Math Forum / Mathematics / Mathematical Logic / March 2004

I'm having some trouble with Cantor's diagonal argument.  I used to
buy it, but I'm not so sure if I do anymore.  To simplify matters,
let's show that the unit interval has uncountably many real numbers by
working with base-2 expansions...

I have written a converter in Java which converts from a Turing Machine
description to CA Rule 110 configuration.
http://www.andrebetz.de/TuringMachine.zip
so if you are interested feel free to download this file.

                       UCLA LOGIC COLLOQUIUM
                      Friday, March 12, 2004
                             4:00 p.m.
                     Mathematical Sciences 6627

Quoting from Suppe's axiomatic set theory book, p. 19:
"We shall occasionally introduce definition schemata which, like the
axiom schema of separation, should properly be formulated in the
metalanguage".

I found some material that might be of interest.  There will be more,
including information on de Morgan algebras and Lukasiewicz algebras.
But the latter are related to Post algebras  In turn, Post algebras
relate to Stone algebras.

A few years ago I posted a short essay in response to
arguments on the internet:
 http://masonc.home.netcom.com/misssubj.html
The essence, in the first few lines is this:

Prof. Man and wife are browsing a large mulit level dept store that
had just opened.  Wife stops for a few minutes to examine a display
of summer froks, and then realizes her husband had gone on without
her.  she was about to wander aimlessly in search of him, when she

Here goes:
An "irregular hexagon" is a two-dimensional shape with 6 straight
sides, of varying lengths, which can otherwise have any size or
conformation. That is, a given angle at whih two adjacent sides meet

I have a scholarship exam in 3 days and am trying to work some past
paper questions. The following question appeared last year. I'm
looking for any suggestions on how to approach it. Thanks for any
help.

Goedels Incompleteness Theorem GIT:
-----------------------------------
There is a sentence G of Peano Arithmetic PA
which is true e.g. valid in all Models of

Consider this: A is a contingency, C is a tautology and X is of an
unknown value.  Given this information, we cannot determine the truth-value
of "C->X" (if C then X) since it is completely dependent on the
consequent.  If X is true, so is our conditional.  If it is false, the

Neural networks are "model-free" estimators, in that they do not require an
in-depth understanding of the phenomena they are modeling.
http://www.arcon.com/arconneu.html
THE MATHEMATICS OF CROSSING THE STREET:

Consider the following inference, based on the Pigeonhole Principle:
  (i) There are at least m objects
  (ii) There are exactly n A's
  (iii) The f of each object is an A

With those which think that the body is a goal, that they that
the matter which composes it is into perpetual change, which
this matter remembers belonged to others and which it will
still belong to other A those which think of being able to

No theoretical system can survive without being aware to its
limitations.
It means that any
x output