Re: Simple enough for every reader?

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.

 ...

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.

You could also disprove it. But you carefully evade.

...

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.

Either understand and repeat what I teach or disprove it. Here is a very simple example:
Since all natural numbers can be reduced to the empty set by subtracting them collectively,
ℕ \ {1, 2, 3, ...} = { }
they could also be reduced to the empty set by subtracting them individually - if this was possible. But then the well-order would force the existence of a last one. Contradiction.
Do you understand? Or will you evade again by questioning that 1 is contained?
Regards, WM