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From: Archimedes Plutonium on 8 Jul 2010 15:09


Archimedes Plutonium wrote:
> Funny how infinity needs a discussion for both large infinity and a
> separate discussion
> for infinity on the small scale. Here is another example of Quantum
> Duality in mathematics
> in that infinity, which we usually think of as beyond large, that it
> must be reconciled
> with microscale and infinity there.
>
> In July 2010, this month: I gave this as proof that large scale
> infinity requires a boundary
> such as 10^500 which says that finite is any integer smaller than
> 10^500, and 10^500 itself
> is an infinite number as well as any number greater than 10^500.
>
> I wrote in July 2010:
>
>
> Theorem: In old-math, geometry had well-defined finite-line versus
> infinite-line but
> Algebra or Number theory was ill-defined with its finite-number
> versus
> infinite-number
> and that is why mathematics could never prove Twin Primes, Perfect
> Numbers,
> Goldbach C. , Fermat's Last Theorem, Riemann Hypothesis and
> thousands
> of
> number theory conjectures. In this theorem, we show there never can
> be
> constructed a infinite-line in geometry since the other half of
> mathematics, the old-math never well defined
> infinite-number versus finite-number.
> Proof: Since old math does not recognize infinite-numbers, that no
> matter how many finite number of line segments we put together, they
> still will never
> summon into an infinite-line-ray. However, if a precision definition
> is given in
> mathematics for geometry or algebra saying that finite-number means
> all numbers less than 10^500 and 10^500 and beyond are infinite-
> numbers.
> Well, with that definition we can build an infinite-line-ray in
> geometry by
> adding together 10^500 units of line-segments of finite line
> segments
> building
> an infinite-line-ray. QED
>
> I referred to another proof of mine in 2009 where I said that
> betweeness axiom
> no longer held. So I need to refurbish this betweenness proof to prove
> that in
> small scale that you also need a boundary between finite and infinite
> number,
> and here it is 10^-500
>
> --- quoting old post in part ---
> Newsgroups: sci.logic, sci.math, sci.physics
> From: Archimedes Plutonium <plutonium.archime...(a)gmail.com>
> Date: Thu, 18 Jun 2009 21:51:09 -0700 (PDT)
> Local: Thurs, Jun 18 2009 11:51 pm
> Subject: proving the Betweenness Axiom contradicts the Parallel Axiom
>
> Betweenness Axiom:
> If A and B are any two points, then (1) there is a point C such
> that A-B-C, and (2) there is a point D such that A-D-B.
>
> Parallel Axiom:
> Given a line and a point not on the line there exists one and only
> one line parallel from that point to the given line.
>
> Now I need to prove that those two Euclidean Geometry axioms
> are contradictory. I did this earlier in this book by setting up a
> triangle that becomes smaller and smaller and which would thence
> have two 90 degree angles.
>
> But let me try it using the same scheme a bit differently.
>
> here I have a given line with a parallel line from that point not on
> the
> given line called A:
>
> --------------------------A----------------------------
>
> --------------------------------------------------------
>
> Now what I do is form a right triangle using A
> and two points on the given line called B and C
> like this:
>
> --------------------------A-----------------------------
>
> --------------------------B------------------------C---
>
> Now here is the interesting feature of the Old
> Euclidean geometry axioms in that they are
> contradictory. As I do the infinite-downward
> -regression of Betweenness the C point
> approaches infinitely close to the B point
> such as this picture
>
> --------------------------A-----------------------------
>
> --------------------------BC---------------------------
>
> Since the axiom of Betweenness never ends
> means that C becomes B and the triangle
> is merely a line segment AB and no longer
> a triangle of ABC and before it becomes
> a mere line segment it becomes a triangle
> with two 90 degree angles.
>
> Now if I went the other way of B approaching
> C as such:
>
> --------------------------A-----------------------------
>
> --------------------------------------------------BC---
>
> In this direction what ends up is a line segment
> AC and where the B becomes C.
>
> In the first case I have a triangle which has two
> 90 degree angles, and in the second
> case I have a triangle whose angle sum is equal to
> zero since side AB and BC vanished into becoming AC.
>
> --- end quoting old post in part ---
>
> Some minor adjustments to the above, that if infinity is without end
> and
> no boundary between finite and infinite number, then what happens in
> the Microworld or small scale is that you end up with either a
> triangle
> that has angle sum greater than 180 degrees and two right-angles, or
> you have a very slender scalene triangle whose tiny side, like in
> Calculus,
> making the side as tiny as we want to make it, so that finally, we end
> up with
> a triangle that has two sides of a scalene triangle as parallel since
> they never
> meet.
>
> SUMMARY: in mathematics when we do not admit that there must be a
> boundary
> between finite number versus infinite number such as 10^500 large
> scale and 10^-500 small
> scale, that we end up not able to build a infinite line ray in
> geometry simply because
> infinite-number is not available. And on the small scale, there also
> needs a boundary
> between finite number versus infinite number, or else we have a
> triangle sum greater
> than 180 degrees and a triangle with two parallel sides.
>

You see, what the above two proofs do, is not only tell us the
difference between
infinity at large and infinity for the small, is that it tells us the
meaning of the concept
of infinity, for which none of us have ever realized we are using a
false idea for infinity.

We were thinking infinity means endless, whereas it only really means
the end
of physical measure or physical experimentation. So if you cannot have
a physics,
then mathematics is merely just "ideas of fiction". We can pretend
that a woman becomes
a witch and rides on brooms or we can pretend that lizards become
large and shot fire out
of their mouth. Likewise we can pretend that a line goes on forever or
that a number always
exists between any two numbers no matter how small.

What those two proofs show is that mathematics is no longer math as
the science of precision, so long as finite number versus infinite
number is never well-defined.

Infinity simply means that the end of Physics has arrived, where
Physics is no longer
meaningful and where Physics has duality as logic and not Aristotelian
linear logic. Logic
is nonlinear in Quantum Mechanics. So when we reach 10^500 and go
beyond, we have
reached infinity for the large. And when we reach 10^-500 and try
going smaller, we cannot
because there is no more physics at either end of these numbers.

The reason Twin Primes, Perfect Numbers, FLT, Goldbach, Riemann
Hypothesis were never
proved and never provable is because 10^500 and 10^-500 in the case of
Poincare Conjecture
are the end of the line for infinity. Infinity means the end-of-
physics. Physics is a bigger subject than all of mathematics and, all
of mathematics fits inside of Physics as a subset. The bedroom in your
house is a subset of your house, and mathematics is a bedroom or
closet space of your house.

Notice the difference in those two proofs of infinity at large and
infinity in the small. Infinity at
large when not well defined as 10^500, then noone in geometry can ever
build or construct
or erect a infinite line from finite lines. Since we have no
definition of infinite-number, then
no matter how many finite lines are joined together, they can never
build an infinite line.
Now in the infinite small case, what happens when that is not
precisely defined such as
10^-500, what happens here is that you have triangles that can be
built where the angle
sum in Euclidean geometry is greater than 180 degrees because
triangles can possess two
right-angles. Or, you have the odd situation where, since infinity in
old math means never
ending, even of physics, you have the odd situation of a triangle
between 0 and 1 that never
meets in a third point but has only two points of intersection of its
three sides.

I am afraid that math of old was too much philosophical imagination
run amok rather than
doing their job of precision definition of terms and concepts. Even
the Peano Axioms of the
late 1800s never precision defined finite-number versus infinite-
number. And that is why
Mathematics is so much in the weeds and is the least progressive of
the sciences. At least
when someone like Pons and Fleischmann announce cold fusion in a test
tube, the physics
community can clear that up in a matter of 3 years. In the mathematics
community, time
moves slothlike and something as important as precision definition of
finite-number takes
more than 3 milleniums because we have already endured 3 milleniums of
math without the
community so much as taking notice, and precision defining finite-
number versus infinite-number.

Archimedes Plutonium
http://www.iw.net/~a_plutonium/
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
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