🚀 go-pugleaf

In article <1010@sdcc13.ucsd.EDU: ln63wgq@sdcc13.ucsd.edu.UUCP (Keith Messer) writes:
:
:> Your program NEVER will succeed because there are an infinite number of
:> cases, it can only fail.
:
:Ahh!  This points up the exact problem we're having in communicating here.
:I'm not a mathematician, I don't write papers, and I feel no urge to know
:for sure whether my hypothetical regularity is universal or not.  My point
:is that, although a hypothesis may or may not be true, if it's a little bit
:useful then it's worth implementing in an algorithm.  So, perhaps one day
:the algorithm flails.  I can take note of that and know that the hypothesis
 
If you see my previous aritcle the problem is that you would never KNOW
if it failed. It might report a composite number as being prime and you
would have no way of knowing otherwise. (unless you used a different
algorithm).

:is incorrect, or at least needs refinement.  By "winning either way," I don't
:mean proving the hypothesis, I mean getting some value out of using it to
:develop algorithms that may be valid in the specific cases I'm interested in,
:though they may bomb if taken generally. :-)
 
You have no way of verifying whether the algorithm is correct for your
'specific cases I'm interested in'.

:
:  If a general result of
:quantificantion theory is that set theory and number theory contain contra-
:dictions (ie. It's possible to construct a proof for a statement and one for
 
Number theory does NOT contain contradictions. CERTAIN set theories can be
constructed which are formally inconsistent but that is irrelevent to the
discussion about number theory.

:not be true.  To some extent, this problem extends into other mathematical
:fields.  On one hand I want to know how we can put so much emphasis on proof,
:if it is known that our postulates are contradictory (and therefore not
:representative of reality either), and on the other hand I'm curious as to
 
see above. Go take a formal course in logic and Goedel's theorem. You
might learn something.

:why, assuming that our math is formal enough to be used mechanically, one of
:you sharp mathematicians out there don't write a proof machine to construct
:and prove every theorem in every field of mathematics.  Doubtless there are
 
I suggest you look at what is known as the halting problem.


Bob Silverman