Re: The non-existence of "dark numbers"

Moebius <invalid@example.invalid> wrote:

Am 18.03.2025 um 17:14 schrieb Alan Mackenzie:

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

On 18.03.2025 12:57, Alan Mackenzie wrote:

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

The set of FISONs is an inductive set. But it is not ℕ because <bla
bla bla>

Mückenheim, ich weiß nicht, wie oft man es Dir schon erklärt hat, aber
wenn die natürlichen Zahlen bzw. IN nach von Neumann definiert sind (was
heute "Standard" ist), *ist* IN gleich the set of FISONs.

Yes.

Perhaps you can help me with something that WM refuses to answer: In
German mathematical texts, is the verb "subtrahieren" used to refer to
the removal of an element or subset of a set from that set?

Thanks!

Hint: IN = {{}, {{}}, {{}, {{}}}, ...} = {{}, {0}, {0, 1}, ...} = {F : F
is a FISON} = the_set_of_FISONs.

That "because" doesn't hold

Indeed! Especially, since his claim ("the set of FISONs is not ℕ") is
wrong in the context of ZF(C) [with IN defined due to von Neumann].

I've given up arguing with him.  He just plays malicious troll tricks to
divert attention away from the pertinent questions.  I think I read
somewhere that he has a Doctor title in physics.  I think this must have
been a long time ago, before he developed his contempt for mathematics.

Because you say so? That's not significant.

Nein, Mückenheim. Sondern, weil es so ist. (Siehe Erklärung weiter
oben.) It seems that you are just too dumb to get it.

There's no connection between the bit before the because and the bit
afterwards.  You're the one who's lacking a degree in maths, not me, and
it shows.

Indeed!

Even if you can't understand the correct argument, ....

*lol*

--
Alan Mackenzie (Nuremberg, Germany).