TOPOLOGY FOR PLUTONIUM INTEGERS (Analytic Structure)
Alexander Abian
A Topology for the set P* of all the Plutonium integers (ap-integers
for short) can be introduced based on the following definition of
a LIMIT point of a subset of P*
DEFINITION: Let K be an infinite set of Plutonium integers whose
infinitely many elements are listed, say as:
...............6754302
...............3458711
K ...............4320502
...............1214332
...............1658502
......................
.....................
Since K has infinitely many elements, there must be a digit which
occurs infinitely often as a first coordinate of the elements of K
and say that digit is 2.
Let F be the subset of all those elements of K having 2 as
their first coordinate. Since F is an infinite set, there must
be a digit which occurs infinitely often as a second coordinate of
the elements of F and say that digit is 0.
Let S be the subset of all those elements of F having 0 as
their second coordinate. Since S is an infinite set, there must
be a digit which occurs infinitely often as a third coordinate of
the elements of S and say that digit is 5
Let T be the subset of all those elements of S having 5 as
their third coordinate. Since T is an infinite set, there must
be a digit which occurs infinitely often as a fourth coordinate of
the elements of T and say that digit is 8 .........
and so on and so forth. In this way we construct then Plutonium
integer
m = ......... 8502
which is called a LIMIT point of K. Clearly K may have many
limit points. If K has one limit point then we say K converges
to that limit point.
THEOREM. Every infinite set of Plutomium integers has a limit point
PROOF. by the above construction
THEOREM. Plutonium integers form a compact space
PROOF. Every sequence has a convergent subsequence
As soon as the notion of LIMIT is defined (say as in the above)
the notion of a CLOSED subset of P* is defined as usual (i.e.,
a set which contains all its limit points) Then the notion of an
OPEN subset of P* is defied as a complement of a closed set w.r.t P*
(our definition ensures) that all the usual topological axioms
concerning closed and open sets are valid) AND THE ENTIRE ANALYTIC
MACHINERY CAN BE DEFINED AND DEVELOPED in the set P* of all
Plutonium integers such as convergence of sequences, continuity
of functions, differentiability of functions etc, etc from P* into P*.
Enough, I am exhausted.
So PLUTONIUM INTEGERS not only have a nontrivial algebraic
structure they also have a hopefully interesting ANALYTIC STRUCTURE.
Shortly (when I feel up to it - don't rush me! I have lots
of other things to do!!) I will post a summary of PLUTONIUM ALGEBRA
AND ITS ANALYSIS.
(Archie, you may become well-known in the annals of Mathematics)
I said "may" - all depends on to what extent the above ideas will
be developed by yourself and others.
--
-------------------------------------------------------------------------
ABIAN TIME-MASS EQUIVALENCE FORMULA T = A m^2 in Abian units.
ALTER EARTH'S ORBIT AND TILT TO STOP GLOBAL DISASTERS AND EPIDEMICS.
JOLT THE MOON TO JOLT THE EARTH INTO A SANER ORBIT.ALTER THE SOLAR SYSTEM.
REORBIT VENUS INTO A NEAR EARTH-LIKE ORBIT TO CREATE A BORN AGAIN EARTH(1990)
THERE WAS A BIG SUCK AND DILUTION OF PRIMEVAL MASS INTO THE VOID OF SPACE
Archimedes Plutonium
ab...@iastate.edu (Alexander Abian) writes:
= A Topology for the set P* of all the Plutonium integers
(ap-integers
= for short) can be introduced based on the following definition of
= a LIMIT point of a subset of P*
=
Thanks Dr. Abian, I did not know that one had to define the Limit
before one understood the Topology. And I am confused at this moment as
to the differences between Topology and Geometry. I assume that
Geometry contains Topology as a subset. And that there exists a
Euclidean Topology, and independently a Riemannian Topology and
independently a Lobachevskian Topology. Although, I may be wrong and
that there exists only a Euclidean Topology because Riemannian and
Lobachevskian geometries are not rich enough as Euclidean geometry to
possess the subject of Topology (I do not know enough about Topology to
make any intuitive guesses).
I do not know if I have to well-define a Limit in order to understand
a Geometry? I would think that the picture of the Geometry, once seen
by the mind's eye, then the Limit is not necessary. I would think that
the Limit concept is a useful tool in picturing the geometry but that
the Limit concept is not as foundamental and basic as is the Numbers
(in this case P-Adics) and as Geometry. I would think that Numbers,
Geometry are the two most basic, or lowest entities and that the Limit
concept is further up from these two lowest entities.
= DEFINITION: Let K be an infinite set of Plutonium integers
whose
= infinitely many elements are listed, say as:
=
= ...............6754302
= ...............3458711
= K ...............4320502
= ...............1214332
= ...............1658502
= ......................
= .....................
= Since K has infinitely many elements, there must be a digit
which
= occurs infinitely often as a first coordinate of the elements of K
= and say that digit is 2.
= Let F be the subset of all those elements of K having 2 as
= their first coordinate. Since F is an infinite set, there must
= be a digit which occurs infinitely often as a second coordinate of
= the elements of F and say that digit is 0.
=
= Let S be the subset of all those elements of F having 0 as
= their second coordinate. Since S is an infinite set, there must
= be a digit which occurs infinitely often as a third coordinate of
= the elements of S and say that digit is 5
=
= Let T be the subset of all those elements of S having 5 as
= their third coordinate. Since T is an infinite set, there must
= be a digit which occurs infinitely often as a fourth coordinate of
= the elements of T and say that digit is 8 .........
= and so on and so forth. In this way we construct then Plutonium
= integer
= m = ......... 8502
=
= which is called a LIMIT point of K. Clearly K may have many
= limit points. If K has one limit point then we say K converges
= to that limit point.
=
= THEOREM. Every infinite set of Plutomium integers has a limit point
= PROOF. by the above construction
=
= THEOREM. Plutonium integers form a compact space
= PROOF. Every sequence has a convergent subsequence
=
=
= As soon as the notion of LIMIT is defined (say as in the above)
= the notion of a CLOSED subset of P* is defined as usual (i.e.,
= a set which contains all its limit points) Then the notion of an
= OPEN subset of P* is defied as a complement of a closed set w.r.t
P*
= (our definition ensures) that all the usual topological axioms
= concerning closed and open sets are valid) AND THE ENTIRE ANALYTIC
= MACHINERY CAN BE DEFINED AND DEVELOPED in the set P* of all
= Plutonium integers such as convergence of sequences, continuity
= of functions, differentiability of functions etc, etc from P*
into P*.
=
= Enough, I am exhausted.
=
Thanks Dr. Abian, the above is a start for my question as to whether
the P-adic Numbers form Conic-Section-Systems. I believe they do. And
that the two cones of a conic section system are comprised of (using
2-adics just as an example) the +2-adics and the -2-adics. In your
construction above Dr. Abian, I could use the -10-adics as well as the
+10-adics.
So, I am hopeful that in your construction, Dr. Abian that the
+10-adics Topology is that of a cone configuration, perhaps with the
points disjoint but nonetheless a cone shaped object.
= So PLUTONIUM INTEGERS not only have a nontrivial algebraic
= structure they also have a hopefully interesting ANALYTIC STRUCTURE.
=
= Shortly (when I feel up to it - don't rush me! I have lots
= of other things to do!!) I will post a summary of PLUTONIUM ALGEBRA
= AND ITS ANALYSIS.
=
= (Archie, you may become well-known in the annals of Mathematics)
= I said "may" - all depends on to what extent the above ideas will
= be developed by yourself and others.
A worthwhile achievement in mathematics is perhaps a 100 to 1000
years behind in recognition compared to a similar worthwhile
achievement in physics or engineering. Math is too slow to recognize
great new work, and too slow even to clear out its fake math. The
gravest problem of mathematics is that it does not have experiment to
judge it with reality and to guide it as do the sciences. In fact,
mathematics is all a minor subset of physics and will be a minor
department of physics. This is what will happen in the future. Applied
math can remain as a separate department but all theorem math and pure
math will be subsumed by physics.
Heikki...@no.spam.fi
> ----------
> A Topology for the set P* of all the Plutonium integers (ap-integers
Whatever..
> ----------------------------------------------------------------------
> ABIAN TIME-MASS EQUIVALENCE FORMULA T = A m^2 in Abian units.
> ALTER EARTH'S ORBIT AND TILT TO STOP GLOBAL DISASTERS AND EPIDEMICS.
> JOLT THE MOON TO JOLT THE EARTH INTO A SANER ORBIT.ALTER THE SOLAR
> SYSTEM.
> REORBIT VENUS INTO A NEAR EARTH-LIKE ORBIT TO CREATE A BORN AGAIN
> EARTH(1990)
> THERE WAS A BIG SUCK AND DILUTION OF PRIMEVAL MASS INTO THE VOID OF
> SPACE
Very funny..
I believe someone's trying to revive the myth of Alexander Abian
again! Someone at iastate.edu must have really fun time writing these
incredibly weird theories and incomplete proofs..
PS. I'm sorry I replied to Abian's message (waste of bandwidth) !
Heikki Orsila If you can't work this equation then
heikki...@ee.tut.fi I guess I'll have to show you the door
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