Re: Another proof: The Halting Problem Is Undecidable.

On 11/10/2024 18:11, wij wrote:

Archimedes likely believes that all (real) numbers, including pi, sqrt(2), are
p/q representable. Is that what you suggest?

By the time of Archimedes it had been known for several hundred
years that "sqrt(2)" is irrational.  [The status of "pi" remained unknown
for a further ~2K years.]  So no, Archimedes did not believe that, not
least when he laid some of the foundations of calculus.

Archimedean axiom is an *assertion* that infinitesimal does not exist without
knowing the consequence (violating Wij's Theorem which is provable from the rules
stronger than 'assertion').

If "Wij's Theorem" is inconsistent with the axioms of real numbers,
then it is not a theorem of real numbers.  Try one of the other systems of
numbers, which you would probably find more to your taste, given the other
things you say in this group.
--
Andy Walker, Nottingham.
    Andy's music pages: www.cuboid.me.uk/andy/Music
    Composer of the day: www.cuboid.me.uk/andy/Music/Composers/Valentine