Math Forum / Mathematics / Mathematical Logic / February 2010

Vocabularies of Physicalism
Though what scientific training I do possess is almost all in the
“human sciences”, when I was a young lad I was quite interested in the
physical sciences: and though my knowledge of physics isn’t much more

The following is a theory in FOL with identity "=" membership "e" and
small set-hood "V" , with a universal set in it.
Define: x is small <-> x e V
Extensionality: as in Z

I have some difficulty digesting the diagonal argument of Cantor's.
The argument is that the set of all infinite binary sequences cannot
have a bijection to the set of all natural numbers, thereby proving
that the former set is uncountable?

What are sets?
Can we have a simple intuitive understanding of these objects
called as sets by mathematicians, like those objects in Z
set theory or Aczel's, etc..

http://socyberty.com/holidays/ways-to-have-a-great-valentines-day/
also.. http://www.zazzle.com/nikla01
Thanx

Super Tasks
I see Zuhair is getting beat up on for
questioning the diagonal argument.
So, its time to pull out a golden oldie:

So this maybe the most fantastic irony ever found in
mathematics. The human civilization lived through many ironies of
physics such as the idea that Earth is
a roundish ball that travels in space yet the people

What are sets?
Can we have a simple intuitive understanding of these objects
called as sets by mathematicians, like those objects in Z
set theory or Aczel's, etc..

New Style [FOR HORWICH]:
P and NP: The State of the Art
Material culled from a series of emails sent on June 17, based on
work

I am struggling with terminology. First of all I want to go
fully proof theoretical, so I don't agree when I find
on answer.com:
    Beth Theorem

Hi all, I'm currently reading Goldblatt's /Topoi: The Categorial
Analysis of Logic/, and in it the author uses a propositional theory
which apparently axiomatises intuitionist logic. The theory has one rule
of inference, namely modus ponens, four logical connectives (=>, ~, &,

hello everybody. I think that I don´t understand well the concept of
equivalence class. Let's supose the set of cars of a small village.
ten cars for example. And lets supose the equivalence relation "is the
same color as". Five are green(cars a, b, c, d and e) and five are red

I have some difficulty digesting the diagonal argument of Cantor's.
The argument is that the set of all infinite binary sequences cannot
have a bijection to the set of all natural numbers, thereby proving
that the former set is uncountable?

Suppose m, n, j, k are naturals, with n and k each greater than 0.
Suppose mk = nj.
Suppose y and z are reals such that y = nth_root(x^m) and z = the
kth_root(x^j).

I asked for some wishing of good luck, and it speedily came. I had
remembered the number 36 degrees or
10% of a sphere rotation, and I remembered it was
in association with Luminet and the dodecahedron universe. So I made a