 PM UTC+2, Python wrote:
>
>> What's THAT wrong with Hochschule Augsburg?
>
> Well... you see... from 2003 till 2007 he was the dean of the /faculty of general sciences/ of that "Hochschule".
>
> (Source: https://de.wikipedia.org/wiki/Wolfgang_M%C3%BCckenheim)
>
> It's a shame!

it is interesting on the decline of professors, one proff over here, I took a course from, I met him 30 years later at a technical meeting, and he was
pushing a idea on signal shapes that was obviously wrong on random networks, he too old and stale but still had the ego, still thought he had the best
ideas.

the news groups are one of the last refuges to get a audience for (failed ideas), so that is why WM is here.

I did download his 2015 book, and it does look cut and paste to me.

But I wont let him get away with lying about Math.

WM <askasker48@gmail.com> writes:

> Fritz Feldhase schrieb am Montag, 5. September 2022 um 10:34:43 UTC+2:
>> On Sunday, September 4, 2022 at 11:25:27 PM UTC+2, Ben Bacarisse wrote:
>>
>> > in WMaths (specifically for some potentially infinite sets)
>
> only for such!
>
>> it is possible to have both e ∈ S and S \ {e} = S.
>
> Dark elements can become visible and vice versa.

I've not been following all the interminable threads, but I thought
WMaths did not have dark numbers.

Any progress on defining set membership, equality and difference so that
a student could derive this surprising result of WMaths?

--
Ben.

WM <askasker48@gmail.com> writes:
(AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
Unendlichen" at Hochschule Augsburg.)

> Ben Bacarisse schrieb am Montag, 5. September 2022 um 00:06:08 UTC+2:

>> 1a. Express the initial matrix as a function, F_1, from NxN to {0,1} so
>> that Xs are indicated by 1 and Os by O.
>
> You did it.

Actually I didn't. Like you, I just skipped on to M_1.

>> 1b. Can you express this initial matrix as a function M_1 from N to
>> {0,1}? (Hint, use F_1 and your mapping k).
>
> 1, 1, 0, 1, 0, 0, 1, ... with 0 at 3, 5, 6, 8, 9 and so on.

But this is just a few values of the function. What's the formula? In
WMaths you must have formulas or things are not defined, yes?

I'll give the next exercise, but please show a formula for M_1. I think
it needs to be 100% clear that it's a well-defined WMaths function.

2a. What is the first swap, and what are the first few values of M_2,
the function from N to {0,1}, showing where the Xs and Os are after the
first swap?

2b. Does M_2 have a finite formula? I.e. is it a properly defined
WMaths function from N to {0,1}?

2c. What is the /rule/ for swapping Xs and Os that you want to follow?
Some will get us where we want to go and some won't so you have pick a
good one. Also, make it as simple as you can. The rule should enable
anyone to easily write the first dozen or so values of M_2, M_3 and M_4.

--
Ben.

On 9/5/2022 9:13 AM, WM wrote:
> Fritz Feldhase schrieb am Montag,
> 5. September 2022 um 10:34:43 UTC+2:
>> On Sunday, September 4, 2022
>> at 11:25:27 PM UTC+2, Ben Bacarisse wrote:

>>> in WMaths (specifically for some
>>> potentially infinite sets)
>
> only for such!
>
>>> it is possible to have
>>> both e ∈ S and S \ {e} = S.
>
> Dark elements can become visible and
> vice versa.

Visible elements are able to be seen.

Dark elements are not able to be seen
but are able to be able to be seen.

That seems unhelpful.

----
It would be nice if we could replace
unhelpful claims of visibility with
clear claims of FISON-membership.

A FISON is
a collection with a counting-order
which begins at 0 and ends _somewhere_

What is your latest word on whether
any elements of any FISON are dark?

----
Let 𝓕 be the collection of FISONs
∀𝐹, 𝐹 ∈ 𝓕 <-> 𝐹 is a FISON

Each FISON 𝐹 ends somewhere.
Not all things in 𝐹 in have successors in 𝐹
∀𝐹 ∈ 𝓕, ~(∀n ∈ 𝐹, n+1 ∈ 𝐹)

_All_ the FISONs _do not_ end anywhere.
∀𝐹 ∈ 𝓕, ∃𝐹' ∈ 𝓕, 𝐹 ⊂ 𝐹'

| That arises from
| 𝐹ₙ∪⟨n+1⟩ also being a FISON.

Also,
all things n in a FISON (∃𝐹∈𝓕, n∈𝐹)
do not end anywhere (∃𝐹'∈𝓕, n+1∈𝐹')
∀n, (∃𝐹∈𝓕, n∈𝐹) -> (∃𝐹'∈𝓕, n+1∈𝐹')

| That arises from
| 𝐹ₙ∪⟨n+1⟩ also being a FISON.

The collection ⋃𝓕 of things in a FISON
does not end.
∀n, (n∈⋃𝓕) -> (n+1∈⋃𝓕)

Your (WM's) claim seems to be that,
because
each FISON 𝐹 ends
but
the collection ⋃𝓕 of things in a FISON
does not end,
there must be things in ⋃𝓕 which
are not in any FISON 𝐹: your dark numbers.

The problem with your claim
(as I understand it to be)
is that ⋃𝓕 is exactly the things in FISONs
no more and no less.

The origin of your problem seems to be
in the way you attribute properties of
a set to the elements of that set.
You like to say "A set is its elements".

That doesn't work.
n in a FISON 𝐹 is in a set that ends.
n in ⋃𝓕 is in a set that does not end.
The same n is in both sets.

> Dark elements can become visible
> and vice versa.

Elements of set which do not end
can be in sets which do end
and vice versa.

>> From S \ {e} = S we get that ~(e ∈ S),
>> since ~(e ∈ S \ {e}) by definition of "\".
>> So in WMaths we have (for some e and some S)
>> e ∈ S and ~(e ∈ S). A contradiction.
>
> No,
> to be an element and to be not an element
> is not simultaneously possible.

To be an element of one set and
to be not an element of a different set
is simultaneously possible.

måndag 5 september 2022 kl. 15:13:47 UTC+2 skrev WM:
> Fritz Feldhase schrieb am Montag, 5. September 2022 um 10:34:43 UTC+2:
> > On Sunday, September 4, 2022 at 11:25:27 PM UTC+2, Ben Bacarisse wrote:
> >
> > > in WMaths (specifically for some potentially infinite sets)
> only for such!
> > it is possible to have both e ∈ S and S \ {e} = S.
> Dark elements can become visible and vice versa.

what the FUCK DOES THAT EVEN MEAN!?

> > From S \ {e} = S we get that ~(e ∈ S), since ~(e ∈ S \ {e}) by definition of "\". So in WMaths we have (for some e and some S) e ∈ S and ~(e ∈ S). A contradiction.
> No, to be an element and to be not an element is not simultaneously possible.

Yet you claim it

>
> Regards, WM

Ben Bacarisse schrieb am Montag, 5. September 2022 um 17:48:48 UTC+2:
> WM <askas...@gmail.com> writes:
>
> > Fritz Feldhase schrieb am Montag, 5. September 2022 um 10:34:43 UTC+2:
> >> On Sunday, September 4, 2022 at 11:25:27 PM UTC+2, Ben Bacarisse wrote:
> >>
> >> > in WMaths (specifically for some potentially infinite sets)
> >
> > only for such!
> >
> >> it is possible to have both e ∈ S and S \ {e} = S.
> >
> > Dark elements can become visible and vice versa.
> I've not been following all the interminable threads, but I thought
> WMaths did not have dark numbers.

It doesn't. Nevertheless potential infinity has a growing character. Therefore larger finite sets are created from smaller sets.

In actual infinity the newly created visible numbers are taken from the dark part of the set, in potential infinity they are created from nothing. In both cases only the potentially infinite sets of visible numbers are part of mathematics.

Regards, WM

Ben Bacarisse schrieb am Montag, 5. September 2022 um 18:23:55 UTC+2:
> WM <askas...@gmail.com> writes:
> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
> Unendlichen" at Hochschule Augsburg.)
> > Ben Bacarisse schrieb am Montag, 5. September 2022 um 00:06:08 UTC+2:
>
> >> 1a. Express the initial matrix as a function, F_1, from NxN to {0,1} so
> >> that Xs are indicated by 1 and Os by O.
> >
> > You did it.
> Actually I didn't. Like you, I just skipped on to M_1.
> >> 1b. Can you express this initial matrix as a function M_1 from N to
> >> {0,1}? (Hint, use F_1 and your mapping k).
> >
> > 1, 1, 0, 1, 0, 0, 1, ... with 0 at 3, 5, 6, 8, 9 and so on.
> But this is just a few values of the function. What's the formula? In
> WMaths you must have formulas or things are not defined, yes?

This 1, 1, 0, 1, 0, 0, 1, ... is a formula like 0.999....
>
If you can't read it, I will extend it a bit 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, ... .

I will not fall prey to your tedious attempt to distract from the topic.
Note that the only meaningful argument recently uttered is this: The O's will not disappear in any finite step but behind all finite steps. That is the point. You cannot accomplish more. I will not accept it.

Regards, WM

Jim Burns schrieb am Montag, 5. September 2022 um 22:09:36 UTC+2:
> On 9/5/2022 9:13 AM, WM wrote:

> It would be nice if we could replace
> unhelpful claims of visibility with
> clear claims of FISON-membership.
>
> A FISON is
> a collection with a counting-order
> which begins at 0 and ends _somewhere_
>
> What is your latest word on whether
> any elements of any FISON are dark?

FISONs can become dark if the ressources of the systen decrease.

> > to be an element and to be not an element
> > is not simultaneously possible.
> To be an element of one set and
> to be not an element of a different set
> is simultaneously possible.

Potentially infinite collections are not sets in that sense.

Regards, WM

tisdag 6 september 2022 kl. 12:35:03 UTC+2 skrev WM:
> Jim Burns schrieb am Montag, 5. September 2022 um 22:09:36 UTC+2:
> > On 9/5/2022 9:13 AM, WM wrote:
>
> > It would be nice if we could replace
> > unhelpful claims of visibility with
> > clear claims of FISON-membership.
> >
> > A FISON is
> > a collection with a counting-order
> > which begins at 0 and ends _somewhere_
> >
> > What is your latest word on whether
> > any elements of any FISON are dark?
> FISONs can become dark if the ressources of the systen decrease.
> > > to be an element and to be not an element
> > > is not simultaneously possible.
> > To be an element of one set and
> > to be not an element of a different set
> > is simultaneously possible.
> Potentially infinite collections are not sets in that sense.
>
> Regards, WM
WHAT FUCKING SYSTEM!? WHAT RESOURCES!? THOSE DO NOT EXIST IN MATHEMATICS!

On 9/6/2022 5:19 AM, WM wrote:
> Ben Bacarisse schrieb am Montag, 5. September 2022 um 17:48:48 UTC+2:
>> WM <askas...@gmail.com> writes:
>>
>>> Fritz Feldhase schrieb am Montag, 5. September 2022 um 10:34:43 UTC+2:
>>>> On Sunday, September 4, 2022 at 11:25:27 PM UTC+2, Ben Bacarisse wrote:
>>>>
>>>>> in WMaths (specifically for some potentially infinite sets)
>>>
>>> only for such!
>>>
>>>> it is possible to have both e ∈ S and S \ {e} = S.
>>>
>>> Dark elements can become visible and vice versa.
>> I've not been following all the interminable threads, but I thought
>> WMaths did not have dark numbers.
>
> It doesn't. Nevertheless potential infinity has a growing character. Therefore larger finite sets are created from smaller sets.

and smaller sets are created from larger sets.
..
>
> In actual infinity the newly created visible numbers are taken from the dark part of the set, in potential infinity they are created from nothing. In both cases only the potentially infinite sets of visible numbers are part of mathematics.

So you now conclude that dark numbers are not part of mathematics.

>
> Regards, WM
>

On 9/6/2022 5:34 AM, WM wrote:
> Jim Burns schrieb am Montag, 5. September 2022 um 22:09:36 UTC+2:
>> On 9/5/2022 9:13 AM, WM wrote:
>
>> It would be nice if we could replace
>> unhelpful claims of visibility with
>> clear claims of FISON-membership.
>>
>> A FISON is
>> a collection with a counting-order
>> which begins at 0 and ends _somewhere_
>>
>> What is your latest word on whether
>> any elements of any FISON are dark?
>
> FISONs can become dark if the ressources of the systen decrease.

take a FISON(1) = {1} now how does that become dark using Windows 7 ?

>
>>> to be an element and to be not an element
>>> is not simultaneously possible.
>> To be an element of one set and
>> to be not an element of a different set
>> is simultaneously possible.
>
> Potentially infinite collections are not sets in that sense.

you are calling it a collection, he was posting about sets, did you miss that, Deceiver?

>
> Regards, WM

On 9/6/2022 5:27 AM, WM wrote:
> Ben Bacarisse schrieb am Montag, 5. September 2022 um 18:23:55 UTC+2:
>> WM <askas...@gmail.com> writes:
>> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
>> Unendlichen" at Hochschule Augsburg.)
>>> Ben Bacarisse schrieb am Montag, 5. September 2022 um 00:06:08 UTC+2:
>>
>>>> 1a. Express the initial matrix as a function, F_1, from NxN to {0,1} so
>>>> that Xs are indicated by 1 and Os by O.
>>>
>>> You did it.
>> Actually I didn't. Like you, I just skipped on to M_1.
>>>> 1b. Can you express this initial matrix as a function M_1 from N to
>>>> {0,1}? (Hint, use F_1 and your mapping k).
>>>
>>> 1, 1, 0, 1, 0, 0, 1, ... with 0 at 3, 5, 6, 8, 9 and so on.
>> But this is just a few values of the function. What's the formula? In
>> WMaths you must have formulas or things are not defined, yes?
>
> This 1, 1, 0, 1, 0, 0, 1, ... is a formula like 0.999....

wrong. the first is a SEQUENCE, the second is a NUMBER.

>>
> If you can't read it, I will extend it a bit 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, ... .
>
> I will not fall prey to your tedious attempt to distract from the topic.

That is what WM does BIG TIME.

> Note that the only meaningful argument recently uttered is this: The O's will not disappear in any finite step but behind all finite steps. That is the point. You cannot accomplish more. I will not accept it.

you Lie with your Matrix. It is a step by step process applied to infinite sequence.
ANd you cant even tell the difference between a sequence and a number. Troll.

>
> Regards, WM

On Tuesday, 6 September 2022 at 10:29:24 UTC-3, Sergio wrote:
> On 9/6/2022 5:34 AM, WM wrote:
> > FISONs can become dark if the ressources of the systen decrease.
> take a FISON(1) = {1} now how does that become dark using Windows 7 ?

Well, that's easy: Open a command window, then type “format c: /fs:ntfs”

On 9/6/2022 10:36 AM, Gus Gassmann wrote:
> On Tuesday, 6 September 2022 at 10:29:24 UTC-3, Sergio wrote:
>> On 9/6/2022 5:34 AM, WM wrote:
>>> FISONs can become dark if the ressources of the systen decrease.
>> take a FISON(1) = {1} now how does that become dark using Windows 7 ?
>
> Well, that's easy: Open a command window, then type “format c: /fs:ntfs”

been there done that, I couldn't say Oh Shi* fast enough...
very clearing, makes Win7 dark for sure

zelos...@gmail.com schrieb am Dienstag, 6. September 2022 um 14:39:22 UTC+2:
> tisdag 6 september 2022 kl. 12:35:03 UTC+2 skrev WM:

> > Potentially infinite collections are not sets in that sense.
> >
> WHAT FUCKING SYSTEM!? WHAT RESOURCES!? THOSE DO NOT EXIST IN MATHEMATICS!

They do. Infinitely many X's are not enough to cover the whole matrix.

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

In the first 3 steps we get the following matrices

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

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

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

and so on.

Regards, WM

On Tuesday, September 6, 2022 at 6:42:20 PM UTC+2, WM wrote:

> Infinitely many X's are not enough to cover the whole matrix.

Oh really?! Which element in the following matrix is not covered by an X?

X X X X...
X X X X...
X X X X...
X X X X...
....

On Tuesday, September 6, 2022 at 6:42:20 PM UTC+2, WM wrote:
> zelos...@gmail.com schrieb am Dienstag, 6. September 2022 um 14:39:22 UTC+2:
> > tisdag 6 september 2022 kl. 12:35:03 UTC+2 skrev WM:
>
> > > Potentially infinite collections are not sets in that sense.
> > >
> > WHAT FUCKING SYSTEM!? WHAT RESOURCES!? THOSE DO NOT EXIST IN MATHEMATICS!
> They do. Infinitely many X's are not enough to cover the whole matrix.
>
> XOOO...
> XOOO...
> XOOO...
> XOOO...
> ...
>
> In the first 3 steps we get the following matrices
>
> XXOO...
> OOOO...
> XOOO...
> XOOO...
> ...
>
> XXOO...
> XOOO...
> OOOO...
> XOOO...
> ...
>
> XXXO...
> XOOO...
> OOOO...
> OOOO...
> ...
>
> and so on.
>
> Regards, WM

Mücke, you are a tedious, repetitive, humorless dullard.
You are boring.

On 9/6/2022 6:34 AM, WM wrote:
> Jim Burns schrieb am Montag,
> 5. September 2022 um 22:09:36 UTC+2:
>> On 9/5/2022 9:13 AM, WM wrote:

>>> Dark elements can become visible and
>>> vice versa.

>> It would be nice if we could replace
>> unhelpful claims of visibility with
>> clear claims of FISON-membership.
>>
>> A FISON is
>> a collection with a counting-order
>> which begins at 0 and ends _somewhere_
>>
>> What is your latest word on whether
>> any elements of any FISON are dark?
>
> FISONs can become dark if
> the ressources of the systen decrease.

But your "darkness" claims aren't that
FISONs become non-FISONs, or that
non-FISONs become FISONs.
Correct?

Let us remind ourselves that a FISON is
a collection with a counting-order
which begins at 0 and ends _somewhere_

>>> to be an element and to be not an element
>>> is not simultaneously possible.
>>
>> To be an element of one set and
>> to be not an element of a different set
>> is simultaneously possible.
>
> Potentially infinite collections
> are not sets in that sense.

However,
the set of all FISONs is a set in that sense.
No FISONs become non-FISONs.
No non-FISONs become FISONs.
Correct?

The next[2] set after all
infinite end segments of ⋃𝓕
is ∅

where ⋃𝓕 us the union of the set of FISONs.

On 9/6/2022 11:36 AM, Gus Gassmann wrote:
> On Tuesday, 6 September 2022
> at 10:29:24 UTC-3, Sergio wrote:
>> On 9/6/2022 5:34 AM, WM wrote:

>>> FISONs can become dark if
>>> the ressources of the systen decrease.
>>
>> take a FISON(1) = {1}
>> now how does that become dark using Windows 7 ?
>
> Well, that's easy:
> Open a command window,
> then type “format c: /fs:ntfs”

So, have you ever worked tech support?
No reason to ask, just curious.

https://www.youtube.com/watch?v=qjCfWs_AjTc
Doctor Who:
The Woman Who Fell To Earth
- Reformatting

On Tuesday, 6 September 2022 at 17:23:09 UTC-3, Jim Burns wrote:
[...]
> So, have you ever worked tech support?

I have not. More often than I care to admit, I am the guy on the right...
https://www.youtube.com/watch?v=pQHX-SjgQvQ

WM <askasker48@gmail.com> writes:

> Ben Bacarisse schrieb am Montag, 5. September 2022 um 18:23:55 UTC+2:
>> WM <askas...@gmail.com> writes:
>> (AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des
>> Unendlichen" at Hochschule Augsburg.)
>> > Ben Bacarisse schrieb am Montag, 5. September 2022 um 00:06:08 UTC+2:
>>
>> >> 1a. Express the initial matrix as a function, F_1, from NxN to {0,1} so
>> >> that Xs are indicated by 1 and Os by O.
>> >
>> > You did it.
>> Actually I didn't. Like you, I just skipped on to M_1.
>> >> 1b. Can you express this initial matrix as a function M_1 from N to
>> >> {0,1}? (Hint, use F_1 and your mapping k).
>> >
>> > 1, 1, 0, 1, 0, 0, 1, ... with 0 at 3, 5, 6, 8, 9 and so on.
>> But this is just a few values of the function. What's the formula? In
>> WMaths you must have formulas or things are not defined, yes?
>
> This 1, 1, 0, 1, 0, 0, 1, ... is a formula like 0.999....
>>
> If you can't read it, I will extend it a bit 1, 1, 0, 1, 0, 0, 1, 0,
> 0, 0, 1, ... .

Too hard? Sorry.

> I will not fall prey to your tedious attempt to distract from the
> topic.

The only topic I care about is helping you see how all the Os "disappear"
in WMaths as easily as in any other kind of mathematics.

I'm not sure if you /can't/ write the formula for M_1 or you'd rather
not since you know here that leads. Anyway, we'll never find out...

> Note that the only meaningful argument recently uttered is this: The
> O's will not disappear in any finite step but behind all finite steps.

I thought you'd like to see how that is done in WMaths, but you did not
follow the argument when I wrote it out for you and you've decided ditch
the exercises that will take you through it step by step.

--
Ben.

tisdag 6 september 2022 kl. 18:42:20 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Dienstag, 6. September 2022 um 14:39:22 UTC+2:
> > tisdag 6 september 2022 kl. 12:35:03 UTC+2 skrev WM:
>
> > > Potentially infinite collections are not sets in that sense.
> > >
> > WHAT FUCKING SYSTEM!? WHAT RESOURCES!? THOSE DO NOT EXIST IN MATHEMATICS!
> They do.

No they don't!

>Infinitely many X's are not enough to cover the whole matrix.

I can make a matrix with only X in it.

>
> XOOO...
> XOOO...
> XOOO...
> XOOO...
> ...
>
> In the first 3 steps we get the following matrices
>
> XXOO...
> OOOO...
> XOOO...
> XOOO...
> ...
>
> XXOO...
> XOOO...
> OOOO...
> XOOO...
> ...
>
> XXXO...
> XOOO...
> OOOO...
> OOOO...
> ...
>
> and so on.
>
> Regards, WM

YOu are talking about a step by step process, IRRELEVANT IN MATHEMATICS!

Fritz Feldhase schrieb am Dienstag, 6. September 2022 um 19:14:19 UTC+2:
> On Tuesday, September 6, 2022 at 6:42:20 PM UTC+2, WM wrote:
>
> > Infinitely many X's are not enough to cover the whole matrix.
> Oh really?! Which element in the following matrix is not covered by an X?
>
> X X X X...
> X X X X...
> X X X X...
> X X X X...
> ...

Almost all (if you start from
XOO...
XOO...
XOO...
....
and do not add further X's).

The reason is that shuffling the X will never remove an O.

Regards, WM