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 05.06.2025 23:51, Ben Bacarisse wrote:

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

On 04.06.2025 02:35, Ben Bacarisse wrote:

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

On 02.06.2025 03:56, Ben Bacarisse wrote:

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

>

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

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

>
It is for the set of definable numbers, it is not for the dark
numbers.

No, the topic is your exam papers and the nonsense

>
You cannot disprove any of my results.

You have admitted that in WMaths you can't (yet?) define set membership,
equality and difference so how could any result like you claim that, in
WMaths E and P exist such that E in P and P \ {E} = P be disproved?  You
can state anything you like about WMaths and it can't be disproved
without definitions of set membership, equality and difference.

Is this still the state of WMaths or have you been able to define set
membership, equality and difference so as to be able to prove this most
surprising of results in WMaths?

that a student must
accept to get full marks.

>
Have you something substantial to say about dark numbers?

Have you nothing substantial to say about why the exam questions you
posed and challenged me to answer was wrong?  I posted a function b : N
-> Q+ and you won't say whether it is not injective and/or surjective.

As soon as anything technical comes up you retreat into waffle and a
suddenly find a desire to talk about anything other than the exam
question you were happy to talk about before.

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

>
So it is. The reason is what you refuse to answer:

(...(((ℕ \ {1}) \ {2}) \ {3}) ...) = { }
is wrong for all singletons of definable numbers.
>

Not all natural numbers of Cantor's set can be individually defined:
All natural numbers can be thought as defining the diagonal but not
individually. The well-order would force the existence of a last
one. Contradiction.
>
Therefore most indices of the diagonal elements are undefined, dark.

You cannot contradict even one of many proofs.

Not to your satisfaction, no.

>
Not at all. Then you would try it.

>
But I have shown my students how it goes.

I feel for any student who knows how mathematics works.  With luck they
know how German exams work as well and will just write stuff they know
to be wrong so they get the marks.

>
You "know" what is wrong without being able to disprove it. That is
not the way to pass an exam.

I know how to prove that b is both injective and surjective.  In fact,
it's likely that you do too.  But you would not accept any such proof
(even your own) because it contradicts your assertion that b is not a
bijection between N and Q+.  But note that you don't ask your students
to prove anything.  All they have to do is repeat the nonsense they've
been told.

--
Ben.