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ZF is inconsistent (laut Wolfgang Mückenheim)

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Fritz Feldhase

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Jan 6, 2023, 7:03:44 AM1/6/23
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In sci.logic hat Herr Prof. Wolfgang Mückenheim vor ein paar Tagen verlauten lassen:

| ZF is inconsistent.

Die Antwort eines Teilnehmers in sci.logic darauf lautete:

| Crank statement. Unless you can list those finitely many ZF axioms _you_ have used in your claimed SYNTACTICAL inconsistency-proof. Can you do that?

Worauf Herr Prof. Wolfgang Mückenheim wie folgt reagiert hat:

| Yes, the applied axioms are listed here: https://www.hs-augsburg.de/~mueckenh/Transfinity/Transfinity/pdf pp.43-48. [...]

Dazu ist leider folgendes zu sagen:

| What Mückenheim calls "axiom of infinity" on page 45 in his book IS NOT the _axiom of infinity_ (AoI) as accepted/adopted in ZF(C).
|
| His version(s) is(are) erroneous.
|
| See: https://de.wikipedia.org/wiki/Unendlichkeitsaxiom

Traurig aber wahr: Herr Prof. Wolfgang Mückenheim kann nicht einmal wohlbekannte Axiome der ZF(C) korrekt zitieren/wiedergeben.

Sein "Beweis" für die Inkosistenz von ZF ist daher schon vom Ansatz her ein Rohrkrepierer. Sorry, Mückenheim.

WM

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Jan 6, 2023, 6:06:53 PM1/6/23
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Fritz Feldhase schrieb am Freitag, 6. Januar 2023 um 13:03:44 UTC+1:

> Traurig aber wahr: Herr Prof. Wolfgang Mückenheim kann nicht einmal wohlbekannte Axiome der ZF(C) korrekt zitieren/wiedergeben.

Unsinn. Ich lasse lediglich den überflüssigen Ballast weg.
(X ∈ S ==> {X} ∈ S) bedeutet: Wenn X irgendein Element von S ist, so ist {X} ∈ S.
Das betrifft also alle Elemente von S, weshalb es nicht nochmals betont werden muss, dass es alle Elemente von S betrifft.

Gruß, WM


Ralf Bader

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Jan 6, 2023, 6:12:56 PM1/6/23
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S lbrn nr diotschn Schßdrck dhr.

Carlo XYZ

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Jan 7, 2023, 2:29:23 AM1/7/23
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Ralf Bader wrote on 07.01.23 00:12:
> On 01/07/2023 12:06 AM, WM wrote:
[...]

> S lbrn nr diotschn Schßdrck dhr.

*gähn*

WM

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Jan 7, 2023, 4:47:54 AM1/7/23
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Carlo XYZ schrieb am Samstag, 7. Januar 2023 um 08:29:23 UTC+1:

> *gähn*

Um halb neun noch müde?

Gruß, WM

Carlo XYZ

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Jan 7, 2023, 4:50:40 AM1/7/23
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WM wrote on 07.01.23 10:47:

> Carlo XYZ schrieb am Samstag, 7. Januar 2023 um 08:29:23 UTC+1:
>
>> *gähn*
>
> Um halb neun noch müde?

Das darf ich. Seit 3 Uhr Mathematik gemacht.

Und dann diese langweiligen immergleichen deutschen Schimpfwörter.

Jens Kallup

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Jan 7, 2023, 5:23:33 AM1/7/23
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Am 07.01.2023 um 10:50 schrieb Carlo XYZ:
>
> Das darf ich. Seit 3 Uhr Mathematik gemacht.
>
> Und dann diese langweiligen immergleichen deutschen Schimpfwörter.

reg Dich nicht darüber auf.
Ich habs auch schon bemängelt.
genützt hat es auch nichts.

Aber wie das so ist: im Netz kann man ja sein wer man will.
Und eine Etikette haben, die dem Großteil der "Gemein"schaft
anspricht - scheint so nen Hype so sein - ich komm da nicht
mehr mit.

Naja, mein Senf dazu gebend: Jens


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Mostowski Collapse

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Jan 10, 2023, 6:43:24 AM1/10/23
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Zurzeit bekommt Wolfgang Mückenheim Gefasel Konkurrenz
durch ChatGPT. Mal schauen was passiert, erste Runde mit ChatGPT:

Q: Do dark numbers exist?

A: The term "dark numbers" is not a commonly used term in
science or mathematics, so it is unclear exactly what you are
asking about. It's possible that you may be thinking of a different
concept that is related to "dark" or "hidden" information or entities.

One concept that is related to "dark" numbers is "dark matter."
Dark matter is a hypothetical form of matter that is thought to
make up approximately 85% of the universe's total mass. Scientists
infer the existence of dark matter because of its gravitational effects
on visible matter, but its composition and properties are still not well understood.

Another concept that is related to "dark" numbers is "dark energy,"
which is thought to be responsible for the accelerating expansion
of the universe. Like dark matter, dark energy is inferred to exist based
on its effects on the universe, but its properties are not well understood.

It's possible you are thinking of something else, Can you please provide
more context about what you meant by "dark numbers"?

Fritz Feldhase schrieb am Freitag, 6. Januar 2023 um 13:03:44 UTC+1:

Mostowski Collapse

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Jan 10, 2023, 6:51:59 AM1/10/23
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That escalated quickly now ChatGPT has also an argument
in favor that the intersection all end-segments is non-empty.
I guess the creativity of ChatGPT spans also truth. The

error comes possibly from a wrong interpretation of
end-segment, leaning towards segment, i.e. a closed
interval [a,b]. Woa! Thats a splendid blooper:

Q: The intersection of all end-segments cannot be empty,
which shows the existence of dark numbers. Is that right?

A: It sounds like you may be referring to a specific mathematical
concept or proof, but without more information, it is
difficult to know for certain.

In general, an "end-segment" can refer to a subset of the real numbers
that have an upper and lower bound. If the intersection of all end-segments
is non-empty, it would mean that there is at least one number that
is common to all end-segments.

It's important to note that intersection of all end-segments cannot be empty.
Since the set of real numbers are a union of all end-segments, so there must
be an overlap, otherwise the union will not be the real numbers set.
The intersection of all end-segments is the set of all its accumulation
points, which are the limit points of the end-segments.

The concept of "dark numbers" is not typically used in mathematics and
I'm not aware of any proof that refers to dark numbers in the way that
you described. If you could provide more information or context about
the specific proof or concept you're referring to, I would be happy to try
to help you understand it better.

I made a screenshot.
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