Math Forum / Mathematics / Mathematical Logic / November 2004

Yesterday I saw a interesting program of NOVA titled "Ancient Refuge in
the Holy Land" What interests me is the ongoing theory I have about
Jesus in that he was a revolter of Romans who married Mary Magdalene and
had a son named Barrabas. I feel confident that within this 21st ...

An infinite number of people each toss a coin infinite times,
can you guarantee a new sequence of heads and tails?
Herc

As all the programmers here know, the infinite list of all computable numbers UTM(n) neN
produces all numbers with every combination of digits.  You cannot defeat infinity.
Say you have an *infinite* list of computable real numbers.
Then Cantor comes along and shows an anti-diagonal ...

Summary from the first thread:
L_1 is a list of reals. This creates an implied
mapping (injection) F_1 from the naturals to the reals.
D_n is the Cantor number, CN (anti-diagonal number),

We're learing at Peano Arithmetic and in the definition
of it we encounter the expression "the set of universal
closures" (that happen to be the PA).
What we don't understand is a very simple thing. What

I have some problem to solve following exercise:
(G, . ) is an infinite group and f a function on G. Find g and h injective
functions defined on G such as f(x) = g(x) . h(x) for all x in G.
Any help will be much appreciated!

(All this is for my independent study)
Let phi be a FOL formula with one free variable.
Let p be the Godel code of phi
Let q be the Godel code of phi after its free variable is replaced with p

The idea of having no axioms is for several reasons.  
Primarily, it seemed intuitive that the sets, as soon as you define
empty, or an ur-element or minimal element, exist, that from anything
anything.  That is to say, from any one thing any possible thing.

I am a engineer and PhD student (signal processing and electrical)
with a basic undergraduate background in Quantum Mechanics and almost
no training in abstract algebra. I am searching for an introductory
text to Quantum Logic (von Neumann QL not quantum computing QL) that

In the news tonight was word that the new Indian prime minister was
attacked in Kashmir. Although it was brought under control, there is no
time to waste.
If we have outbreaks such as that of 2002 where Pakistan and India were

An infinite number of people each toss a coin infinite times.  Can you
guarantee a new sequence of heads and tails?
A ____
You hand the sequence to me in a locked box and keep the key.

Any list of reals forms a countable set. For every such
set, there exists a countable set of "Cantor" methods or
"diagonal numbers" or "anti-diagonal numbers."
(There's no consistency in what these things are called.)

We have computers and they can do all the logic stuff for us ...

Curry's paradox is negation-free; it may be generated irrespective of one's
theory of negation. An intuitive version of the paradox runs as follows.
Consider the following list of sentences, named ‘The List’:
  1. Tasmanian devils have strong jaws.

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