On 9/4/2022 1:10 PM, WM wrote:
> Gus Gassmann schrieb am Sonntag, 4. September 2022 um 16:20:32 UTC+2:
>> On Sunday, 4 September 2022 at 10:55:28 UTC-3, WM wrote:
>> [...]
>>> I have this understanding of logic: If two symbols are exchanged, then none of them is deleted.
>> This is correct, but insufficient.
>
> It is all that is needed.

wrong, you are incompetent.

>
>>>> A In order to prove an inconsistency in ZFC
>>>
>>> it issufficient to prove that no O can leave the matrix.
>> Ah, no. The fact that the reciprocal 1/n is positive for every natural number n is insufficient to conclude that the limit of the sequence {1, 1/2, 1/3, ..} cannot be 0.
>
> The limit of a sequence is a number which is approached.

insufficient. what do YOU mean by "approached" ?

>
> Regards, WM

On 9/4/2022 3:29 PM, WM wrote:
> Ben Bacarisse schrieb am Sonntag, 4. September 2022 um 21:26:47 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 Sonntag, 4. September 2022 um 18:14:07 UTC+2:
>>>> WM <askas...@gmail.com> writes:
>>>

<snip crap>

>
> Cantor used the natural numbers for indexing, I use the integer fractions.

that is just one of your mistakes. The other is using a step by step process (swapparoos) in an infinite matrix...

No wonder you could only Fail.

Cantor is correct and he proved he could one to one map the fractions.

You cannot.

Fail.

>
> Regards, WM

JVR <jrennenkampff@googlemail.com> writes:

> There is only one immutable rule in what you call WMaths and I call
> Muckmeatics: "You cannot nail a pudding to the wall."

That's my feeling, most of the time. But while you can't nail up a
whole one, I've managed, over the years, to nail up a few tiny scraps of
pudding.

For example, there is the theorem that states that in WMaths, certain
bounded monotonic sequences of rationals don't converge to a real
number. The theorem hit the rails, though, when WM could not pin down
which ones, but not before the existence of such sequences was agreed.

Sometimes the pudding scraps drop off because WM just pulls the nail out
by flat-out denial of overwhelming evidence. He has asserted that (in
WMaths) no non-constant sequences of sets converge despite his textbook
making it plain that (a) functions are just sets, and (b) some
non-constant sequences of functions converge.

But the most beautiful scrap of nailed-on pudding is the clear statement
that, in WMaths (specifically for some potentially infinite sets) it is
possible to have both e ∈ S and S \ {e} = S. WM himself described this
as a "surprise". No shit!

Pressing for an explanation resulted in WM saying that he could not
define set membership, equality and difference in a way that would
enable a student of WMaths to get this result for themselves. Quite an
admission.

--
Ben.

Sergio explained :
> On 9/4/2022 1:10 PM, WM wrote:
>> Gus Gassmann schrieb am Sonntag, 4. September 2022 um 16:20:32 UTC+2:
>>> On Sunday, 4 September 2022 at 10:55:28 UTC-3, WM wrote:
>>> [...]
>>>> I have this understanding of logic: If two symbols are exchanged, then
>>>> none of them is deleted.
>>> This is correct, but insufficient.
>>
>> It is all that is needed.
>
> wrong, you are incompetent.
>
>>
>>>>> A In order to prove an inconsistency in ZFC
>>>>
>>>> it issufficient to prove that no O can leave the matrix.
>>> Ah, no. The fact that the reciprocal 1/n is positive for every natural
>>> number n is insufficient to conclude that the limit of the sequence {1,
>>> 1/2, 1/3, ..} cannot be 0.
>>
>> The limit of a sequence is a number which is approached.
>
> insufficient. what do YOU mean by "approached" ?

When an ant becomes a roach, it has been approached.

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

> Ben Bacarisse schrieb am Sonntag, 4. September 2022 um 21:26:47 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 Sonntag, 4. September 2022 um 18:14:07 UTC+2:
>> >> WM <askas...@gmail.com> writes:
>> >
>> >> > according to every kind of
>> >> > mathematics, never an O leaves the matrix. The only change of the
>> >> > initial matrix
>> >> >
>> >> > XOOO...
>> >> > XOOO...
>> >> > XOOO...
>> >> > XOOO...
>> >> > ...
>> >> >
>> >> > consists of exchanging an O and an X. Exchanging two symbols does not
>> >> > delete any of them.
>> >> And yet, in WMaths, the result of an endless sequence of swaps is a matrix,
>> >> conveniently written as a function from N to {0,1}, has no 0s in the
>> >> image.
>> >
>> > You are lying.
>> I showed you how.
>
> You cannot show it because it is wrong. It is nonsense to believe that
> by exchanging two items, one of them disappears.

I do not believe that, and a curious intellectual might want to examine
the argument to see how this apparent paradox is resolved. But you
don't want (or can't) to do that, despite the argument using only the
maths in your textbook. No actual infinities. Everything potential.

>> You flipped immediately back into whatever you are
>> calling maths that isn't yours these day. You appeared not to have
>> grasped even the first stage of my argument.
>
> Your argument started with a wrong image of Cantor's matrix which I
> corrected.

Doing the exercises will avoid any such problems because /you/ will be
providing everything right from the start! Do you want to continue with
them?

>> > The result of an endless sequence ℵo, ℵo, ℵo, ... is ℵo.
>> We're doing this with the maths in your book. I don't think ℵo is
>> defined in you textbook, is it?
>
> There is no actual infinity in my book. There is no 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, ...
> ...

Indeed, but (as you often do in your book) one can write 20 typical
elements to help the reader without implying an actual infinity. This
is all WMaths after all. But you'll see when you do the exercises that
there is no need for these diagrams in WMaths, so there can be no
suspicion that an "actual infinity" has crept in.

> But we have to assume it in order to discuss it by means of correct
> mathematics from hatever books.

No! That's the great thing I am offering to help you see. Your WMaths
can do it to! No actual infinity needed.

>> Anyway, that's not the result given by
>> WMaths as my argument showed.
>
> Your argument failed to produce exchanges.

Nope. There were right there. You did cut them all from your reply. I
wonder why?

>> > I prefer to write X and O in the way I did. Nothing in my book
>> > contradicts that.
>> Indeed. It all works in WMaths. If do decide to take me up on the
>> offer, and do the exercises, you'll see how it's done.
>>
>> When you said "please try it" in reply to may offer of taking you
>> through some exercises
>
> I am looking foreward to your yexplaination of the argument.

I wrote out the argument but you misinterpreted the very first step and
then cut most of the rest of it without comment. I assume you will do
the same again, no matter how often I explain it.

No, my offer, which you seemed to accept, was to take you through it by
having /you/ produce the argument, as the answers to a series of
exercises. That, as I am sure you know, is a good way to get students
to really understand things.

>> The offer still stands and, as I said, I can break it down (into two) if
>> you think that would help.
>
> Show what you have, but adhere to the topic and don't try to change
> it.

I have the first exercise for you. I'm going to break it down since you
didn't tackle it last time when it was all-in-one.

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.

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).

Note: while you wrote a part of an actually infinite matrix, everything
from now on is going to be potentially infinite so it would be a good
idea not to write any grids in case you confuse yourself and think that
you've flipped back into actual infinity. Remember, nothing but WMaths
permitted!

--
Ben.

fredag 2 september 2022 kl. 15:54:00 UTC+2 skrev WM:
> zelos...@gmail.com schrieb am Freitag, 2. September 2022 um 11:26:23 UTC+2:
> > torsdag 1 september 2022 kl. 15:25:36 UTC+2 skrev WM:
> > > Gus Gassmann schrieb am Mittwoch, 31. August 2022 um 19:35:11 UTC+2:
> > >
> > > > (4) "Because I (WM) say so."
> > > >
> > > Yes. This is so because I say so (and because every sober mind will agree): The intersection of non-empty inclusion-monotonic sets is not empty.
> > >
> > That is what a crazy person that doesn't understand mathematics will say because in sensible mathematics where logical people work, there is no such implication
> The states of water flowing out of a bathub will never have an empty intersection before the bathtub is empty. "Mathematics" contradicting this basic principle is rubbish.
>
> Regards, WM

Bathtub is a physical object, therefore your analogy is invalid.

"intersection" is not applicable to it either.

Everything here shows how retarded you are.

Mathematics contradicts "common sense", but guess what? Common sense has no place in mathematics.

On Sunday, September 4, 2022 at 11:25:27 PM UTC+2, Ben Bacarisse wrote:
> JVR <jrenne...@googlemail.com> writes:
>
> > There is only one immutable rule in what you call WMaths and I call
> > Muckmeatics: "You cannot nail a pudding to the wall."
> That's my feeling, most of the time. But while you can't nail up a
> whole one, I've managed, over the years, to nail up a few tiny scraps of
> pudding.
>
> For example, there is the theorem that states that in WMaths, certain
> bounded monotonic sequences of rationals don't converge to a real
> number. The theorem hit the rails, though, when WM could not pin down
> which ones, but not before the existence of such sequences was agreed.
>
> Sometimes the pudding scraps drop off because WM just pulls the nail out
> by flat-out denial of overwhelming evidence. He has asserted that (in
> WMaths) no non-constant sequences of sets converge despite his textbook
> making it plain that (a) functions are just sets, and (b) some
> non-constant sequences of functions converge.
>
> But the most beautiful scrap of nailed-on pudding is the clear statement
> that, in WMaths (specifically for some potentially infinite sets) it is
> possible to have both e ∈ S and S \ {e} = S. WM himself described this
> as a "surprise". No shit!
>
> Pressing for an explanation resulted in WM saying that he could not
> define set membership, equality and difference in a way that would
> enable a student of WMaths to get this result for themselves. Quite an
> admission.
>
> --
> Ben.

You might think that it should be possible to focus on a single simple clear-cut error
and get him to understand that. But it isn't possible.

For example, in the present context Mücke keeps stating as fact that the intersection of
an infinite monotone sequence of non-empty sets is necessarily non-empty.
There is no way to disabuse him of this notion.

So the conclusion is inevitable - it doesn't matter whether his problem is
stupidity or a psychological abnormality - the effect is the same.

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.

What a surprise!

Now a REASONABLE person would (at least) question some of his or her "existence assumptions" concerning "potentially infinite sets".

But WM is no REASONABLE person. Actually, even this devastating result will not have any effect on him.

Fritz Feldhase <franz.fritschee.ff@gmail.com> 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?

--
Ben.

On Monday, September 5, 2022 at 12:24:46 PM UTC+2, Ben Bacarisse wrote:
> Fritz Feldhase <franz.fri...@gmail.com> 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?
>
> --
> Ben.

In the German language math group I have recently, and also a few years ago,
posted lists of errors in his book. Here is a particularly blatant one:
https://drive.google.com/file/d/1cDDjfnWyz4DU53cMv47oxoDKQVl5fuO5/view?usp=sharing

In the ensuing discussion it became clear that he copied this from somewhere else and
doesn't understand why it is nonsense. And - this is the really weird part - he insists that his
source is authoritative.

Other crass examples of his incompetence are his redefinition of continuity and his improvement of the
Peano axioms. The resulting discussion showed that he simply doesn't understand
the issues involved.

On Sunday, September 4, 2022 at 10:34:35 PM UTC+2, WM wrote:
> JVR schrieb am Sonntag, 4. September 2022 um 22:14:39 UTC+2:
> >
> > "You cannot nail a pudding to the wall."
> You are the pudding! You claimed you could explain how the O's were removed from the matrix
>
> XOO...
> XOO...
> XOO...
> ...
>
> by simple exchanges with the X's.
>
> When you are challenged to show it, either you escape to insults or poems..
>
> Regards, WM

No, Mücke, I asked you how you constructed the infinite matrix containing the
silly X's and O's.

The point being that, since you visualize your silly X's and O's as
coming from somewhere, we can surely invert the process and simply send them
back where they came from. (Maybe you can even get a refund!)

And every time we send one back home we number the now empty seat (m,n) according to
the formula k = (m + n - 1)(m + n - 2)/2 + m.

And everybody will live happily ever after.

On 9/5/2022 6:24 AM, Ben Bacarisse wrote:
> Fritz Feldhase <franz.fritschee.ff@gmail.com>
> 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/

Ben Bacarisse schrieb am Sonntag, 4. September 2022 um 03:33:25 UTC+2:
> WM <askas...@gmail.com> writes:

> >> > Cantor's approach is modelled by exchanging X's and O's in
> >> >
> >> > XOO...
> >> > XOO...
> >> > XOO...
> >> > ...
> >> >
> >> > until all O's have disappeared. Do you agree?
> >> Here are the cells as numbered by your bijective mapping:
> >>
> >> 1, 3, 6, 10, 15, ...
> >> 2, 5, 9, 14, 20, ...
> >> 4, 8, 13, 19, 26, ...
> >> 7, 12, 18, 25, 33, ...
> >> 11, 17, 24, 32, 41, ...
> >> ...
> >
> > Yes, all visible cells are filled with X's as Cantor has taught us.
> No. I've just written some numbers down to illustrate what you
> bijective mapping k looks like.

> >> With Os at 3, 5, 6, 8, 9 and so on.
> >
> > No, the above matrix does not contain O's any longer.

Sorry, I misunderstood. You have described the original matrix
XOO...
XOO...
XOO...
....
But as you enumerated every position by a natural number, it looked like the final matrix to me:
XXX...
XXX...
XXX...
....

Regards, WM

On 9/5/2022 8:14 AM, Jim Burns wrote:
> On 9/5/2022 6:24 AM, Ben Bacarisse wrote:

>> 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?

> | 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.

<WM<JB>>
>>
>> This description does immediately not rule out
>> your dark numbers and dark end segments.
>> Dark numbers could conceivably be in 𝐸
>> which are > each i in ⋃𝓕\𝐸
>>
>> However,
>> this description requires 𝐸 subset ⋃𝓕
>
> That is a wrong desription.
>
</WM<JB>>

Date: Fri, 2 Sep 2022 06:32:56 -0700 (PDT)
Subject: Re: Natural numbers and vases III

>
> https://blog.ted.com/are-we-getting-more-intelligent-jim-flynn-at-ted2013/
>

Ben Bacarisse schrieb am Montag, 5. September 2022 um 00:06:08 UTC+2:
> WM <askas...@gmail.com> writes:

> >> I showed you how.
> >
> > You cannot show it because it is wrong. It is nonsense to believe that
> > by exchanging two items, one of them disappears.
> I do not believe that,

That is worth to be nailed to the wall.

> and a curious intellectual might want to examine
> the argument to see how this apparent paradox is resolved.

However you may try it, not by disappearing O's.

> But you
> don't want (or can't) to do that,

Then do it yourself.

> despite the argument using only the
> maths in your textbook. No actual infinities. Everything potential.

You seem to have missed the point. Without actual infinities there are no completed enumerations of infinite sets and there are no dark numbers.

> Doing the exercises will avoid any such problems because /you/ will be
> providing everything right from the start! Do you want to continue with
> them?

I have seen your description of the initial matrix. No problem. But if you think to hanlde it by potential infinity, you cannot follow Cantor.

> >> > The result of an endless sequence ℵo, ℵo, ℵo, ... is ℵo.
> >> We're doing this with the maths in your book. I don't think ℵo is
> >> defined in you textbook, is it?
> >
> > There is no actual infinity in my book. There is no 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, ...
> > ...
> Indeed, but (as you often do in your book) one can write 20 typical
> elements to help the reader without implying an actual infinity. This
> is all WMaths after all. But you'll see when you do the exercises that
> there is no need for these diagrams in WMaths, so there can be no
> suspicion that an "actual infinity" has crept in.

The we can close the case. Dark nubers and complete enumerations are a matter of actual infinity.

> > But we have to assume it in order to discuss it by means of correct
> > mathematics from hatever books.
> No! That's the great thing I am offering to help you see. Your WMaths
> can do it to! No actual infinity needed.

Try to understand Cantor's set theory:
"In spite of significant difference between the notions of the potential and actual infinite, where the former is a variable finite magnitude, growing above all limits, the latter a constant quantity fixed in itself but beyond all finite magnitudes, it happens deplorably often that the one is confused with the other." [Cantor, p. 374]
"By the actual infinite we have to understand a quantity that on the one hand is not variable but fixed and definite in all its parts, a real constant, but at the same time, on the other hand, exceeds every finite size of the same kind by size. As an example I mention the totality, the embodiment of all finite positive integers; this set is a self-contained thing and forms, apart from the natural sequence of its numbers, a fixed, definite quantity, an , which we obviously have to call larger than every finite number." [G. Cantor, letter to A. Eulenburg (28 Feb 1886)]

Potential infinity is variable:
"Should we briefly characterize the new view of the infinite introduced by Cantor, we could certainly say: In analysis we have to deal only with the infinitely small and the infinitely large as a limit-notion, as something becoming, emerging, produced, i.e., as we put it, with the potential infinite.. But this is not the proper infinite. That we have for instance when we consider the entirety of the numbers 1, 2, 3, 4, ... itself as a completed unit, or the points of a line as an entirety of things which is completely available. That sort of infinity is named actual infinite." [D. Hilbert: "Über das Unendliche", Mathematische Annalen 95 (1925) p. 167]

> > Your argument failed to produce exchanges.
> Nope. There were right there. You did cut them all from your reply. I
> wonder why?

Sorry, I did not see exchanges. What do you exchange?

> > I am looking foreward to your explaination of the argument.

> I wrote out the argument but you misinterpreted the very first step

Yes, you wrote integers which I interpreted as indices. Now I got it that you made a sequence.

> Os at 3, 5, 6, 8, 9 and so on.

> Since this is the first step, you really need to be able to see how M_0
represents the initial matrix a WMaths function from N to {0,1}.

I see. But that does not change anything except that you will never cross the diagonal / of the matrix.

>No completed anything, everything potential

and visible. No dark numbers. You need to interpret your sequence as completed.

> 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.
>
> 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.
>
> Note: while you wrote a part of an actually infinite matrix, everything
> from now on is going to be potentially infinite

You may stop immediately if you can't understand the difference between potential infinity (of mathematics including my book) and Cantor's actual infinity.

> Remember, nothing but WMaths
> permitted!

For analyzing the facts yes, but not for the outset.

Regards, 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.

> 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.

Regards, WM

JVR schrieb am Montag, 5. September 2022 um 13:35:29 UTC+2:
> On Sunday, September 4, 2022 at 10:34:35 PM UTC+2, WM wrote:

> I asked you how you constructed the infinite matrix containing the
> X's and O's.touk Cantor's finished infinity. A finished column of integer fractions and a finihed infinity of finihed columns of other fractions.

> The point being that, since you visualize your silly X's and O's as
> coming from somewhere, we can surely invert the process and simply send them
> back where they came from. (Maybe you can even get a refund!)

Forget Cantor and his disciples. The they all have disappeared.
>
> And every time we send one back home we number the now empty seat (m,n) according to
> the formula k = (m + n - 1)(m + n - 2)/2 + m.

I am analyzing Cantor's version. There all fractions O are remaining in the matrix and are becoming enumerated by integer fractions X

Regards, WM

On 9/5/2022 8:21 AM, WM wrote:
> JVR schrieb am Montag, 5. September 2022 um 13:35:29 UTC+2:
>> On Sunday, September 4, 2022 at 10:34:35 PM UTC+2, WM wrote:
>
>> I asked you how you constructed the infinite matrix containing the
>> X's and O's.touk Cantor's finished infinity. A finished column of integer fractions and a finihed infinity of finihed columns of other fractions.
>
>> The point being that, since you visualize your silly X's and O's as
>> coming from somewhere, we can surely invert the process and simply send them
>> back where they came from. (Maybe you can even get a refund!)
>
> Forget Cantor and his disciples. The they all have disappeared.

But Cantors Proof lives on forever, and it cannot be disproved.

>>
>> And every time we send one back home we number the now empty seat (m,n) according to
>> the formula k = (m + n - 1)(m + n - 2)/2 + m.
>
> I am analyzing Cantor's version.

come on dude!

that is a 3 min task at most, and you have spent decades ?

>
> Regards, WM

On Monday, September 5, 2022 at 3:21:35 PM UTC+2, WM wrote:
> JVR schrieb am Montag, 5. September 2022 um 13:35:29 UTC+2:
> > On Sunday, September 4, 2022 at 10:34:35 PM UTC+2, WM wrote:
>
> > I asked you how you constructed the infinite matrix containing the
> > X's and O's.touk Cantor's finished infinity. A finished column of integer fractions and a finihed infinity of finihed columns of other fractions.
> > The point being that, since you visualize your silly X's and O's as
> > coming from somewhere, we can surely invert the process and simply send them
> > back where they came from. (Maybe you can even get a refund!)
> Forget Cantor and his disciples. The they all have disappeared.
> >
> > And every time we send one back home we number the now empty seat (m,n) according to
> > the formula k = (m + n - 1)(m + n - 2)/2 + m.
> I am analyzing Cantor's version. There all fractions O are remaining in the matrix and are becoming enumerated by integer fractions X
>
> Regards, WM

Well - I'm definitely not going to try to make sense of this gobble-dee-gook.

On 9/5/2022 8:13 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.

that is your bullshit.

>
>> 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.
>
> Regards, WM

On 9/5/2022 8:06 AM, WM wrote:
>
> Ben Bacarisse schrieb am Montag, 5. September 2022 um 00:06:08 UTC+2:
>> WM <askas...@gmail.com> writes:
>
>>>> I showed you how.
>>>
>>> You cannot show it because it is wrong. It is nonsense to believe that
>>> by exchanging two items, one of them disappears.
>> I do not believe that,
>

<snip spoof math>

>
> Regards, WM

On 9/5/2022 6:00 AM, JVR wrote:
> On Monday, September 5, 2022 at 12:24:46 PM UTC+2, Ben Bacarisse wrote:
>> Fritz Feldhase <franz.fri...@gmail.com> 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?
>>
>> --
>> Ben.
>
> In the German language math group I have recently, and also a few years ago,
> posted lists of errors in his book. Here is a particularly blatant one:
> https://drive.google.com/file/d/1cDDjfnWyz4DU53cMv47oxoDKQVl5fuO5/view?usp=sharing
>
> In the ensuing discussion it became clear that he copied this from somewhere else and
> doesn't understand why it is nonsense. And - this is the really weird part - he insists that his
> source is authoritative.

I reviewed that book, and to me it was obvious it was a cut and paste, as the span was too great, and the depth of each level too deep, making the book
unusable, especially to students.

>
> Other crass examples of his incompetence are his redefinition of continuity and his improvement of the
> Peano axioms. The resulting discussion showed that he simply doesn't understand
> the issues involved.

On Monday, September 5, 2022 at 12:24:46 PM UTC+2, 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.

Yes. It's clear that he only has some "notions" like "potentially infinite sets" and some rather vague ideas concerning these "notions", but no concrete system (i. e. an "alternative" set theory) in WMaths. WM is all talk.

> > 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.

I'd tend to agree. Imho he's actually a so called crank.

> > 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?

Hard to tell, I've never met a (math) crank in real live!

Maybe he would just quit the discussion (prematurely) at some point.

WM laid this down on his screen :
> 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.
>
>> 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.

But he has just shown you it *is* possible in your 'system' using your
WMaths. Refuse to see it if you must, but it is not a good look for a
professed professor.

Then again, it seems you *do* have a different notion of the definition
of "\" probably something to do with subtraction, bathtubs and Xs and
Os. Maybe you could share that with us?

FromTheRafters wrote:
> WM laid this down on his screen :
>> 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.
>>
>>> 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.
>
> But he has just shown you it *is* possible in your 'system' using your
> WMaths. Refuse to see it if you must, but it is not a good look for a
> professed professor.

There is 0% chances he will ever admit being 100% wrong (and he is), but
there is a solution for that issue: ensure that he's not allow to be a
professor ever in the future, including this academic year.

As he should be for ages, and would be in almost all places where math
is taught in the entire world.

What's THAT wrong with Hochschule Augsburg?

> Then again, it seems you *do* have a different notion of the definition
> of "\" probably something to do with subtraction, bathtubs and Xs and
> Os. Maybe you could share that with us?