Fritz Feldhase schrieb am Freitag, 10. Februar 2023 um 15:40:09 UTC+1:
> On Thursday, February 9, 2023 at 6:40:23 PM UTC+1, WM wrote:
>
> > Will you [claim] that every unit fraction has ℵo successors before zero?
>
> Indeed!

Then your claim is inconsistent because the successors are also unit fractions. But there is a position, namely at zero, where all unit fractions lie behind the cursor. Hence there must have been a last one passed by the cursor.
>
> Hint: Let U := {1/n : n e IN}.
>
> Then for each and every u e U: card({v e U : 0 < v < u}) = ℵo
>
> Hint: For each and every natural number n: 1/n > 1/(n+1) > 1/(n+2) > ... > 0

If this was true, set theory would be inconsistent. Only dark unit fractions can remedy this problem.

Regards, WM

Fritz Feldhase schrieb am Freitag, 10. Februar 2023 um 15:42:51 UTC+1:
> On Thursday, February 9, 2023 at 6:40:23 PM UTC+1, WM wrote:
> > If the cursor does not discern the last one, then there are dark unit fractions.
> Because you say so?

Because when passing from a realm with unit fractions into a realm without unit fractions in a one-dimensional medium, then there is certainly a last unit fraction passed. But this cannot be discerned.
>
> Hint:

Mathematical logic as abused by set theorists shows that they are refusing basic logic.

Regards, WM

zelos...@gmail.com schrieb am Freitag, 10. Februar 2023 um 12:48:46 UTC+1:
> torsdag 9 februari 2023 kl. 18:36:15 UTC+1 skrev WM:
> > zelos...@gmail.com schrieb am Donnerstag, 9. Februar 2023 um 10:19:31 UTC+1:
> > > torsdag 9 februari 2023 kl. 09:23:17 UTC+1 skrev WM:
> > > > Doesn't it?
> > > wtf does "discerned" even mean?
> > Consult a dictionary.
> >
> I want a mathematical meaning, clearly defined.

So you want an explanation that can be discerned.

> A dictionary reports usage, not definitions.

Every definition is based upon usage of words.

Regards, WM

WM formulated on Saturday :
> zelos...@gmail.com schrieb am Freitag, 10. Februar 2023 um 12:48:46 UTC+1:
>> torsdag 9 februari 2023 kl. 18:36:15 UTC+1 skrev WM:
>>> zelos...@gmail.com schrieb am Donnerstag, 9. Februar 2023 um 10:19:31
>>> UTC+1:
>>>> torsdag 9 februari 2023 kl. 09:23:17 UTC+1 skrev WM:
>>>>> Doesn't it?
>>>> wtf does "discerned" even mean?
>>> Consult a dictionary.
>>>
>> I want a mathematical meaning, clearly defined.
>
> So you want an explanation that can be discerned.
>
>> A dictionary reports usage, not definitions.
>
> Every definition is based upon usage of words.

That's a major part of your problem in conveying your ideas to others.

https://fuelgreatminds.com/academic-language-speaking-language-discipline/

On Saturday, February 11, 2023 at 11:35:14 AM UTC+1, WM wrote:

> there is certainly a last unit fraction passed

We usually don't "pass" unit fractions in math.

> But this cannot be discerned.

"wtf does '[cannot be] discerned' even mean?!"

On Saturday, February 11, 2023 at 11:37:45 AM UTC+1, WM wrote:
> zelos...@gmail.com schrieb am Freitag, 10. Februar 2023 um 12:48:46 UTC+1:
> > torsdag 9 februari 2023 kl. 18:36:15 UTC+1 skrev WM:
> > > zelos...@gmail.com schrieb am Donnerstag, 9. Februar 2023 um 10:19:31 UTC+1:
> > > > torsdag 9 februari 2023 kl. 09:23:17 UTC+1 skrev WM:
> > > >
> > > > wtf does "discerned" even mean?
> > > >
> > > Consult a dictionary.
> > >
> > I want a mathematical meaning, clearly defined.
> > A dictionary reports usage, not definitions.
> >
> Every definition is based upon usage of words.

Look, dumbo, Zelos didn't ask for more of your bullshit, he asked for a definition of [can be/cannot be] /discerned/ in the present context (which is mathematics).

Hint: You won't find (proper) mathematical definitions in dictionaries.

If you don't know the meaning of the term "definition", please consult a dictionary.

Hint: "[Mückenheim's] conclusions are based on the sloppiness of his notions, his inability of giving precise definitions, his fundamental misunderstanding of elementary mathematical concepts, and sometimes, as the late Dik Winter remarked [...], on nothing at all."

Fritz Feldhase schrieb am Samstag, 11. Februar 2023 um 16:11:38 UTC+1:
> On Saturday, February 11, 2023 at 11:35:14 AM UTC+1, WM wrote:
>
> > there is certainly a last unit fraction passed
> We usually don't "pass" unit fractions in math.

Take a very sharp needle and follow the real line. Follow Cantor.

"This has created my desire to replace the mechanical explanation of nature by a more complete one, which I would call in opposition to the former an 'organic' one." [G. Cantor, letter to W. Wundt (4 Mar 1883)]

Cantor was obliged to "the teaching of the courses required for the education of mathematics teachers, like calculus, anal. geometry, and mechanics," which includes kinematics.

"Ich unterscheide in der reinen Mathematik dreierlei Axiome ... die Axiome der Mechanik."

"so fange ich denn morgen 4. Mai meine angekündigte 5 stündige Vorlesung über analyt. Mechanik an."

Only if ZFC is considered as useless sterile nonsense, you can refuse to apply kinematics. It appears as if you like that sterile nonsense. Hopefully not many will join it in future.

> > But this cannot be discerned.
> "wtf does '[cannot be] discerned' even mean?!"

Either you know it and can do mathematics, or you don't know it and cannot even understand mathematics.

Regards, WM