On Friday, September 16, 2022 at 11:18:58 AM UTC-7, Ben Bacarisse wrote:
> Sergio <inv...@invalid.com> writes:
>
> > I think his course is an elective for business types, not mainstream
> > math.
> I imagine anyone can take it as it's a history course in the general
> studies faculty. The college does not have a degree program in
> mathematics so there is no one there to call him out.
>
> The course is mainly history and as such is mainly unobjectionable.
> Sadly, to get full marks the students do appear to have to repeat one or
> more of his mantras, but it's all words, I think. They are not forced
> to write fake proofs.

Guffaw!!

Can you imagine our beloved Professor trying to grade a proof?!

On 9/16/2022 3:31 AM, WM wrote:
> zelos...@gmail.com schrieb am Donnerstag,
> 15. September 2022 um 11:35:18 UTC+2:

>> You are thinking in terms of
>> a step by step process. That is WRONG
>
> Why?

There is an end to a process.

>> The function f: N-> Q and such
>> exist in its entirety already.
>
> Every definable natnumber can be reached
> step by step by its FISON.

There is an end to a FISON.
There is NO end to all things-in-FISONs.

If
n is a thing-in-a-FISON.
then
n is the end to FISON 𝐹ₙ
and
n+1 is the end to FISON 𝐹ₙ⊕⟨n+1⟩
and
n is NOT the end to all things-in-FISONs

If
n is NOT a thing-in-a-FISON.
then
n is NOT the end to all things-in-FISONs

There is NO end to all things-in-FISONs.

On 9/17/2022 12:36 PM, Jim Burns wrote:
> On 9/16/2022 3:31 AM, WM wrote:
>> zelos...@gmail.com schrieb am Donnerstag,
>> 15. September 2022 um 11:35:18 UTC+2:

>>> You are thinking in terms of
>>> a step by step process.
>>> That is WRONG
>>
>> Why?
>
> There is an end to a process.

Correction:
It's not only that there is an end
to a process, a last state.

A process has last and first states,
and _also_ each split of its states
has last-before and first-after states.

>>> The function f: N-> Q and such
>>> exist in its entirety already.
>>
>> Every definable natnumber can be reached
>> step by step by its FISON.
>
> There is an end to a FISON.

A FISON has last and first numbers,
and each split of its numbers
has last-before and first-after numbers.

A FISON can represent a process.

> There is NO end to all things-in-FISONs.

(i)
If nothing is appended to the things-in-FISONs,
they don't represent a process
because
there is no last thing-in-a-FISON.

Because
𝐹ₙ⊕⟨n+1⟩ is a FISON too.

(ii)
If anything (dark) is appended to
the things-in-FISONs,
things+dark still don't represent a process
because
not all splits have last-before and first-after.

Because
there is a split between things-in-FISONs
and the appended dark,
and
there is no last-before thing-in-a-FISON

Because
𝐹ₙ⊕⟨n+1⟩ is a FISON too.

All the things-in-FISONs cannot represent
a process.

All the things-in-FISONs cannot represent
an _initial segment_ of a process,
no matter what dark things are appended.

On 9/17/2022 1:57 PM, Jim Burns wrote:
> On 9/17/2022 12:36 PM, Jim Burns wrote:
>> On 9/16/2022 3:31 AM, WM wrote:
>>> zelos...@gmail.com schrieb am Donnerstag,
>>> 15. September 2022 um 11:35:18 UTC+2:
>
>>>> You are thinking in terms of
>>>> a step by step process.
>>>> That is WRONG
>>>
>>> Why?
>>
>> There is an end to a process.
>
> Correction:
> It's not only that there is an end
> to a process, a last state.
>
> A process has last and first states,
> and _also_ each split of its states
> has last-before and first-after states.
>
>>>> The function f: N-> Q and such
>>>> exist in its entirety already.
>>>
>>> Every definable natnumber can be reached
>>> step by step by its FISON.
>>
>> There is an end to a FISON.
>
> A FISON has last and first numbers,
> and each split of its numbers
> has last-before and first-after numbers.
>
> A FISON can represent a process.

A FISON is a specific set of elements.

a FISON can be used in a process, but a FISON is not a process.

Sets do not change.

>
>> There is NO end to all things-in-FISONs.
>
> (i)
> If nothing is appended to the things-in-FISONs,
> they don't represent a process
> because
> there is no last thing-in-a-FISON.
>
> Because
> 𝐹ₙ⊕⟨n+1⟩ is a FISON too.
>
> (ii)
> If anything (dark) is appended to
> the things-in-FISONs,
> things+dark still don't represent a process
> because
> not all splits have last-before and first-after.
>
> Because
> there is a split between things-in-FISONs
> and the appended dark,
> and
> there is no last-before thing-in-a-FISON
>
> Because
> 𝐹ₙ⊕⟨n+1⟩ is a FISON too.
>
>
> All the things-in-FISONs cannot represent
> a process.
>
> All the things-in-FISONs cannot represent
> an _initial segment_ of a process,
> no matter what dark things are appended.
>

On 9/17/2022 5:34 PM, Sergio wrote:
> On 9/17/2022 1:57 PM, Jim Burns wrote:

>> A process has last and first states,
>> and _also_ each split of its states
>> has last-before and first-after states.

>> A FISON has last and first numbers,
>> and each split of its numbers
>> has last-before and first-after numbers.
>>
>> A FISON can represent a process.
>
> A FISON is a specific set of elements.
>
> a FISON can be used in a process,
> but a FISON is not a process.

I'm not disagreeing with you.
A FISON is not a process.

but neither is a number a herd of sheep.
We can use a number to represent a herd of
sheep, or at least some aspect of a herd of
sheep.

Also, I know that we use the word "process"
to describe things which _don't_ have
last-before and first-after for each split.

In my limited understanding, _float glass_
is produced by pouring molten onto some
molten metal with a low melting-point, such
as tin. I suspect that there are no steps
such as adding a column of numbers has.
https://en.wikipedia.org/wiki/Float_glass

I don't have any other examples of float-glass
style processes in mind right now, but I feel
confident that there are many.

However,
a FISON can _represent_ certain processes,
within my restricted sense of "process".
I don't see anything to be concerned about.
It seems to me that most of what mathematics
is put to use for is _representing_

> Sets do not change.

Oh, I agree.
Whether WM agrees gets tricky.

WM has certainly said that sets do not change.

What is "change" for WM?
I'm exaggerating for effect:
If,
at one point, we say "It can fly"
(true, because we refer to a plane)
and
at another point, we say "It can't fly"
(true, because we refer to a boat),
then
whatever "it" refers to has _changed_
from a plane to a boat.

That's my currently-best guess at what
WM is thinking. The usual caveats apply.

Perhaps? WM sees a variable as needing
some act of being pointed at a value within
its domain. I think we all agree that can be
done (in principle) for a FISON.
I think WM claims that Cantor claims that
it can be done for infinite collections.

I offer an alternative to that notion of
"variable": the notion of a reference to
_one of_ a domain, finite or infinite,
and of claims that we know are true without
knowing _which_ one of the domain is
referred to.

We are finite. We can only express and
manipulate finitely-many finite sentences.
But referring is not expressing and not
manipulating. Our finiteness does not
keep us from referring to infinitely-many.

On 9/17/2022 5:53 PM, Jim Burns wrote:
> On 9/17/2022 5:34 PM, Sergio wrote:
>> On 9/17/2022 1:57 PM, Jim Burns wrote:
>
>>> A process has last and first states,
>>> and _also_ each split of its states
>>> has last-before and first-after states.
>
>>> A FISON has last and first numbers,
>>> and each split of its numbers
>>> has last-before and first-after numbers.
>>>
>>> A FISON can represent a process.
>>
>> A FISON is a specific set of elements.
>>
>> a FISON can be used in a process,
>> but a FISON is not a process.
>
> I'm not disagreeing with you.
> A FISON is not a process.
>
> but neither is a number a herd of sheep.
> We can use a number to represent a herd of
> sheep, or at least some aspect of a herd of
> sheep.
>
> Also, I know that we use the word "process"
> to describe things which _don't_ have
> last-before and first-after for each split.
>
> In my limited understanding, _float glass_
> is produced by pouring molten onto some
> molten metal with a low melting-point, such
> as tin. I suspect that there are no steps
> such as adding a column of numbers has.
> https://en.wikipedia.org/wiki/Float_glass
>
> I don't have any other examples of float-glass
> style processes in mind right now, but I feel
> confident that there are many.
>
> However,
> a FISON can _represent_ certain processes,
> within my restricted sense of "process".
> I don't see anything to be concerned about.
> It seems to me that most of what mathematics
> is put to use for is _representing_
>
>> Sets do not change.
>
> Oh, I agree.
> Whether WM agrees gets tricky.
>
> WM has certainly said that sets do not change.
>
> What is "change" for WM?
> I'm exaggerating for effect:
> If,
> at one point, we say "It can fly"
> (true, because we refer to a plane)
> and
> at another point, we say "It can't fly"
> (true, because we refer to a boat),
> then
> whatever "it" refers to has _changed_
> from a plane to a boat.
>
> That's my currently-best guess at what
> WM is thinking. The usual caveats apply.
>
> Perhaps? WM sees a variable as needing
> some act of being pointed at a value within
> its domain. I think we all agree that can be
> done (in principle) for a FISON.
> I think WM claims that Cantor claims that
> it can be done for infinite collections.
>
>
> I offer an alternative to that notion of
> "variable": the notion of a reference to
> _one of_ a domain, finite or infinite,
> and of claims that we know are true without
> knowing _which_ one of the domain is
> referred to.
>
> We are finite. We can only express and
> manipulate finitely-many finite sentences.
> But referring is not expressing and not
> manipulating. Our finiteness does not
> keep us from referring to infinitely-many.
>

agree, a FISON can be part of a process, like an input vector to Neural Networks, or its output as a goal. but FISONs are an object, no working parts.

AND WM uses sets as variables, like his Matrix of X and Os swapadoodle-festival. And WM has stated he does not believe in variables, (he does not know
algebra) nor proofs, nor ...

On Saturday, September 17, 2022 at 6:53:57 PM UTC-4, Jim Burns wrote:
> On 9/17/2022 5:34 PM, Sergio wrote:
> > On 9/17/2022 1:57 PM, Jim Burns wrote:
>
> >> A process has last and first states,
> >> and _also_ each split of its states
> >> has last-before and first-after states.
> >> A FISON has last and first numbers,
> >> and each split of its numbers
> >> has last-before and first-after numbers.
> >>
> >> A FISON can represent a process.
> >
> > A FISON is a specific set of elements.
> >
> > a FISON can be used in a process,
> > but a FISON is not a process.
> I'm not disagreeing with you.
> A FISON is not a process.
>
> but neither is a number a herd of sheep.
> We can use a number to represent a herd of
> sheep, or at least some aspect of a herd of
> sheep.
>
> Also, I know that we use the word "process"
> to describe things which _don't_ have
> last-before and first-after for each split.
>
> In my limited understanding, _float glass_
> is produced by pouring molten onto some
> molten metal with a low melting-point, such
> as tin. I suspect that there are no steps
> such as adding a column of numbers has.
> https://en.wikipedia.org/wiki/Float_glass
>
> I don't have any other examples of float-glass
> style processes in mind right now, but I feel
> confident that there are many.
>
> However,
> a FISON can _represent_ certain processes,
> within my restricted sense of "process".
> I don't see anything to be concerned about.
> It seems to me that most of what mathematics
> is put to use for is _representing_
>
> > Sets do not change.
>
> Oh, I agree.
> Whether WM agrees gets tricky.
>
> WM has certainly said that sets do not change.
>
> What is "change" for WM?
> I'm exaggerating for effect:
> If,
> at one point, we say "It can fly"
> (true, because we refer to a plane)
> and
> at another point, we say "It can't fly"
> (true, because we refer to a boat),
> then
> whatever "it" refers to has _changed_
> from a plane to a boat.
>
> That's my currently-best guess at what
> WM is thinking. The usual caveats apply.
>
> Perhaps? WM sees a variable as needing
> some act of being pointed at a value within
> its domain. I think we all agree that can be
> done (in principle) for a FISON.
> I think WM claims that Cantor claims that
> it can be done for infinite collections.
>
>
> I offer an alternative to that notion of
> "variable": the notion of a reference to
> _one of_ a domain, finite or infinite,
> and of claims that we know are true without
> knowing _which_ one of the domain is
> referred to.
>
> We are finite. We can only express and
> manipulate finitely-many finite sentences.
> But referring is not expressing and not
> manipulating. Our finiteness does not
> keep us from referring to infinitely-many.

In that induction is the process that allows these discussions then we can induce these large values. For instance:
333...34
is well defined. It's successor is:
333...35
and we can even take the product of these two. It is done via induction. Yet the result is a doubly induced value. It has twice as many digits as its forebears, as does any product generally speaking. Rather to anticipate the product (n)(m) one should anticipate the quantity of digits in n plus the quantity of digits in m for general work. This is a two aleph situation and it takes two sets of ellipses to get the correct answer. In that constructions with ellipses do need to be scrutinized; well, do you refuse the above values as valid? Do these values modify your interpretation of infinity? After all, they are not so lonely. I suggest that the proposition of dark numbers is partially true, but clearly by the conditions of Muckenheim himself these are not they. Any mathematician who willingly works past the value 10, and I do place these infinite concerns in this department, will have to reconsider their assumptions won't they? Instantiability is meaningful, and this is not the first place that this argument has been made. The lack of instantiability within mathematics as a quagmire is simply upheld in order that there be room for rather a lot of works. Of course the value of those works sits upon quite a structure, and one kick down low could wreak havoc if your footings are trigged.

It is too easy to attack the rational value, and especially to mix it up into such arguments on infinite forms: in this regard it is possible that WM is authentic and has exposed the problem with the rational value indirectly.. Who is concerned with integers that mixes up their talk with rationals is concocting an explosive mixture...

On 9/18/2022 8:55 AM, Timothy Golden wrote:
> On Saturday, September 17, 2022 at 6:53:57 PM UTC-4, Jim Burns wrote:
>> On 9/17/2022 5:34 PM, Sergio wrote:
>>> On 9/17/2022 1:57 PM, Jim Burns wrote:
>>
>>>> A process has last and first states,
>>>> and _also_ each split of its states
>>>> has last-before and first-after states.
>>>> A FISON has last and first numbers,
>>>> and each split of its numbers
>>>> has last-before and first-after numbers.
>>>>
>>>> A FISON can represent a process.
>>>
>>> A FISON is a specific set of elements.
>>>
>>> a FISON can be used in a process,
>>> but a FISON is not a process.
>> I'm not disagreeing with you.
>> A FISON is not a process.
>>
>> but neither is a number a herd of sheep.
>> We can use a number to represent a herd of
>> sheep, or at least some aspect of a herd of
>> sheep.
>>
>> Also, I know that we use the word "process"
>> to describe things which _don't_ have
>> last-before and first-after for each split.
>>
>> In my limited understanding, _float glass_
>> is produced by pouring molten onto some
>> molten metal with a low melting-point, such
>> as tin. I suspect that there are no steps
>> such as adding a column of numbers has.
>> https://en.wikipedia.org/wiki/Float_glass
>>
>> I don't have any other examples of float-glass
>> style processes in mind right now, but I feel
>> confident that there are many.
>>
>> However,
>> a FISON can _represent_ certain processes,
>> within my restricted sense of "process".
>> I don't see anything to be concerned about.
>> It seems to me that most of what mathematics
>> is put to use for is _representing_
>>
>>> Sets do not change.
>>
>> Oh, I agree.
>> Whether WM agrees gets tricky.
>>
>> WM has certainly said that sets do not change.
>>
>> What is "change" for WM?
>> I'm exaggerating for effect:
>> If,
>> at one point, we say "It can fly"
>> (true, because we refer to a plane)
>> and
>> at another point, we say "It can't fly"
>> (true, because we refer to a boat),
>> then
>> whatever "it" refers to has _changed_
>> from a plane to a boat.
>>
>> That's my currently-best guess at what
>> WM is thinking. The usual caveats apply.
>>
>> Perhaps? WM sees a variable as needing
>> some act of being pointed at a value within
>> its domain. I think we all agree that can be
>> done (in principle) for a FISON.
>> I think WM claims that Cantor claims that
>> it can be done for infinite collections.
>>
>>
>> I offer an alternative to that notion of
>> "variable": the notion of a reference to
>> _one of_ a domain, finite or infinite,
>> and of claims that we know are true without
>> knowing _which_ one of the domain is
>> referred to.
>>
>> We are finite. We can only express and
>> manipulate finitely-many finite sentences.
>> But referring is not expressing and not
>> manipulating. Our finiteness does not
>> keep us from referring to infinitely-many.
>
> In that induction is the process that allows these discussions then we can induce these large values. For instance:
> 333...34
> is well defined.

Not at all, it takes on an infinite range of values.

Please fix it and post back here for grading.

Fritz Feldhase schrieb am Freitag, 16. September 2022 um 11:35:57 UTC+2:
> On Friday, September 16, 2022 at 9:32:01 AM UTC+2, WM wrote:
> > zelos...@gmail.com schrieb am Donnerstag, 15. September 2022 um 11:35:18 UTC+2:
> > >
> > > You are thinking in terms of a step by step process [here]. That is WRONG
> > >
> > Why?
>
> Because a function is not a process, you silly idiot!
>
> Hnt:
> > > The function f: N-> Q and such exist in its entirety already.
> Hint: f is just a certain set of pairs

Every definable n can be reached by the process 1, 2, 3, ..., n.

Regards, WM

Gus Gassmann schrieb am Freitag, 16. September 2022 um 13:47:11 UTC+2:
> On Friday, 16 September 2022 at 04:32:01 UTC-3, WM wrote:
> > zelos...@gmail.com schrieb am Donnerstag, 15. September 2022 um 11:35:18 UTC+2:
> [...]
> > > You are thinking in terms of a step by step process. That is WRONG
> > Why?
> Because you are dealing with an *INFINITE* process. Infinite processes need to be analyzed through their limiting behaviour,

Then explain it. The matrix

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

turns into the matrix

XXXXX...
XXXXX...
XXXXX...
XXXXX...
XXXXX...
....

in the limit by exchanging X,O-pairs. But no O leaves the matrix. Where do they remain?

Regards, WM

Ben Bacarisse schrieb am Freitag, 16. September 2022 um 16:42:09 UTC+2:

> WM likes to talk about processes because they don't end, but properties
> of functions can be proved using finite arguments. In effect he wants
> to deny another part of his book -- the final words in a proof by
> induction. He'd be quite happy with "P(1) and P(x) implies P(x+1)" to
> be the end of it, but because he needs to sell the book, he concludes
> (as does every author)
>
> "so ist sie für alle natürlichen Zahlen richtig"

Yes, alas only for definable natural numbers.
>
> That's why I got him to confirm that a student of his (reading his own
> textbook) could prove that k(m,n) = (m + n - 1)(m + n - 2)/2 + m is a
> bijection from NxN to N. It is so "für alle natürlichen Zahlen"..

Yes, alas only for definble natural numbers.

Where do the O's go? They end at undefinable positions.

> >> Every definable natnumber can be reached step by step by its FISON.
> >
> > definables are fake math.
> ... and don't exist in WMaths anyway where k(m,n) is a bijection "für
> alle natürlichen Zahlen".

When I wrote this book I did not wish to include Cantor and thought that he was entirely wrong with his actual infinity. But meanwhile I have found a way to save part of his work.

Mathematics transforms the matrix

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

into the matrix

XXXXX...
XXXXX...
XXXXX...
XXXXX...
XXXXX...
....

by merely exchanging X,O-pairs. But no O leaves the matrix. Where do they remain?

Either actual infinity is nonsense and no such matrix exists, or there are dark places.

Regards, WM

Ben Bacarisse schrieb am Freitag, 16. September 2022 um 20:18:58 UTC+2:
> Sergio <inv...@invalid.com> writes:
>
> > I think his course is an elective for business types, not mainstream
> > math.
> I imagine anyone can take it as it's a history course in the general
> studies faculty.

Yes.

> The college

Technische Hochschule Augsburg

> does not have a degree program in
> mathematics.

So it is.
>
> The course is mainly history and as such is mainly unobjectionable.
> Sadly, to get full marks the students do appear to have to repeat one or
> more of his mantras,

No student is forced to repeat that. If any student could explain where the O's remain, he would get mentioned for outstanding achievements. But I am sceptical, because not even mathematicians are able to do that.

Regards, WM

Jim Burns schrieb am Samstag, 17. September 2022 um 18:36:11 UTC+2:
> On 9/16/2022 3:31 AM, WM wrote:
> > zelos...@gmail.com schrieb am Donnerstag,
> > 15. September 2022 um 11:35:18 UTC+2:
> >> You are thinking in terms of
> >> a step by step process. That is WRONG
> >
> > Why?
> There is an end to a process.

It can be completed:

"If two well-defined manifolds, M and N, can be related completely, element by element, to each other [...], then for the following the expression may be permitted that these manifolds have the same cardinality or that they are equivalent."

"Every well-defined set has a definite cardinality; two sets are ascribed the same cardinality if they mutually uniquely, element by element, can be mapped onto each other."

"Two sets are called 'equivalent' if they mutually uniquely, element by element, can be mapped onto each other."

> > Every definable natnumber can be reached
> > step by step by its FISON.
> There is an end to a FISON.
> There is NO end to all things-in-FISONs.

Every end of a FISON can be reached by steps. All things in all FISONs can be reached by steps. Find a counter example!
>
> There is NO end to all things-in-FISONs.

There is an end, but it is changing. Never an n outside of all FISONs is reached.

Regards, WM

Sergio wrote :
> On 9/18/2022 8:55 AM, Timothy Golden wrote:
>> On Saturday, September 17, 2022 at 6:53:57 PM UTC-4, Jim Burns wrote:
>>> On 9/17/2022 5:34 PM, Sergio wrote:
>>>> On 9/17/2022 1:57 PM, Jim Burns wrote:
>>>
>>>>> A process has last and first states,
>>>>> and _also_ each split of its states
>>>>> has last-before and first-after states.
>>>>> A FISON has last and first numbers,
>>>>> and each split of its numbers
>>>>> has last-before and first-after numbers.
>>>>>
>>>>> A FISON can represent a process.
>>>>
>>>> A FISON is a specific set of elements.
>>>>
>>>> a FISON can be used in a process,
>>>> but a FISON is not a process.
>>> I'm not disagreeing with you.
>>> A FISON is not a process.
>>>
>>> but neither is a number a herd of sheep.
>>> We can use a number to represent a herd of
>>> sheep, or at least some aspect of a herd of
>>> sheep.
>>>
>>> Also, I know that we use the word "process"
>>> to describe things which _don't_ have
>>> last-before and first-after for each split.
>>>
>>> In my limited understanding, _float glass_
>>> is produced by pouring molten onto some
>>> molten metal with a low melting-point, such
>>> as tin. I suspect that there are no steps
>>> such as adding a column of numbers has.
>>> https://en.wikipedia.org/wiki/Float_glass
>>>
>>> I don't have any other examples of float-glass
>>> style processes in mind right now, but I feel
>>> confident that there are many.
>>>
>>> However,
>>> a FISON can _represent_ certain processes,
>>> within my restricted sense of "process".
>>> I don't see anything to be concerned about.
>>> It seems to me that most of what mathematics
>>> is put to use for is _representing_
>>>
>>>> Sets do not change.
>>>
>>> Oh, I agree.
>>> Whether WM agrees gets tricky.
>>>
>>> WM has certainly said that sets do not change.
>>>
>>> What is "change" for WM?
>>> I'm exaggerating for effect:
>>> If,
>>> at one point, we say "It can fly"
>>> (true, because we refer to a plane)
>>> and
>>> at another point, we say "It can't fly"
>>> (true, because we refer to a boat),
>>> then
>>> whatever "it" refers to has _changed_
>>> from a plane to a boat.
>>>
>>> That's my currently-best guess at what
>>> WM is thinking. The usual caveats apply.
>>>
>>> Perhaps? WM sees a variable as needing
>>> some act of being pointed at a value within
>>> its domain. I think we all agree that can be
>>> done (in principle) for a FISON.
>>> I think WM claims that Cantor claims that
>>> it can be done for infinite collections.
>>>
>>>
>>> I offer an alternative to that notion of
>>> "variable": the notion of a reference to
>>> _one of_ a domain, finite or infinite,
>>> and of claims that we know are true without
>>> knowing _which_ one of the domain is
>>> referred to.
>>>
>>> We are finite. We can only express and
>>> manipulate finitely-many finite sentences.
>>> But referring is not expressing and not
>>> manipulating. Our finiteness does not
>>> keep us from referring to infinitely-many.
>>
>> In that induction is the process that allows these discussions then we can
>> induce these large values. For instance:
>> 333...34
>> is well defined.
>
> Not at all, it takes on an infinite range of values.
>
> Please fix it and post back here for grading.

I've seen notation similar to that, but his is definitely not a prime
example.

https://en.wikipedia.org/wiki/Largest_known_prime_number#History_of_largest_known_prime_numbers

On 9/18/2022 1:44 PM, WM wrote:
> Fritz Feldhase schrieb am Freitag, 16. September 2022 um 11:35:57 UTC+2:
>> On Friday, September 16, 2022 at 9:32:01 AM UTC+2, WM wrote:
>>> zelos...@gmail.com schrieb am Donnerstag, 15. September 2022 um 11:35:18 UTC+2:
>>>>
>>>> You are thinking in terms of a step by step process [here]. That is WRONG
>>>>
>>> Why?
>>
>> Because a function is not a process, you silly idiot!
>>
>> Hnt:
>>>> The function f: N-> Q and such exist in its entirety already.
>> Hint: f is just a certain set of pairs
>
> Every definable n can be reached by the process 1, 2, 3, ..., n.

your daffynition also says your n is defined as a color of the rainbow.

>
> Regards, WM

On 9/18/2022 1:47 PM, WM wrote:
> Gus Gassmann schrieb am Freitag, 16. September 2022 um 13:47:11 UTC+2:
>> On Friday, 16 September 2022 at 04:32:01 UTC-3, WM wrote:
>>> zelos...@gmail.com schrieb am Donnerstag, 15. September 2022 um 11:35:18 UTC+2:
>> [...]
>>>> You are thinking in terms of a step by step process. That is WRONG
>>> Why?
>> Because you are dealing with an *INFINITE* process. Infinite processes need to be analyzed through their limiting behaviour,
>
> Then explain it. The matrix
>
> XOOOO...
> XOOOO...
> XOOOO...
> XOOOO...
> XOOOO...
> ...
>
> turns into the matrix
>
> XXXXX...
> XXXXX...
> XXXXX...
> XXXXX...
> XXXXX...
> ...
>
> in the limit by exchanging X,O-pairs. But no O leaves the matrix. Where do they remain?

wrong, you replace each O with an X as you index them.

>
> Regards, WM
>

On 9/18/2022 2:01 PM, WM wrote:
> Ben Bacarisse schrieb am Freitag, 16. September 2022 um 20:18:58 UTC+2:
>> Sergio <inv...@invalid.com> writes:
>>
>>> I think his course is an elective for business types, not mainstream
>>> math.
>> I imagine anyone can take it as it's a history course in the general
>> studies faculty.
>
> Yes.
>
>> The college
>
> Technische Hochschule Augsburg
>
>> does not have a degree program in
>> mathematics.
>
> So it is.
>>
>> The course is mainly history and as such is mainly unobjectionable.
>> Sadly, to get full marks the students do appear to have to repeat one or
>> more of his mantras,
>
> No student is forced to repeat that. If any student could explain where the O's remain, he would get mentioned for outstanding achievements. But I am sceptical, because not even mathematicians are able to do that.

you are lost in your own fog.

>
> Regards, WM

On 9/18/2022 9:55 AM, Timothy Golden wrote:
> On Saturday, September 17, 2022
> at 6:53:57 PM UTC-4, Jim Burns wrote:
>> On 9/17/2022 5:34 PM, Sergio wrote:
>>> On 9/17/2022 1:57 PM, Jim Burns wrote:

>>>> A process has last and first states,
>>>> and _also_ each split of its states
>>>> has last-before and first-after states.
>>>> A FISON has last and first numbers,
>>>> and each split of its numbers
>>>> has last-before and first-after numbers.
>>>>
>>>> A FISON can represent a process.
>>>
>>> A FISON is a specific set of elements.
>>>
>>> a FISON can be used in a process,
>>> but a FISON is not a process.

>>> Sets do not change.
>>
>> Oh, I agree.
>> Whether WM agrees gets tricky.

>> I offer an alternative to that notion of
>> "variable": the notion of a reference to
>> _one of_ a domain, finite or infinite,
>> and of claims that we know are true without
>> knowing _which_ one of the domain is
>> referred to.
>>
>> We are finite. We can only express and
>> manipulate finitely-many finite sentences.
>> But referring is not expressing and not
>> manipulating. Our finiteness does not
>> keep us from referring to infinitely-many.
>
> In that induction is the process that allows
> these discussions then we can induce
> these large values. For instance:
> 333...34
> is well defined. It's successor is:
> 333...35
> and we can even take the product of these two.
> It is done via induction.

What if we were to consider the infinite
by carefully describing the finite and then
saying "Not that"?

That is the approach I'm taking.

For each natural number n,
an ordered set ⟨0,1,⋯,n-1,n⟩ exists
with two ends 0 and n, first and last,
and,
for each _split_
( for each partition into two pieces,
( all of one before all of the other,
there is a number i last-before the split,
there is a number j first-after the split,
and j = i+1

> In that induction is the process that allows
> these discussions then we can induce
> these large values. For instance:
> 333...34
> is well defined.

It's very unclear to me what '333...34'
is intended to mean.

If there is an ordered set ⟨0,⋯,333...34⟩
in which, for each split,
there is a pair i,i+1 across that split,
then I would say, yes, that's what we mean
by "natural number".
If not, then not.

----
The idea behind my definition is that,
if
⟨0,⋯,333...34⟩ represents the procedure
of counting from 0 to 333...34
and
if that procedure only ever advances
from i to i+1, for some i,
and
if there is a split of ⟨0,⋯,333...34⟩
then
there is some way i,i+1 across that split.

Otherwise,
you can't get there (333...34) from here (0).

----
Induction is a property of each end n
of a set ⟨0,1,⋯,n-1,n⟩ with i,i+1 for splits.

| Assume ⟨0,1,⋯,n-1,n⟩ exists.
| Assume P(0) and ~P(n)
| | There is a split of ⟨0,1,⋯,n-1,n⟩
| such that
| i is last-before the split,
| i+1 is first-after the split,
| and P(i) and ~P(i+1)

Let's abbreviate
"an ordered set ⟨0,1,⋯,n-1,n⟩ exists etc etc"
as
'n ∈ ℕ'

| If n ∈ ℕ exists, P(0) and ~P(n)
| then i ∈ ℕ exists, P(i) and ~P(i+1)

With some easy manipulation, that gives us:

| If
| P(0) and, for all i ∈ ℕ, P(i) -> P(i+1),
| then,
| for all n ∈ ℕ, P(n)

That is the familiar statement of induction.

----
For each ⟨0,1,⋯,n-1,n⟩
n is in ⟨0,1,⋯,n-1,n⟩ but
n+1 is not in ⟨0,1,⋯,n-1,n⟩

Let ℕ be the set of
all ends n of all ⟨0,1,⋯,n-1,n⟩

If
n ∈ ℕ
then
n ends ⟨0,1,⋯,n-1,n⟩

If
n ends ⟨0,1,⋯,n-1,n⟩
then
n+1 ends ⟨0,1,⋯,n-1,n⟩⊕⟨n+1⟩
(⟨0,1,⋯,n-1,n⟩ with ⟨n+1⟩ appended)
and
⟨0,1,⋯,n-1,n⟩⊕⟨n+1⟩ is also an ordered set
with two ends, 0 first,
and,
for each _split_
there is a number i last-before the split,
there is a number i+1 first-after the split.
so
n+1 ∈ ℕ

What if we were to consider the infinite
by carefully describing the finite and then
saying "Not that"?

For each ⟨0,1,⋯,n-1,n⟩
there is some n in ⟨0,1,⋯,n-1,n⟩
for which n+1 is not in ⟨0,1,⋯,n-1,n⟩

Let's say that ⟨0,1,⋯,n-1,n⟩ is _finite_

For ℕ
there is NO n in ℕ
for which n+1 is not in ℕ

ℕ is not like any ⟨0,1,⋯,n-1,n⟩
ℕ is not finite.

On 9/18/2022 2:09 PM, FromTheRafters wrote:
> Sergio wrote :
>> On 9/18/2022 8:55 AM, Timothy Golden wrote:
>>> On Saturday, September 17, 2022 at 6:53:57 PM UTC-4, Jim Burns wrote:
>>>> On 9/17/2022 5:34 PM, Sergio wrote:
>>>>> On 9/17/2022 1:57 PM, Jim Burns wrote:
>>>>
>>>>>> A process has last and first states,
>>>>>> and _also_ each split of its states
>>>>>> has last-before and first-after states.
>>>>>> A FISON has last and first numbers,
>>>>>> and each split of its numbers
>>>>>> has last-before and first-after numbers.
>>>>>>
>>>>>> A FISON can represent a process.
>>>>>
>>>>> A FISON is a specific set of elements.
>>>>>
>>>>> a FISON can be used in a process,
>>>>> but a FISON is not a process.
>>>> I'm not disagreeing with you.
>>>> A FISON is not a process.
>>>>
>>>> but neither is a number a herd of sheep.
>>>> We can use a number to represent a herd of
>>>> sheep, or at least some aspect of a herd of
>>>> sheep.
>>>>
>>>> Also, I know that we use the word "process"
>>>> to describe things which _don't_ have
>>>> last-before and first-after for each split.
>>>>
>>>> In my limited understanding, _float glass_
>>>> is produced by pouring molten onto some
>>>> molten metal with a low melting-point, such
>>>> as tin. I suspect that there are no steps
>>>> such as adding a column of numbers has.
>>>> https://en.wikipedia.org/wiki/Float_glass
>>>>
>>>> I don't have any other examples of float-glass
>>>> style processes in mind right now, but I feel
>>>> confident that there are many.
>>>>
>>>> However,
>>>> a FISON can _represent_ certain processes,
>>>> within my restricted sense of "process".
>>>> I don't see anything to be concerned about.
>>>> It seems to me that most of what mathematics
>>>> is put to use for is _representing_
>>>>
>>>>> Sets do not change.
>>>>
>>>> Oh, I agree.
>>>> Whether WM agrees gets tricky.
>>>>
>>>> WM has certainly said that sets do not change.
>>>>
>>>> What is "change" for WM?
>>>> I'm exaggerating for effect:
>>>> If,
>>>> at one point, we say "It can fly"
>>>> (true, because we refer to a plane)
>>>> and
>>>> at another point, we say "It can't fly"
>>>> (true, because we refer to a boat),
>>>> then
>>>> whatever "it" refers to has _changed_
>>>> from a plane to a boat.
>>>>
>>>> That's my currently-best guess at what
>>>> WM is thinking. The usual caveats apply.
>>>>
>>>> Perhaps? WM sees a variable as needing
>>>> some act of being pointed at a value within
>>>> its domain. I think we all agree that can be
>>>> done (in principle) for a FISON.
>>>> I think WM claims that Cantor claims that
>>>> it can be done for infinite collections.
>>>>
>>>>
>>>> I offer an alternative to that notion of
>>>> "variable": the notion of a reference to
>>>> _one of_ a domain, finite or infinite,
>>>> and of claims that we know are true without
>>>> knowing _which_ one of the domain is
>>>> referred to.
>>>>
>>>> We are finite. We can only express and
>>>> manipulate finitely-many finite sentences.
>>>> But referring is not expressing and not
>>>> manipulating. Our finiteness does not
>>>> keep us from referring to infinitely-many.
>>>
>>> In that induction is the process that allows these discussions then we can induce these large values. For instance:
>>>     333...34
>>> is well defined.
>>
>> Not at all, it takes on an infinite range of values.
>>
>>   Please fix it and post back here for grading.
>
> I've seen notation similar to that, but his is definitely not a prime example.
>
> https://en.wikipedia.org/wiki/Largest_known_prime_number#History_of_largest_known_prime_numbers

when the number is specifically known, like M1279 sure, but his is not well defined.

On 9/18/2022 2:05 PM, WM wrote:
> Jim Burns schrieb am Samstag, 17. September 2022 um 18:36:11 UTC+2:
>> On 9/16/2022 3:31 AM, WM wrote:
>>> zelos...@gmail.com schrieb am Donnerstag,
>>> 15. September 2022 um 11:35:18 UTC+2:
>>>> You are thinking in terms of
>>>> a step by step process. That is WRONG
>>>
>>> Why?
>> There is an end to a process.
>
> It can be completed:
>
> "If two well-defined manifolds, M and N, can be related completely, element by element, to each other [...], then for the following the expression may be permitted that these manifolds have the same cardinality or that they are equivalent."
>
> "Every well-defined set has a definite cardinality; two sets are ascribed the same cardinality if they mutually uniquely, element by element, can be mapped onto each other."
>
> "Two sets are called 'equivalent' if they mutually uniquely, element by element, can be mapped onto each other."

those are called MAPPINGS not step by step.

>
>>> Every definable natnumber can be reached
>>> step by step by its FISON.
>> There is an end to a FISON.
>> There is NO end to all things-in-FISONs.
>
> Every end of a FISON can be reached by steps.

that is silly, each FISON already has the count at its end FISON(4) = {1,2,3,4}

no steps are required.

>> There is NO end to all things-in-FISONs.
>

>
> Regards, WM

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

> Ben Bacarisse schrieb am Freitag, 16. September 2022 um 16:42:09 UTC+2:
>
>> WM likes to talk about processes because they don't end, but properties
>> of functions can be proved using finite arguments. In effect he wants
>> to deny another part of his book -- the final words in a proof by
>> induction. He'd be quite happy with "P(1) and P(x) implies P(x+1)" to
>> be the end of it, but because he needs to sell the book, he concludes
>> (as does every author)
>>
>> "so ist sie für alle natürlichen Zahlen richtig"
>
> Yes, alas only for definable natural numbers.

So another mistake in your book! How did this mistake stay in the book
for so long? You've had many opportunities to revise it.

Just to be clear, are you saying that there is nowhere anyone can lean
WMaths? Any proofs based on the definitions and theorems of your book
are likely to be wrong because the book makes incorrect statements about
"alle natürlichen Zahlen" that should really be about all 'definable'
natural numbers -- with that key notion currently unspecified?

Are you, then, the only person who produce any correct theorems of
WMaths?

--
Ben.

Ben Bacarisse schrieb am Sonntag, 18. September 2022 um 22:04:56 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 Freitag, 16. September 2022 um 16:42:09 UTC+2:
> >
> >> WM likes to talk about processes because they don't end, but properties
> >> of functions can be proved using finite arguments. In effect he wants
> >> to deny another part of his book -- the final words in a proof by
> >> induction. He'd be quite happy with "P(1) and P(x) implies P(x+1)" to
> >> be the end of it, but because he needs to sell the book, he concludes
> >> (as does every author)
> >>
> >> "so ist sie für alle natürlichen Zahlen richtig"
> >
> > Yes, alas only for definable natural numbers.
> So another mistake in your book! How did this mistake stay in the book
> for so long?

Not a mistake. In potential infinity all definable natnumbers all all natnumbers. I told you frequently already: Only if accepting Cantor, dark numbers come into the play. Nobody is forced to accept Cantor.

> You've had many opportunities to revise it.

No, there will be no further printed edition. The seventh edition of my Geschichte des Unendlichen and the fourth edition of Mathematik für die ersten Semester will remain the final editions because any number of copies can be made by PDF.
>
> Any proofs based on the definitions and theorems of your book
> are likely to be wrong because the book makes incorrect statements about
> "alle natürlichen Zahlen" that should really be about all 'definable'
> natural numbers -- with that key notion currently unspecified?

All of that is wrong. And the definition of definable number has been given here: https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf

But you have yet to explain "Where Have All The O's Gone?"

Regards, WM

The abhoring clown WM drivels:

> The matrix
>
> XOOOO...
> XOOOO...
> XOOOO...
> XOOOO...
> XOOOO...
> ...
>
> turns into the matrix
>
> XXXXX...
> XXXXX...
> XXXXX...
> XXXXX...
> XXXXX...
> ...
>
> in the limit by exchanging X,O-pairs.

ROTFL. Idiot...

Crank Wolfgang Mückenheim, aka WM wrote:
> Ben Bacarisse schrieb am Sonntag, 18. September 2022 um 22:04:56 UTC+2:
....
>> You've had many opportunities to revise it.
>
> No, there will be no further printed edition.

That is a very good news.

On 9/18/2022 3:52 PM, WM wrote:
> Ben Bacarisse schrieb am Sonntag, 18. September 2022 um 22:04:56 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 Freitag, 16. September 2022 um 16:42:09 UTC+2:
>>>
>>>> WM likes to talk about processes because they don't end, but properties
>>>> of functions can be proved using finite arguments. In effect he wants
>>>> to deny another part of his book -- the final words in a proof by
>>>> induction. He'd be quite happy with "P(1) and P(x) implies P(x+1)" to
>>>> be the end of it, but because he needs to sell the book, he concludes
>>>> (as does every author)
>>>>
>>>> "so ist sie für alle natürlichen Zahlen richtig"
>>>
>>> Yes, alas only for definable natural numbers.
>> So another mistake in your book! How did this mistake stay in the book
>> for so long?
>
> Not a mistake. In potential infinity all definable natnumbers all all natnumbers. I told you frequently already: Only if accepting Cantor, dark numbers come into the play. Nobody is forced to accept Cantor.

No, no one uses your dark numbers at all. All of your dark numbers remain in your head.

>
>> You've had many opportunities to revise it.
>
> No, there will be no further printed edition.

There are much better, peer reviewed mainstream books out there...

You wrote those books because your students had to buy them for your course.

>>
>> Any proofs based on the definitions and theorems of your book
>> are likely to be wrong because the book makes incorrect statements about
>> "alle natürlichen Zahlen" that should really be about all 'definable'
>> natural numbers -- with that key notion currently unspecified?
>
> All of that is wrong. And the definition of definable number has been given here: https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf

that is simply a bad math troll book based upon posts in sci.math by trolls.

>
> But you have yet to explain "Where Have All The O's Gone?"

As you explained, you replaced the Os when the number is indexed, and put an X on it. did you forget ?

>
> Regards, WM