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Dear all,

Can someone answer the following question for me?

If a real function f(x) from R to R converges to 0 as x goes to infinity, does f(z) goes to 0 as well when the complex variable goes to the point of infinity?

Thanks a lot!!

Ying

I'm in the middle of an argument with a physicist. I'm arguing that
section 3 of Einstein's famous paper, On the Electrodynamics of Moving
Bodies [1], is a tortured derivation of the Lorentz transformation and
that the derivation by Professor Rick Field, University of Florida, in
his online lecture notes for Physics 3063, doesn't have that tortured
quality. [2].

Thus, I need a practical definition from a professional mathematician.
What constitutes a tortured derivation or proof in mathematics? Any
help will be sincerely appreciated.

Shubee
1. http://www.fourmilab.ch/etexts/einstein/specrel/www/
2. http://www.phys.ufl.edu/~rfield/PHY3063/
3. http://www.everythingimportant.org/relativity/special.pdf

I am a long term sub at a high school tutor program. i am trying to think of ways to help prepare students to take or retake the SAT in a way that isn't mere tedious review. are there any suggestions from Math Pro's?
Thank you,
Shahriar Davaran

http://www.pickensplan.com/

FINALLY....somebody with some balls comes along, I just hope that
there are enough people like this guy who share his desire for a new
vision and a new way of using energy.

GOD KNOWS that there are plenty of folks who HATE green technologies,
because that's not where their money is parked at the moment.

Here's the problem that has confronted implementation of green
technology.

[1] Stupid, idiotic and facist-centric ZONING laws which exist at the
community level which make it illegal to install wind turbines and
solar collectors.

[2] Backward headed BUILDING CODES which make things difficult, cost
prohibitive, and difficult to install without jumping through
impossible hoops for the city code enforcement police, and yes they
carry guns.

[3] Crazy boneheaded LICENSING requirements which seem to assume that
Americans are too stupid to screw bolts together without first having
a 4 year degree from a trade school.

(1) There is an F-sigma-delta additive subgroup of R namely G = {x in
R | limit (n! * pi * x) exists}.

Question: What about the existence of such groups at the higher F
levels?

(2) All analytic proper additive subgroups of R are meager. As a
consequence there is no proper additive subgroup of R which is G-
delta.

Question: What about higher G levels?

(3) Given an additive subgroup G of R there exists a unique additive
subgroup H of R such that G + H = R and G intersection H = {0}.

(4) If G and H are two analytic additive subgroups of R such that G +
H = R and G intersection H = {0} then G = R and H = {0} or vice versa.

Question: If G is analytic and non trivial ( != R or {0}) then H is
necessarily non analytic. If, further, G is countable (like Q or Z)
then H is not even measurable. What if G is uncountable? Is H
measurable in that case? Or does the answer depend on the specific G
we choose. What if G is the group in (1)?

(5) That measurable non analytic additive subgroups of R exist follows
easily by a cardinality argument. Is there a definable example?

I've had a little trouble with one aspect of combinatorial covers
recently, and I'd be grateful if anyone could help me.

Let R be a cover of (U x V), where for some Boolean function f, U =
f^{-1}(0) and V = f^{-1}(1). Then, alpha(R) is defined as the smallest
disjoint cover of (U x V) embedded in R.

However, I have not been able to find out whether, in the situation
described, a disjoint cover is always embedded in R. In addition, I
can't tell whether, should no disjoint cover be embedded, alpha(R) is
defined as zero, infinity, or simply "undefined". Can anyone help me
out?

Thanks,

James McLaughlin.

Now I titled the first edition of this textbook as Mathematical
Physics, mostly because all of mathematics
comes from physics, but I want to start to talk more about physics
than of mathematics and how
mathematics is merely a byproduct of physics.

Also I want to do something which has never been done in the history
of science, is to predict something
of Quantum Mechanics from purely a look at pure mathematics. In other
words, I am going to make
a physics prediction of astronomy from purely assembling the pieces of
mathematics together in a
symmetry.

Example: Dirac predicted the positron from his symmetry of the Dirac
Equation.

What I am going to do, is predict some truths of Quantum Mechanics
from purely the assembly of
mathematics into a better symmetry.

Does any Boolean function exist which cannot be represented by a
Boolean formula?

Thanks,

James McLaughlin.