THE MOST FOUNDAMENTAL FIXED POINT OF ABIAN
Alexander Abian
att: Claude Chaunier
Daniel K. Mc Kiernan
First of all if you want me to answer your posting you better post your
postings under Subject: THE MOST FUNDAMENTAL FIXED POINT THEOREM OF ABIAN
since very, very seldom I read postings which do not have " Subject" which
I would readily recognize that it refers to my postings. I barely
missed your posting - I will try to reply to your profound challenge
to give an example. However, I am sure that I will never be able to
satisfy you with my postings since they are much, much below your
profound, mature and intelligent mentality. So my silence to your
further challenges would be based on not being able to match your
profound, mature and intelligent intellect (which tried and tries
to reduce my reasonings to ashes and my ego to dust - instead of
building it up).
Your desired Example:
Tarski's classical Fixed point Theorem.
An order preserving mapping f from a complete lattice (which is
always nonempty) L into itself has a fixed point.
PROOF. Let a be the minimum element of L. for ordinals k
define f^0(a) = a f^1(a) = f(a) ... f^(k+1)(a) = f(f^(k)a0 and
for limit ordinal w let f^w(a) = lub f^k(a) with k < w.
So for every ordinal k (as required by my Theorem) f^k(a) is defined
(Please note that as my reply to Mr. Kastanas) in my theorem f^k(a)
need not be necessarily the k-th iterates of f for nonlimit ordinals and I
have no recipe for assigning an element of L to f^k(a) - it is
given by the hypothesis they just have to be elements of L) . Since f
is order preserving f^0(a) <= f1(a) <= f^2(a) <= ...<= f^k(a) <= ...
(for any limit or nonlimit ordinal k). { <= is read less than or equal}
Observe all the lines above are not a part of the prove - it is
mentioned to remind people of the definitions)
Using my Theorem I give one-line proof. If f has no fixed point
then by my Theorem there exists v such that p < q and f^p(a) = f^q (a)
But by orderpreservation of f we must then have
f^p(a) < = f^p+1(a) <=....<= f^q(a) = f^p(a) implying
that f^p(a) is a fixed point. Contradiction.
So the particular choice of the definitions of f^k(a) in the above
reduced Tarski's Theorem to a Corollary of my Theorem.
As far as your Theorem involving Generalized Fermat Theorem - I do
not know the status of the Generalized Fermat Theorem since the margin
of your paper did not allow you to elaborate on that.
Mr Mc Kiernan did any of your Math colleagues prove my Theorem
without seeing my proof ?!!
With love, Alexander Abian
--
--------------------------------------------------------------------------
ABIAN MASS-TIME EQUIVALENCE FORMULA m = Mo(1-exp(T/(kT-Mo))) Abian units.
ALTER EARTH'S ORBIT AND TILT - STOP GLOBAL DISASTERS AND EPIDEMICS
ALTER THE SOLAR SYSTEM. REORBIT VENUS INTO A NEAR EARTH-LIKE ORBIT
TO CREATE A BORN AGAIN EARTH (1990)
Daniel Kian Mc Kiernan
On 10 Jan 1998, Alexander Abian wrote:
> Mr Mc Kiernan did any of your Math colleagues prove my Theorem
> without seeing my proof ?!!
Thus far, none to whom I have spoken have exhibited any interest in
looking at the theorem, with or without proof.
It's always Dark. Light only hides the Darkness.
Daniel Kian Mc Kiernan (619) 535 - 0546
atha...@UCSD.edu 132.239.147.2 http://weber.ucsd.edu/~dmckiern
Claude Chaunier
Alexander Abian wrote:
> First of all if you want me to answer your posting you better post
The universal way is to use a command like reply on the newsreader,
which makes a reference to your posting. Then on every newsreader I
know, my posting can be seen just beside your posting, if the
corresponding option is set on the newsreader. It's very useful to
have all a conversation automatically gathered in the same place
and ordered according to whom is answering to whom. Can't the system
you use act like that too? I agree however that changing the subject
title without any reason is a nuisance too.
It would be nice if you used such a reply command. So far, your
replies are spread all over the others like new topics of
conversation. It's tiering for people not interested. How do you
want people to love you if you jump everywhere repeating the same,
while they naturally restrain themselves to do it? You would also
help an archiver like DejaNews and the users of it, as it works on
such a basis.
Please don't get upset by these technicalities, especially if your
system cannot solve them, but understand how people may see you,
always breaking conventions.
> to reduce my reasonings to ashes and my ego to dust - instead of
I realize it, seeing how you react, but my intention was only to
clearly show a hole in your meta-proof through a counterexample:
it isn't enough to have less hypotheses to be more foundamental.
I didn't mimic your way to state the theorem to mock you. Only to
make it clear. We were on the same side, looking at an absurdity.
I like when people do it with my wrong statements, it puzzles me
like a paradox and then I see the difference between my thoughts
and the result. I don't know a fastest way to improve a statement.
I admit it's also quite the sharpest for people not accustomed.
I didn't thought enough of it, only pleased by mathematics.
I should have added a smiley for example to help you to take it cool.
Don't be so obsessed with questions of superiority. It's you who
fill everything with it. I was deceived by your answer to my
first posting. Already in the title, your claim is going in
that psychological direction.
> As far as your Theorem involving Generalized Fermat Theorem - I do
> not know the status of the Generalized Fermat Theorem since the margin
> of your paper did not allow you to elaborate on that.
It was like your claim of reduction. There was nothing to discuss and
appreciate, because you were keeping for you any element which would
have helped people to know its status. A claim of reduction is a
mathematical statement, it needs a proof, all the more as it was the
main point of your posting. Mathematics is not an art without any
constraint.
You'd better have presented your strong claim as a feeling or suggestion
or sustain it with the new interesting details you've now provided or at
least suggest that you'll provide a proof someday.
> With love, Alexander Abian
Why then do you shout with your subject titles all in uppercase?
The first thing I see on this newsgroup everyday is often you for
this trivial reason. It easily yields an opposite effect.
I'm happy you kept your point fixed and answered me.
Claude