On 2/8/24 6:32 AM, WM wrote:
> Le 07/02/2024 à 13:29, Richard Damon a écrit :
>> On 2/7/24 2:15 AM, WM wrote:
>>> Le 05/02/2024 à 13:50, Richard Damon a écrit :
>>>> On 2/5/24 4:08 AM, WM wrote:
>>>
>>>>>> Yes, every counted unit fraction is finite, but you can't start
>>>>>> counted from the unbounded end with finite numbers.
>>>>>
>>>>> So they are dark.
>>>>
>>>> So the first from the "end" without and "end" doesn't exsit.
>>>
>>> For every eps > 0 there exist ℵ unit fractions in (0, eps), don't
>>> they? But ℵ of which cannot be distinguished by any means, can they.
>
>> YOU may not be able to distinguish them, because you close your eyes
>> to those definition, but, as I have shown, I can distinguish them.
>
> By what eps have you distinguished all?
>
> Rehards, WM

That's a non-sense question, as eps doesn't "distinguish" points at all.

And there doesn't need to be a finite eps that is below all the unit
fractions, in fact, there CAN'T Be.

So again, you are just showing that you are using logic that is
inconsistant.

Your logic is just based on the incorrect assumption that there exists a
number n, that you can't form an n+1 from (or an number 1/n, that you
can't form 1/(n+1) from)

In other words, a system built on a LIE.

Your "Darkness" is just your lying to yourself and not letting your self
see the light of the truth.

Le 08/02/2024 à 13:35, Richard Damon a écrit :
> On 2/8/24 6:32 AM, WM wrote:
>> Le 07/02/2024 à 13:29, Richard Damon a écrit :
>>> On 2/7/24 2:15 AM, WM wrote:
>>>> Le 05/02/2024 à 13:50, Richard Damon a écrit :
>>>>> On 2/5/24 4:08 AM, WM wrote:
>>>>
>>>>>>> Yes, every counted unit fraction is finite, but you can't start
>>>>>>> counted from the unbounded end with finite numbers.
>>>>>>
>>>>>> So they are dark.
>>>>>
>>>>> So the first from the "end" without and "end" doesn't exsit.
>>>>
>>>> For every eps > 0 there exist ℵ unit fractions in (0, eps), don't
>>>> they? But ℵ of which cannot be distinguished by any means, can they.
>>
>>> YOU may not be able to distinguish them, because you close your eyes
>>> to those definition, but, as I have shown, I can distinguish them.
>>
>> By what eps have you distinguished all?

> That's a non-sense question,

No.

> as eps doesn't "distinguish" points at all.

eps = 4/10 distinguishes 1/2 and 1/3 because 1/3 < 4/10 < 1/2.
>
> And there doesn't need to be a finite eps that is below all the unit
> fractions, in fact, there CAN'T Be.

So it is. But for every distinguishable unit fraction there is a smaller
eps.

Regards, WM

On 2/8/24 7:50 AM, WM wrote:
> Le 08/02/2024 à 13:35, Richard Damon a écrit :
>> On 2/8/24 6:32 AM, WM wrote:
>>> Le 07/02/2024 à 13:29, Richard Damon a écrit :
>>>> On 2/7/24 2:15 AM, WM wrote:
>>>>> Le 05/02/2024 à 13:50, Richard Damon a écrit :
>>>>>> On 2/5/24 4:08 AM, WM wrote:
>>>>>
>>>>>>>> Yes, every counted unit fraction is finite, but you can't start
>>>>>>>> counted from the unbounded end with finite numbers.
>>>>>>>
>>>>>>> So they are dark.
>>>>>>
>>>>>> So the first from the "end" without and "end" doesn't exsit.
>>>>>
>>>>> For every eps > 0 there exist ℵ unit fractions in (0, eps), don't
>>>>> they? But ℵ of which cannot be distinguished by any means, can they.
>>>
>>>> YOU may not be able to distinguish them, because you close your eyes
>>>> to those definition, but, as I have shown, I can distinguish them.
>>>
>>> By what eps have you distinguished all?
>
>> That's a non-sense question,
>
> No.

Then what does it actually MEAN, and why do you think such a thing needs
to exist.

>
>> as eps doesn't "distinguish" points at all.
>
> eps = 4/10 distinguishes 1/2 and 1/3 because 1/3 < 4/10 < 1/2.

And why is that useful or important.

And what eps disitinguesh even 3 points, to get you toward you "ALL".

I think you have a screw loose.

>>
>> And there doesn't need to be a finite eps that is below all the unit
>> fractions, in fact, there CAN'T Be.
>
> So it is. But for every distinguishable unit fraction there is a smaller
> eps.

So?

That just means that for every unit fraction, there is a smaller unit
fraction, so there is no lowest unit fractioin.

>
> Regards, WM

You keep on hitting these things that tell you your idea that there must
be a smallest unit fraction can't be true, and you keep on shutting your
eyes and saying there is darkness there.

Your "Darkness" is just your lies catching up with you. The things are
clearly visible to people who are willing to look.

You are just falling off the cliff because you are shutting your eyes.

Le 08/02/2024 à 13:59, Richard Damon a écrit :
> On 2/8/24 7:50 AM, WM wrote:

>>>>> YOU may not be able to distinguish them, because you close your eyes
>>>>> to those definition, but, as I have shown, I can distinguish them.
>>>>
>>>> By what eps have you distinguished all?
>>
>>> That's a non-sense question,
>>
>> No.
>
> Then what does it actually MEAN, and why do you think such a thing needs
> to exist.

Read Borel's nice little book: Les nombres inaccessible:
"This little book is the result of half a century of reflections on the
principles of mathematical analysis and, in particular, on the definition
of numbers. Some of these reflections have already been sketched
here and there in the works of this Collection, but it seemed to me
that it would be useful to coordinate them in a connected account."

Borel's thesis is that the overwhelming majority of numbers will
always remain inaccessible to the human race as we know it, in the
sense that it will never be possible to define these numbers effectively
in such a manner that any two mathematicians will be certain that
they are speaking about one and the same entity. (F. Bagemihl)

>>> as eps doesn't "distinguish" points at all.
>>
>> eps = 4/10 distinguishes 1/2 and 1/3 because 1/3 < 4/10 < 1/2.
>
> And why is that useful or important.

First in order to show that you are wrong.

Second because every visible unit fractions, a smaller eps can be defined,
but not for dark unit fractions.
>
>> for every distinguishable unit fraction there is a smaller
>> eps.
>
> That just means that for every unit fraction, there is a smaller unit
> fraction, so there is no lowest unit fractioin.

But almost all of them cannot be defined in such a manner that any two
mathematicians will be certain that
they are speaking about one and the same entity.

Regards, WM

On 2/8/24 9:37 AM, WM wrote:
> Le 08/02/2024 à 13:59, Richard Damon a écrit :
>> On 2/8/24 7:50 AM, WM wrote:
>
>>>>>> YOU may not be able to distinguish them, because you close your
>>>>>> eyes to those definition, but, as I have shown, I can distinguish
>>>>>> them.
>>>>>
>>>>> By what eps have you distinguished all?
>>>
>>>> That's a non-sense question,
>>>
>>> No.
>>
>> Then what does it actually MEAN, and why do you think such a thing
>> needs to exist.
>
> Read Borel's nice little book: Les nombres inaccessible:
> "This little book is the result of half a century of reflections on the
> principles of mathematical analysis and, in particular, on the definition
> of numbers. Some of these reflections have already been sketched
> here and there in the works of this Collection, but it seemed to me
> that it would be useful to coordinate them in a connected account."
>
> Borel's thesis is that the overwhelming majority of numbers will
> always remain inaccessible to the human race as we know it, in the
> sense that it will never be possible to define these numbers effectively
> in such a manner that any two mathematicians will be certain that
> they are speaking about one and the same entity. (F. Bagemihl)

But that is a limit of PEOPLE, not the numbers.

All the numbers are "Definable" even if no person will ever write its name.

>
>
>>>> as eps doesn't "distinguish" points at all.
>>>
>>> eps = 4/10 distinguishes 1/2 and 1/3 because 1/3 < 4/10 < 1/2.
>>
>> And why is that useful or important.
>
> First in order to show that you are wrong.

How am I wrong?

You said an eps that distinguisjhed ALL the points, but no eps
distinguishes more than 2 by this definition, so I guess you can't count
to 3.

>
> Second because every visible unit fractions, a smaller eps can be
> defined, but not for dark unit fractions.

But there aren't any dark unit fractions, only ones that you you close
your eyes to.

Your "dark" unit fractions just can'

>>
>>> for every distinguishable unit fraction there is a smaller eps.
>>
>> That just means that for every unit fraction, there is a smaller unit
>> fraction, so there is no lowest unit fractioin.
>
> But almost all of them cannot be defined in such a manner that any two
> mathematicians will be certain that
> they are speaking about one and the same entity.

Sure they can.

ANY natural number can be expressed in a number of different ways that
EXACTLY specify it, and thus its multiplicative inverse, the unit
fraction is exactly specifiable.

>
> Regards, WM

Le 09/02/2024 à 04:40, Richard Damon a écrit :
> On 2/8/24 9:37 AM, WM wrote:

>> Borel's thesis is that the overwhelming majority of numbers will
>> always remain inaccessible to the human race as we know it, in the
>> sense that it will never be possible to define these numbers effectively
>> in such a manner that any two mathematicians will be certain that
>> they are speaking about one and the same entity. (F. Bagemihl)
>
> But that is a limit of PEOPLE, not the numbers.

Not only. The ℵ smallest *existing* unit fractions will remain undefined
forever.
>
> All the numbers are "Definable" even if no person will ever write its name.

All means without exception. That is impossible, because whatever will be
defined, it fails to define almost all unit fractions.

Regards, WM

Fritz Feldhase schrieb am Freitag, 9. Februar 2024 um 10:17:40 UTC+1:

> Using these names "any two mathematicians may be certain that they are speaking
> about one and the same entity."

Name a unit fraction that has less than ℵ smaller ones. Fail. Therefore
ℵ unit fractions cannot be named.

Regards, WM

On 02/09/2024 05:52 AM, Fritz Feldhase wrote:
> On Friday, February 9, 2024 at 10:17:40 AM UTC+1, Fritz Feldhase wrote:
>> On Thursday, February 8, 2024 at 3:37:17 PM UTC+1, WM wrote:
>>> Le 08/02/2024 à 13:59, Richard Damon a écrit :
>>>>
>>>> That just means that for every unit fraction, there is a smaller unit
>>>> fraction, so there is no lowest unit fractioin.
>>>>
>>> But almost all of them cannot be [labled] in such a manner that any two
>>> mathematicians will be certain that they are speaking about one and the
>>> same entity.
>>>
>> Unsinn. Ich habe Dir das schon einige Male erklärt, Mückenheim:
>>
>> Als Namen wählen wir Zeichen der Form "I/I...I". Die Namen beginnen also mit der Zeichenfolge "I/" gefolgt von einer beliebigen Anzahl von "I" (Strichen) (aber mindestens einem).
>>
>> Den Stammbrüchen, die als Folge so gegeben sein sollen:
>>
>> 1/1, 1/2, 1/3, ...
>>
>> ordenen wir nun IN GESETZMÄßIGER WEISE die Namen
>>
>> "I/I", "I/II", "I/III", usw.
>>
>> zu. Das ZUORDNUNGSGESETZ ist dabei ziemlich einfach. Viell. kommst Du ja selbst drauf. (Die Folgen oben dienen nur der VERANSCHAULICHUNG.)
>>
>> Jeder Stammbruch "hat" dann also einen Namen.
>>
>> Hier eine kleine Hilfestellung dazu: Sei WM ein BELIEBIGER Stammbruch. Dann gibt es (genau eine) natürliche Zahl n, so dass WM = 1/n gilt. Sei n0 diese natürliche Zahl. Es gilt dann also WM = 1/n0. Der Name für WM ist dann "I/" gefolgt von n0 Strichen. WM "hat" also einen Namen. Da WM ein beliebiger Stammbruch war, gibt es also keinen Stammbruch ohne einen Namen.
>>
>> Using these names "any two mathematicians may be certain that they are speaking about one and the same entity."
>>
>> Example. I'm thinking of a unit fraction, its name is "I/III". Now if you tell me that you are thinking of a unit fraction the name of which is "I/III" too, we can be quite certain that we are thinking of THE VERY SAME unit fraction ("entity").
>>
>> Btw. For each and every unit fraction there's a smaller one. If the name of an unit fraction is X then the unit fraction with the name XI is a smaller one.
>
> Assume that a mathematician tells me that he's thinking of a certain unit fraction and that the name of this unit fraction is X. Then all I have to do is to count the strokes (|) occurring after "|/" in X. Say the number of these strokes is n. Then I know that this mathematician is thinking of the unit fraction 1/n.
>

Mann hat Fragen, ich werde fragen fur die Worten fur "continuum limit",
you know, comment dit le mot, wie heisst du, "limit of functions".

"Range of Unit Fractions"

f(n) = n/d, n -> d, d-> oo

f(0) = 0, f(oo) = 1
constant monotone strictly increasing

extent [0,1]
density [0,1]
completeness [0,1]
measure [0,1]

Zu, es gibt Zwei Konnens, eins, das Field ("field-reals", R^dots), zwei,
das semi-ring ("line-reals", R^bar).

Es gibt ein Dreier alzo, "signal-reals" wie R^tilde.

R^bar line-reals, "iota-values", "sweep", equivalency function, Aristotle

R^dots field-reals, "R", complete ordered field, Eudoxus/Cauchy/Dedekind

R^tilde signal-reals, "analog", Nyquist/Shannon

Es gibt drei "models" dieser "continuous domains".

Das f(n), es ist nich Cartesian, Funktion.

Mea culpa immer est fur die Worten schlecht aber ich hoffe
du finde oder sie finden dieser worklich "continuous domains",
drei-viel.

MfG

On 02/09/2024 10:34 AM, Ross Finlayson wrote:
> On 02/09/2024 05:52 AM, Fritz Feldhase wrote:
>> On Friday, February 9, 2024 at 10:17:40 AM UTC+1, Fritz Feldhase wrote:
>>> On Thursday, February 8, 2024 at 3:37:17 PM UTC+1, WM wrote:
>>>> Le 08/02/2024 à 13:59, Richard Damon a écrit :
>>>>>
>>>>> That just means that for every unit fraction, there is a smaller unit
>>>>> fraction, so there is no lowest unit fractioin.
>>>>>
>>>> But almost all of them cannot be [labled] in such a manner that any two
>>>> mathematicians will be certain that they are speaking about one and the
>>>> same entity.
>>>>
>>> Unsinn. Ich habe Dir das schon einige Male erklärt, Mückenheim:
>>>
>>> Als Namen wählen wir Zeichen der Form "I/I...I". Die Namen beginnen
>>> also mit der Zeichenfolge "I/" gefolgt von einer beliebigen Anzahl
>>> von "I" (Strichen) (aber mindestens einem).
>>>
>>> Den Stammbrüchen, die als Folge so gegeben sein sollen:
>>>
>>> 1/1, 1/2, 1/3, ...
>>>
>>> ordenen wir nun IN GESETZMÄßIGER WEISE die Namen
>>>
>>> "I/I", "I/II", "I/III", usw.
>>>
>>> zu. Das ZUORDNUNGSGESETZ ist dabei ziemlich einfach. Viell. kommst Du
>>> ja selbst drauf. (Die Folgen oben dienen nur der VERANSCHAULICHUNG.)
>>>
>>> Jeder Stammbruch "hat" dann also einen Namen.
>>>
>>> Hier eine kleine Hilfestellung dazu: Sei WM ein BELIEBIGER
>>> Stammbruch. Dann gibt es (genau eine) natürliche Zahl n, so dass WM =
>>> 1/n gilt. Sei n0 diese natürliche Zahl. Es gilt dann also WM = 1/n0.
>>> Der Name für WM ist dann "I/" gefolgt von n0 Strichen. WM "hat" also
>>> einen Namen. Da WM ein beliebiger Stammbruch war, gibt es also keinen
>>> Stammbruch ohne einen Namen.
>>>
>>> Using these names "any two mathematicians may be certain that they
>>> are speaking about one and the same entity."
>>>
>>> Example. I'm thinking of a unit fraction, its name is "I/III". Now if
>>> you tell me that you are thinking of a unit fraction the name of
>>> which is "I/III" too, we can be quite certain that we are thinking of
>>> THE VERY SAME unit fraction ("entity").
>>>
>>> Btw. For each and every unit fraction there's a smaller one. If the
>>> name of an unit fraction is X then the unit fraction with the name XI
>>> is a smaller one.
>>
>> Assume that a mathematician tells me that he's thinking of a certain
>> unit fraction and that the name of this unit fraction is X. Then all I
>> have to do is to count the strokes (|) occurring after "|/" in X. Say
>> the number of these strokes is n. Then I know that this mathematician
>> is thinking of the unit fraction 1/n.
>>
>
> Mann hat Fragen, ich werde fragen fur die Worten fur "continuum limit",
> you know, comment dit le mot, wie heisst du, "limit of functions".
>
>
> "Range of Unit Fractions"
>
> f(n) = n/d, n -> d, d-> oo
>
> f(0) = 0, f(oo) = 1
> constant monotone strictly increasing
>
> extent [0,1]
> density [0,1]
> completeness [0,1]
> measure [0,1]
>
> Zu, es gibt Zwei Konnens, eins, das Field ("field-reals", R^dots), zwei,
> das semi-ring ("line-reals", R^bar).
>
> Es gibt ein Dreier alzo, "signal-reals" wie R^tilde.
>
>
> R^bar line-reals, "iota-values", "sweep", equivalency function, Aristotle
>
> R^dots field-reals, "R", complete ordered field, Eudoxus/Cauchy/Dedekind
>
> R^tilde signal-reals, "analog", Nyquist/Shannon
>
>
>
> Es gibt drei "models" dieser "continuous domains".
>
> Das f(n), es ist nich Cartesian, Funktion.
>
> Mea culpa immer est fur die Worten schlecht aber ich hoffe
> du finde oder sie finden dieser worklich "continuous domains",
> drei-viel.
>
> MfG
>
>
>
>
>

Fur die Worten mathematische, was ich hoffe gefinder es ist aber
fur dieser Worten fur die Namen for dieser Dingen.

"line-reals" "Zeilereellerzahlen"
"field-reals" "Feldreelleerzahlen"
"signal-reals" "Signalreellerzaheln"

Ich weiss nich t wieviel oder Worten wirdent machen
the "same" (meme) letters, dieser Worten "equi-interpreted".

Italian: puntos, tire un riga, points, draw a line
English: points, draw a line,
French: pointes, faisse un regle
German: Punkten, triedl das zeile

Mann hoffe das es gibt ein Wortbuch, mit dieser Worten,
oder, besser Worten, fur "formal" Worten.

Das Continuum hat drei, vier, funf, "models".

integer continuum

line reals

field reals

signal reals

long-line reals

Es gibt "Descriptiv" models fur das Mengenlhre,
und, _und_, das Fonktiontheorie, Funktionlehre.
Es gibt DesCartes und es gibt nicht DesCartes,
es gibt Cantor und es gibt nicht Cantor,
es gibt Dedekind und es gibt nicht Dedekind.

Es gibt Poincare und Dirichlet, ..., Camille Jordan, ....

MfG

On 02/09/2024 10:34 AM, Ross Finlayson wrote:
> On 02/09/2024 05:52 AM, Fritz Feldhase wrote:
>> On Friday, February 9, 2024 at 10:17:40 AM UTC+1, Fritz Feldhase wrote:
>>> On Thursday, February 8, 2024 at 3:37:17 PM UTC+1, WM wrote:
>>>> Le 08/02/2024 à 13:59, Richard Damon a écrit :
>>>>>
>>>>> That just means that for every unit fraction, there is a smaller unit
>>>>> fraction, so there is no lowest unit fractioin.
>>>>>
>>>> But almost all of them cannot be [labled] in such a manner that any two
>>>> mathematicians will be certain that they are speaking about one and the
>>>> same entity.
>>>>
>>> Unsinn. Ich habe Dir das schon einige Male erklärt, Mückenheim:
>>>
>>> Als Namen wählen wir Zeichen der Form "I/I...I". Die Namen beginnen
>>> also mit der Zeichenfolge "I/" gefolgt von einer beliebigen Anzahl
>>> von "I" (Strichen) (aber mindestens einem).
>>>
>>> Den Stammbrüchen, die als Folge so gegeben sein sollen:
>>>
>>> 1/1, 1/2, 1/3, ...
>>>
>>> ordenen wir nun IN GESETZMÄßIGER WEISE die Namen
>>>
>>> "I/I", "I/II", "I/III", usw.
>>>
>>> zu. Das ZUORDNUNGSGESETZ ist dabei ziemlich einfach. Viell. kommst Du
>>> ja selbst drauf. (Die Folgen oben dienen nur der VERANSCHAULICHUNG.)
>>>
>>> Jeder Stammbruch "hat" dann also einen Namen.
>>>
>>> Hier eine kleine Hilfestellung dazu: Sei WM ein BELIEBIGER
>>> Stammbruch. Dann gibt es (genau eine) natürliche Zahl n, so dass WM =
>>> 1/n gilt. Sei n0 diese natürliche Zahl. Es gilt dann also WM = 1/n0.
>>> Der Name für WM ist dann "I/" gefolgt von n0 Strichen. WM "hat" also
>>> einen Namen. Da WM ein beliebiger Stammbruch war, gibt es also keinen
>>> Stammbruch ohne einen Namen.
>>>
>>> Using these names "any two mathematicians may be certain that they
>>> are speaking about one and the same entity."
>>>
>>> Example. I'm thinking of a unit fraction, its name is "I/III". Now if
>>> you tell me that you are thinking of a unit fraction the name of
>>> which is "I/III" too, we can be quite certain that we are thinking of
>>> THE VERY SAME unit fraction ("entity").
>>>
>>> Btw. For each and every unit fraction there's a smaller one. If the
>>> name of an unit fraction is X then the unit fraction with the name XI
>>> is a smaller one.
>>
>> Assume that a mathematician tells me that he's thinking of a certain
>> unit fraction and that the name of this unit fraction is X. Then all I
>> have to do is to count the strokes (|) occurring after "|/" in X. Say
>> the number of these strokes is n. Then I know that this mathematician
>> is thinking of the unit fraction 1/n.
>>
>
> Mann hat Fragen, ich werde fragen fur die Worten fur "continuum limit",
> you know, comment dit le mot, wie heisst du, "limit of functions".
>
>
> "Range of Unit Fractions"
>
> f(n) = n/d, n -> d, d-> oo
>
> f(0) = 0, f(oo) = 1
> constant monotone strictly increasing
>
> extent [0,1]
> density [0,1]
> completeness [0,1]
> measure [0,1]
>
> Zu, es gibt Zwei Konnens, eins, das Field ("field-reals", R^dots), zwei,
> das semi-ring ("line-reals", R^bar).
>
> Es gibt ein Dreier alzo, "signal-reals" wie R^tilde.
>
>
> R^bar line-reals, "iota-values", "sweep", equivalency function, Aristotle
>
> R^dots field-reals, "R", complete ordered field, Eudoxus/Cauchy/Dedekind
>
> R^tilde signal-reals, "analog", Nyquist/Shannon
>
>
>
> Es gibt drei "models" dieser "continuous domains".
>
> Das f(n), es ist nich Cartesian, Funktion.
>
> Mea culpa immer est fur die Worten schlecht aber ich hoffe
> du finde oder sie finden dieser worklich "continuous domains",
> drei-viel.
>
> MfG
>
>
>
>
>

How does one say,
comment dit-on ces mots,
wie sagt Mann dieser Worten, ....

yet yet yet yet, ....
that that that that, ....

Plus ca change, plus le meme chose.

Yo quiero los parlamos, ....

The, equi-interpretability,
c'est pour les langues naturelles,
aussi pour les langues formalles,
si on ne dit pas incorrectement,
the equi-interpretability,
dans le mathematiques,
c'est pour l'infini,
parce que les points ne jamais faire le ligne,
et le ligne, no jamais faire le point.

Mais, ils soient, ....

Hein?

How does one say,
"please excuse my lack of understanding,
in the exercise of equi-interpretability,
I have full command of the English language,
and its terms in mathematics,
so: 'se, no se'."

Yo se.

Dieser Ansaetzen, "thought-experiments", "setups",
fur dieser Ansschauung, "theory", bitte immer sagen Sie mir,
op es heisse nicht.

So, thanks for reading, what I am describing is that
these three relevant models of continuous domains:

line-reals
field-reals
signal-reals

are each having their own _completions_, only all together.

In the universal language called mathematics,
ou c'est comme un "langue Comenius",
Dieser sind die Worten zum Anglisch,
ich werde machen das "Matrix", das Ansaetze, c'est simple.

Si il y avait une chose particularement,
op es gibt ein tal, es gibt immer "Das", "Es",
c'est neutral, mais bien sur les personnes peut
avoir leurs gendres. C'est simple.

Alors, merci ou danke oder danke bissche,
these concepts of "standard non-standard infinitesimal analysis",
ils seraient pour le pluspart avec leurs nommes, Namen,
qu'ils deja avaient.

C'est simple, and it's standard.

C'est le canon, c'est magnifique. C'est moderne.

line-reals R^bar
field-reals R^dots, R
signal-reals R^tilde

Ces sonts continus, es gibt "Das Continuum".

Regards

On 2/9/24 4:53 AM, WM wrote:
> Le 09/02/2024 à 04:40, Richard Damon a écrit :
>> On 2/8/24 9:37 AM, WM wrote:
>
>>> Borel's thesis is that the overwhelming majority of numbers will
>>> always remain inaccessible to the human race as we know it, in the
>>> sense that it will never be possible to define these numbers effectively
>>> in such a manner that any two mathematicians will be certain that
>>> they are speaking about one and the same entity. (F. Bagemihl)
>>
>> But that is a limit of PEOPLE, not the numbers.
>
> Not only. The ℵ smallest *existing* unit fractions will remain undefined
> forever.

Ah, so you think that the existance and definition of numbers is
dependent on us?

All the Numbers exists, and are fully defined, because they are,

You claim to be using "Natural Mathematics", so you have to accept that
the numbers exists without us, as your concept of Mathematics is based
on what we can discover from that which pre-existed us.

You get caught you your own errors, which you refuse to look at, which
is what makes things "dark" to you.

>>
>> All the numbers are "Definable" even if no person will ever write its
>> name.
>
> All means without exception. That is impossible, because whatever will
> be defined, it fails to define almost all unit fractions.

So, you just don't understand the definition.

This is because you logic system can't handle unbounded sets.

The "Darkness" is in YOU, not the numbers. They are nice a bright and
vibible to those willing to look.

>
> Regards, WM
>

Le 10/02/2024 à 00:36, Richard Damon a écrit :
> On 2/9/24 4:53 AM, WM wrote:
>> Le 09/02/2024 à 04:40, Richard Damon a écrit :
>>> On 2/8/24 9:37 AM, WM wrote:
>>
>>>> Borel's thesis is that the overwhelming majority of numbers will
>>>> always remain inaccessible to the human race as we know it, in the
>>>> sense that it will never be possible to define these numbers effectively
>>>> in such a manner that any two mathematicians will be certain that
>>>> they are speaking about one and the same entity. (F. Bagemihl)
>>>
>>> But that is a limit of PEOPLE, not the numbers.
>>
>> Not only. The ℵ smallest *existing* unit fractions will remain undefined
>> forever.
>
> Ah, so you think that the existance and definition of numbers is
> dependent on us?

No, the infinite cannot be traversed. Therefore almost all remains dark.

Regards, WM

> On 02/09/2024 05:52 AM, Fritz Feldhase wrote:

>>
>> Assume that a mathematician tells me that he's thinking of a certain unit
>> fraction and that the name of this unit fraction is X. Then all I have to do is to
>> count the strokes (|) occurring after "|/" in X. Say the number of these strokes is
>> n. Then I know that this mathematician is thinking of the unit fraction 1/n.

Dark numbers cannot be thought of. Assume the smallest ℵ unit fractions,
I mean such which really exist as fixed points at the real line and can be
manipulated, are divided into two rather equal parts. You cannot remotely
determine a number near the border of the two shares.

Regards, WM

Fritz Feldhase schrieb am Freitag, 9. Februar 2024 um 14:31:34 UTC+1:
> On Friday, February 9, 2024 at 11:10:53 AM UTC+1, WM wrote:
> > Fritz Feldhase schrieb am Freitag, 9. Februar 2024 um 10:17:40 UTC+1:
> >
> > Name a unit fraction that has less than infinitely many smaller ones.
>
> I cannot "name" something which does not exist.

If there are all unit fractions, then the subset of those which have
infinitely many smaller ones is not the whole set because the smaller ones
belong to the set of all.

If infinitely many unit fractions are out of your reach, then you can
reach only elements of a small finite subset.

Regards, WM

Fritz Feldhase schrieb am Freitag, 9. Februar 2024 um 14:41:08 UTC+1:
> On Friday, February 9, 2024 at 10:53:40 AM UTC+1, WM wrote:
> >
> > The ℵ smallest [...] unit fractions will remain undefined forever.
>
> Since the notion "the ℵ smallest [...] unit fractions" is not "well-defined"
> (i.e. not defined at all), no big problem.

It is well enough defined. The subset contains ℵ unit fractions never
definable.
>
> Hint: Does 1/1 belong to "the ℵ smallest [...] unit fractions"? 1/2? 1/3?
> Which is the largest unit fraction which belongs to "the ℵ smallest [...] unit
> fractions"?

The smallest are smaller than every defined unit fractions and even
smaller than every unit fraction which ever will be defined.

> > > All the numbers are "Definable" even if no person will ever write its name.
> > >
> > All means without exception.
> Oh really?! How would you know?
It is the definition of "all". All with smaller unit fractions are not
all. "All" means all which matheology claims to be countable.

Regards, WM

On 2/10/24 1:09 PM, WM wrote:
> Le 10/02/2024 à 00:36, Richard Damon a écrit :
>> On 2/9/24 4:53 AM, WM wrote:
>>> Le 09/02/2024 à 04:40, Richard Damon a écrit :
>>>> On 2/8/24 9:37 AM, WM wrote:
>>>
>>>>> Borel's thesis is that the overwhelming majority of numbers will
>>>>> always remain inaccessible to the human race as we know it, in the
>>>>> sense that it will never be possible to define these numbers
>>>>> effectively
>>>>> in such a manner that any two mathematicians will be certain that
>>>>> they are speaking about one and the same entity. (F. Bagemihl)
>>>>
>>>> But that is a limit of PEOPLE, not the numbers.
>>>
>>> Not only. The ℵ smallest *existing* unit fractions will remain
>>> undefined forever.
>>
>> Ah, so you think that the existance and definition of numbers is
>> dependent on us?
>
> No, the infinite cannot be traversed. Therefore almost all remains dark.
>
> Regards, WM
>
>
>

So, you start by assuming there can not be an infinite that we can
understand, and them defining that something is infinite.

Your logic is just broken.

Why do you say that the infinite cannot be "traversed", is you mind just
to weak to understand the infinite? If so, I feel sorry for you.

You should just leave well enough alone rather that frustrate yourself
trying to understand that which you have defined that you can not
understand.

Your "Darkness" is just your own protective reaction to keep you from
looking at things you don't want to know, because they will break your
preconceived lies to yoursel.

On 2/10/24 1:55 PM, WM wrote:
> Fritz Feldhase schrieb am Freitag, 9. Februar 2024 um 14:31:34 UTC+1:
>> On Friday, February 9, 2024 at 11:10:53 AM UTC+1, WM wrote: > Fritz
>> Feldhase schrieb am Freitag, 9. Februar 2024 um 10:17:40 UTC+1: >
>> > Name a unit fraction that has less than infinitely many smaller ones.
>> I cannot "name" something which does not exist.
>
> If there are all unit fractions, then the subset of those which have
> infinitely many smaller ones is not the whole set because the smaller
> ones belong to the set of all.
>
> If infinitely many unit fractions are out of your reach, then you can
> reach only elements of a small finite subset.
>
> Regards, WM

Which just means that you do not understand how to do math on "infinite"
quantities, but are trying to use the inapplicable finite math on them.

That is your problem, you don't understand that the rules for
"infinities" are different then the rules for "finites".

Le 10/02/2024 à 21:34, Richard Damon a écrit :
> On 2/10/24 1:09 PM, WM wrote:

>> the infinite cannot be traversed. Therefore almost all remains dark.
>>
> So, you start by assuming there can not be an infinite that we can
> understand, and them defining that something is infinite.

No, you cannot understand what I said. The infinite can be understood (by
intelligent persons), but cannot be traversed step by step. Step by step
you will always have ℵ steps in front of you:
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵ
Only collectively, summing up all the dark steps you can get through:
|ℕ \ {1, 2, 3, ...}| = 0

> Why do you say that the infinite cannot be "traversed",

Because it is true.

Regards, WM

WM expressed precisely :

> No, you cannot understand what I said.

Because you have yet to adequately explain using proper mathematics.

On 2/11/24 4:44 AM, WM wrote:
> Le 10/02/2024 à 21:34, Richard Damon a écrit :
>> On 2/10/24 1:09 PM, WM wrote:
>
>>> the infinite cannot be traversed. Therefore almost all remains dark.
>>>
>> So, you start by assuming there can not be an infinite that we can
>> understand, and them defining that something is infinite.
>
> No, you cannot understand what I said. The infinite can be understood
> (by intelligent persons), but cannot be traversed step by step. Step by
> step you will always have ℵ steps in front of you:
> ∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵ
> Only collectively, summing up all the dark steps you can get through:
> |ℕ \ {1, 2, 3, ...}| = 0
>
>> Why do you say that the infinite cannot be "traversed",
>
> Because it is true.
>
> Regards, WM

And why do you need to travese it "step by step"?

That restriction is the restriction of finiteness, and doesn't allow for
the infinite.

So, your "Darkness", is just the misapplication of definitions that do
not apply to that set.

On 02/11/2024 02:55 AM, FromTheRafters wrote:
> WM expressed precisely :
>
>
>> No, you cannot understand what I said.
>
> Because you have yet to adequately explain using proper mathematics.

Leafing through Borges' "Everything and Nothing",
he describes Pierre Menard as having written
an "Les problemes d'un probleme", in Paris 1917,
"which discusses, in chronological order, the
different solutions to the illustrious problem
of Achilles and the tortoise. Two editions of
this book have appeared so far; the second
bears as an epigraph Leibniz' recommendation
'Ne craignez point, monsieur, la tortue' and
revises the chapters dedicated to Russell and
Descartes."

The infinite limit, is of course well-known and
understood by many. This is the infinite limit
of partial sums of a series what results an infinite
series and the reckoning that it results that
the limit is the sum, and vice-versa, or that
the limit exists even if the sum does not.

It's about as clear to have a limit of functions,
here it's as so simple as "n/d, n->d, d->\infty".

(Notice that \infty is just the usual TeX language
what is the usual type-setting language for
usual document packages like "AMS article".)

So, if WM/MW simply wrote that, then suddenly
he would have exchanged puking out a failure
on his way into the chasm of the inductive impasse,
echoing all the way down, into instead a dialectic
making for a bridge between not-wrong and correct.

Once you figure out how to get back-and-forth,
this bridge, this pons, this pont, is no longer
the pons asinorum, the bridge fools never cross,
but a pont regulus, yielding right both ways.

Mind the gap.

On 02/09/2024 11:32 AM, Ross Finlayson wrote:
> On 02/09/2024 10:34 AM, Ross Finlayson wrote:
>> On 02/09/2024 05:52 AM, Fritz Feldhase wrote:
>>> On Friday, February 9, 2024 at 10:17:40 AM UTC+1, Fritz Feldhase wrote:
>>>> On Thursday, February 8, 2024 at 3:37:17 PM UTC+1, WM wrote:
>>>>> Le 08/02/2024 à 13:59, Richard Damon a écrit :
>>>>>>
>>>>>> That just means that for every unit fraction, there is a smaller unit
>>>>>> fraction, so there is no lowest unit fractioin.
>>>>>>
>>>>> But almost all of them cannot be [labled] in such a manner that any
>>>>> two
>>>>> mathematicians will be certain that they are speaking about one and
>>>>> the
>>>>> same entity.
>>>>>
>>>> Unsinn. Ich habe Dir das schon einige Male erklärt, Mückenheim:
>>>>
>>>> Als Namen wählen wir Zeichen der Form "I/I...I". Die Namen beginnen
>>>> also mit der Zeichenfolge "I/" gefolgt von einer beliebigen Anzahl
>>>> von "I" (Strichen) (aber mindestens einem).
>>>>
>>>> Den Stammbrüchen, die als Folge so gegeben sein sollen:
>>>>
>>>> 1/1, 1/2, 1/3, ...
>>>>
>>>> ordenen wir nun IN GESETZMÄßIGER WEISE die Namen
>>>>
>>>> "I/I", "I/II", "I/III", usw.
>>>>
>>>> zu. Das ZUORDNUNGSGESETZ ist dabei ziemlich einfach. Viell. kommst Du
>>>> ja selbst drauf. (Die Folgen oben dienen nur der VERANSCHAULICHUNG.)
>>>>
>>>> Jeder Stammbruch "hat" dann also einen Namen.
>>>>
>>>> Hier eine kleine Hilfestellung dazu: Sei WM ein BELIEBIGER
>>>> Stammbruch. Dann gibt es (genau eine) natürliche Zahl n, so dass WM =
>>>> 1/n gilt. Sei n0 diese natürliche Zahl. Es gilt dann also WM = 1/n0.
>>>> Der Name für WM ist dann "I/" gefolgt von n0 Strichen. WM "hat" also
>>>> einen Namen. Da WM ein beliebiger Stammbruch war, gibt es also keinen
>>>> Stammbruch ohne einen Namen.
>>>>
>>>> Using these names "any two mathematicians may be certain that they
>>>> are speaking about one and the same entity."
>>>>
>>>> Example. I'm thinking of a unit fraction, its name is "I/III". Now if
>>>> you tell me that you are thinking of a unit fraction the name of
>>>> which is "I/III" too, we can be quite certain that we are thinking of
>>>> THE VERY SAME unit fraction ("entity").
>>>>
>>>> Btw. For each and every unit fraction there's a smaller one. If the
>>>> name of an unit fraction is X then the unit fraction with the name XI
>>>> is a smaller one.
>>>
>>> Assume that a mathematician tells me that he's thinking of a certain
>>> unit fraction and that the name of this unit fraction is X. Then all I
>>> have to do is to count the strokes (|) occurring after "|/" in X. Say
>>> the number of these strokes is n. Then I know that this mathematician
>>> is thinking of the unit fraction 1/n.
>>>
>>
>> Mann hat Fragen, ich werde fragen fur die Worten fur "continuum limit",
>> you know, comment dit le mot, wie heisst du, "limit of functions".
>>
>>
>> "Range of Unit Fractions"
>>
>> f(n) = n/d, n -> d, d-> oo
>>
>> f(0) = 0, f(oo) = 1
>> constant monotone strictly increasing
>>
>> extent [0,1]
>> density [0,1]
>> completeness [0,1]
>> measure [0,1]
>>
>> Zu, es gibt Zwei Konnens, eins, das Field ("field-reals", R^dots), zwei,
>> das semi-ring ("line-reals", R^bar).
>>
>> Es gibt ein Dreier alzo, "signal-reals" wie R^tilde.
>>
>>
>> R^bar line-reals, "iota-values", "sweep", equivalency function, Aristotle
>>
>> R^dots field-reals, "R", complete ordered field, Eudoxus/Cauchy/Dedekind
>>
>> R^tilde signal-reals, "analog", Nyquist/Shannon
>>
>>
>>
>> Es gibt drei "models" dieser "continuous domains".
>>
>> Das f(n), es ist nich Cartesian, Funktion.
>>
>> Mea culpa immer est fur die Worten schlecht aber ich hoffe
>> du finde oder sie finden dieser worklich "continuous domains",
>> drei-viel.
>>
>> MfG
>>
>>
>>
>>
>>
>
>
>
> How does one say,
> comment dit-on ces mots,
> wie sagt Mann dieser Worten, ....
>
> yet yet yet yet, ....
> that that that that, ....
>
> Plus ca change, plus le meme chose.
>
>
> Yo quiero los parlamos, ....
>
>
> The, equi-interpretability,
> c'est pour les langues naturelles,
> aussi pour les langues formalles,
> si on ne dit pas incorrectement,
> the equi-interpretability,
> dans le mathematiques,
> c'est pour l'infini,
> parce que les points ne jamais faire le ligne,
> et le ligne, no jamais faire le point.
>
>
> Mais, ils soient, ....
>
>
>
> Hein?
>
>
> How does one say,
> "please excuse my lack of understanding,
> in the exercise of equi-interpretability,
> I have full command of the English language,
> and its terms in mathematics,
> so: 'se, no se'."
>
> Yo se.
>
> Dieser Ansaetzen, "thought-experiments", "setups",
> fur dieser Ansschauung, "theory", bitte immer sagen Sie mir,
> op es heisse nicht.
>
>
> So, thanks for reading, what I am describing is that
> these three relevant models of continuous domains:
>
> line-reals
> field-reals
> signal-reals
>
> are each having their own _completions_, only all together.
>
>
> In the universal language called mathematics,
> ou c'est comme un "langue Comenius",
> Dieser sind die Worten zum Anglisch,
> ich werde machen das "Matrix", das Ansaetze, c'est simple.
>
> Si il y avait une chose particularement,
> op es gibt ein tal, es gibt immer "Das", "Es",
> c'est neutral, mais bien sur les personnes peut
> avoir leurs gendres. C'est simple.
>
>
> Alors, merci ou danke oder danke bissche,
> these concepts of "standard non-standard infinitesimal analysis",
> ils seraient pour le pluspart avec leurs nommes, Namen,
> qu'ils deja avaient.
>
>
> C'est simple, and it's standard.
>
> C'est le canon, c'est magnifique. C'est moderne.
>
>
> line-reals R^bar
> field-reals R^dots, R
> signal-reals R^tilde
>
> Ces sonts continus, es gibt "Das Continuum".
>
>
> Regards
>
>
>

Hier gibt es aber die namen "Korperreellezahlen" nicht "Feldreellezahlen".

https://de.wikipedia.org/wiki/K%C3%B6rper_(Algebra)
https://en.wikipedia.org/wiki/Field_(mathematics)

Lesen van der Waerden "Moderne Algebra" es gibt ich hat es bestimmt.

line-reals
field-reals
signal-reals

Drei-viel Kontinuumem,
https://de.wikipedia.org/wiki/Kontinuum_(Mathematik) .

line-reals: Zielereellen Zahlen
field-reals: Koerperreellen Zahlen
signal-reals: Signalreellen Zahlen

Mann hat fragt, gibt es "Ziele" richtiges?

"Mein Hut, er hat Drei Ecken,
Drei Ecken hat hein Hut."

https://www.germanveryeasy.com/mathematics-in-german#Geometry

z fur Zahler, n fur Nenner,

f(z) = z/n, z -> n, n -> \infty

https://de.wikipedia.org/wiki/Geometrie

https://de.wikipedia.org/wiki/Strecke_(Geometrie)

Aber zo,

line-reals: Streckereellen Zahlen
field-reals: Koerperreellen Zahlen
signal-reals: Signalereellen Zahlen

Strecke-Reellen: line-reals
Koerper-Reellen: field-reals
Signale-Reellen: signal-reals

Hein?

Le 11/02/2024 à 13:47, Richard Damon a écrit :
> On 2/11/24 4:44 AM, WM wrote:

>>
>>> Why do you say that the infinite cannot be "traversed",
>>
>> Because it is true.
>
> And why do you need to travese it "step by step"?

That would be possible, if every element could be visited.
>
> That restriction is the restriction of finiteness, and doesn't allow for
> the infinite.
>
> So, your "Darkness", is just the
recognition that infinite sets consist of dark elements.

Regards, WM

On 2/12/24 9:55 AM, WM wrote:
> Le 11/02/2024 à 13:47, Richard Damon a écrit :
>> On 2/11/24 4:44 AM, WM wrote:
>
>>>
>>>> Why do you say that the infinite cannot be "traversed",
>>>
>>> Because it is true.
>>
>> And why do you need to travese it "step by step"?
>
> That would be possible, if every element could be visited.
>>
>> That restriction is the restriction of finiteness, and doesn't allow
>> for the infinite.
>>
>> So, your "Darkness", is just the
>
> recognition that infinite sets consist of dark elements.
>
> Regards, WM
>
>

Nope, just your own ignorance.

Too small of a mind for the task at hand, that sees darkness because it
shuts its eyes to the truth.

Nice find I:

IBM’s QisKit solving sudoku - Popkov, 2022
https://blog.theodo.com/2022/10/quantum-sudoku/

Nice find II:

About Erwin Schrödinger
He found the standing waves of this relativistic
equation, but the relativistic corrections disagreed
with Sommerfeld's formula. Discouraged, he put
away his calculations and secluded himself with a
mistress in a mountain cabin in December 1925
-- The Lone Ranger of Quantum Mechanics".
The New York Times.