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 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 that a student must
accept to get full marks.  If you don't like the fact that you can't
defend you exams, don't engage in the topic.  You do this all the time.
You take a topic like this until you get stuck and then say that's not
the topic.

b is both injective and surjective.  It is a successor function for Q+
making Q+ as obviously countable as a set could be.  You can't disprove
that and explain why I would loose marks for saying this so now "this is
not the topic"!!

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:
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.

>
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.

--
Ben.