Re: Another proof: The Halting Problem Is Undecidable.

On Fri, 2024-10-11 at 11:42 +0100, Andy Walker wrote:

On 10/10/2024 16:26, wij wrote:

This "0.999...!=1" proof [...].

 
Any such proof would breach the Archimedean [Eudoxus] axiom, so
is not a proof about the real numbers.  You have been told that before.
If you propose to repeat this or to take it further, you /really, really/
do need to tell us what axioms you are using instead of those of the real
numbers.  Without that, your claims, whatever they may be, are worthless,
and no-one qualified to do so can comment more usefully.  WIYF.

Wij's Theorem: x>0 iff x/n >0, where n∈ℤ⁺.

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

This is for elementary school students, might help:
https://sourceforge.net/projects/cscall/files/MisFiles/RealNumber2-en.txt/download