Re: Simple enough for every reader?

WM <wolfgang.mueckenheim@tha.de> writes:
(AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte
des Unendlichen" and "Kleine Geschichte der Mathematik" at Technische
Hochschule Augsburg.)

On 30.05.2025 02:05, Ben Bacarisse wrote:

WM <wolfgang.mueckenheim@tha.de> writes:

>

Ah, so you can't do what you suggested and talk to the student, after
the exam, to try to persuade them that you are right!  That did sound a
bit crazy.

>
Do you never have oral exams in England?

Don't be obtuse.

In the exam there are questions like these:
>
- Beschreiben Sie, was man unter der Abzählbarkeit aller positiven Brüche
  versteht und erörtern Sie ein Gegenargument.
- Beschreiben Sie, was man unter der Überabzählbarkeit der reellen Zahlen
  versteht, und erörtern Sie ein Gegenargument.
- Beschreiben Sie das Spiel "Wir erobern den Binären Baum" und die damit
   verknüpfte Aussage.
- Sehen Sie eine Parallele zwischen MacDuck und der Nummerierung aller
   Brüche? Wenn ja, welche?
- Was halten Sie vom wissenschaftlichen Wert der Mengenlehre unter
   Berücksichtigung von Banach-Tarski-Paradoxon und Verteilung der Brüche in
  (0, 1) und (1, oo).

 From this, it is not obvious that you want students to say anything I'd
consider to be wrong in an exam.  So maybe someone could indeed get full
marks without having to deny mathematics.

>
Correct mathematics should not be denied.

The issue, of course, is what mathematics is correct.  WMaths where you
can't define set membership, difference and equality to show WMath's
most startling result: that E and P exist with E ∈ P and P \ {E} = P or
the mathematics of... well pretty much everyone one else.

Are there any claims in your
lectures that someone at the university down the road would object to?

>
Of course.

 

Try to answer. Then I will give you marks.

I'll try a couple of questions...
 

- Beschreiben Sie, was man unter der Abzählbarkeit aller positiven Brüche
  versteht und erörtern Sie ein Gegenargument.

The positive fractions are said to be countable because the function
   b(0) = 1
   b(n+1) = s(b(n))
   where s(q) = 1 / (2*floor(q) - q + 1)
is a bijection between the natural numbers and the positive fractions
according to the definition in Prof. Mückenheim's textbook.
I am not aware of a valid counter argument since this is simply a
definition of what the term "countable" means.

>
It has been shown to the student by many arguments that the bijection
fails.

Which of the conditions of being a bijection (as presented in your book)
does b fail to meet?  (I'm betting you won't say.)

...

Without giving one of these arguments (if desired also showing that and why
it fails) you would get only half of the full score.

You called me a liar for saying this.  I /would/ actually have to accept
the nonsense you teach (or at least copy it out) to get full marks.

...

Do you not have to write marking schemes for your exams?  And if in
fact you do, what do yours say about alternative answers?

 

If a student had ever disproved my proofs he would have got additional
points.

Do you always refuse to answer simple questions?  Do you have to write
marking schemes for your exams?  I'm just trying to find out if there is
documentary evidence of what a student at your college has to write to
get full marks.

--
Ben.