Re: Simulating termination analyzers by dummies --- criteria is met

Mikko <mikko.levanto@iki.fi> wrote:

On 2024-06-24 20:27:55 +0000, Alan Mackenzie said:

joes <noreply@example.com> wrote:

[ .... ]

--
Man kann mit dunklen Zahlen nicht rechnen. Für die eigentliche
Mathematik> sind sie vollkommen nutzlos. --Wolfgang Mückenheim

Or, in English, "You can't do arithmetic with dark numbers.  For actual
mathematics, they're completely useless.".

Wolfgang Mückenheim is a crank in sci.math and de.sci.mathematik, one of
the few remaining ones after Google shut down their Usenet servers in
February.  He insists on the existence of something he calls "dark
numbers" and gives crank-like justifications for them, which do not hold
up under more robust questioning.

From the first order Peano axioms it is not possible to prove that there
are no non-standard numbers. It is possible to construct (for example in
ZF) a model of the first order Peano arithmetic that has a proper subset
that is another model of the same Peano artichmetic. And it is possible
to do arithmetic with those numbers. Whether useful, I don't know.

Yes.  All that is over Wolfgang Mückenheim's head.  He doesn't have a
degree in maths, but I believe he has a Phd in physics.  His intuitions
in set theory are those of a rebellious teenager, and he refuses to
accept many established mathematical results.  The threads he gets
involved in in sci.math feel similar to the threads in comp.theory
involving Peter Olcott.

Such people completely miss the fascination of surreal numbers, Robinson
integers, and the rest.  Other posters just wish they could get the
cranks to learn new (for them) things.  Personally, I never learnt much
about mathematical logic and the foundations in my maths degree, but I
could catch up if I could be bothered, and I'm broadly aware of what I've
missed.  That distinguishes me from the cranks.

--
Mikko

--
Alan Mackenzie (Nuremberg, Germany).