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 02.06.2025 03:56, Ben Bacarisse wrote:

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

On 31.05.2025 02:20, Ben Bacarisse wrote:

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

>

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.)

>
The condition to be definable.

There are two conditions (as you know perfectly well) and it meets both
(as you also know perfectly well).  Here are the conditions:
   bijektiv (oder eineindeutig), wenn f injektiv und surjektiv ist
Is b not injective?  Is b not surjektiv?  Here's b again so you can
check for yourself that it is both:

>
Not all natural numbers of Cantor's set can be individually defined:

Not an answer.  Is b not injective?  Is b not surjektiv?

...

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.

You really don't want to say, do you?

>
Here are two:
https://www.hs-augsburg.de/~mueckenh/GU/Pruefung%20GU1001.pdf
https://www.hs-augsburg.de/~mueckenh/GU/Pruefung%20GU1007.pdf

Thank you.  Why avoid saying just "yes" for so long?

By the way, I can see why you don't want to show any marking scheme.  It
would have to include the junk you expect the students to say,

>
Why do you call it junk?

Your students need to say thing like "Das Cantorsche Diagonalargument
ist falsch" to get full marks.

You cannot contradict even one of many proofs.

Not to your satisfaction, no.  That's a problem for your poor students.
Cantor, Church, Turing, heck, even my old professor Swinnerton-Dyer
could not get full marks on your silly questions.  Your proofs have a
lot of waffle, but sound proofs need good definitions and your
definition of N:

 1 ∈ M (4.1)
 n ∈ M ⇒ (n + 1) ∈ M (4.2)
 If M satisfies (4.1) and (4.2), then ℕ ⊆ M.

does not even permit a proof that 1 is in N.

If you could, you would not talk about nonsense like whether 1 is a
definable natural number.

Prove that 1 is in N as you define it (or admit that it's not possible)
and I'll stop saying it.

--
Ben.