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

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.
--
Mikko