Math Forum / Mathematics / Mathematical Logic / June 2004

According to Cantor, the natural numbers have an order of infinite magnitude
less than that of the real numbers because the real numbers can not be
exhaustively paired, one-to-one, with any list of natural numbers.
Conversely, this means that the real numbers must be able to exhaust ...

I would welcome any suggestions for commercial applications of first
order logic. Assume one has an efficient, completely automated first
order logic theorem prover. Assume also that the theorem prover can
also be used to do queries for individuals that satisfy a query

PREMISES:
(1) The Halting Problem was defined to have no possible correct
answer. In other words it's an IMPOSSIBLE QUESTION.
function LoopIfHalts (bool YouSayItHalts):

Mathematicians notice intuitive phenomena and attempt to write axioms
to describe them.  These "axioms" are said to be arbitrary and their
syntax is often studied independent of their semantics.  However, they
are not arbitrary - they are chosen to reflect the properties of the

As Peter originally put it, the output of halt should reasonably be
expected to have 3 options :
1 /  the input halts
2 /  the input wont halt

Here's something that probably is of interest only to those interested in
the gory details of computer programming.
So, I'm writing an interface to Bruce Schneier's Blowfish encryption
algorithm.  It's pretty straightforward and I've done it before, but I want

Below is the link from which I am basing my discussion.
http://www.netaxs.com/people/nerp/automata/halting2.html
Because of all of the dialogue of the other threads on this
subject I am able to state my position much more clearly.

    www.kia-ora-yoko.co.nz
    A site dedicated to the ultimate logician!

I posted before that I recall that original Scientology, as founded by
L. Ron Hubbard, did not just contain a route to obtain spiritual
freedom but also a route to stop aging, actually to become immortal
with the body. Many people think it can't be true, but when people

The old corrupt story, who blows the whistle is being discredited, and
when they are even more unlucky, committed to a psychiatric
institution and mishandled till they can't speak out anymore.
Scientists who persisted in publicly raising the issue of harmful

if it is possible to be deceived once, why is it not possible to be deceived all
the time?

hi.  i read abou the E!x|P(x) notation which means "there exists one
and only one x such that P(x)"  I got curious about how to negate it
so I tried to rewrite it as:
E!x|P(x) <-> Ex|{P(x) AND [Ay,P(y) -> (y=x)]}  "Ay means 'for all y'"

T ='consciousness' in a cross between physics & languages ?

N

Secret services know how to make you sick and kill you from a distance
since a very long time. Try to catch the killers miles away!
So, next time you feel sick or drop dead, you might be the victim of a
crime. Law enforcement and the people in general have to know that,

I hope, I'm right in this NG.
I'm desperately trying to prove the following tautology:
(Phi => (Psi => Chi)) => (Psi => (Phi => Chi))
I wrote the following "tutch"-program for this: