But one thing that is not a mistake is that both "pi and e"
are written as Continued Fractions:
pi = 3 + 1/7 +1/15 + 1/1 + 1/292 +...
e = 2 + 1/1 +1/2 + 1/1 + 1/1 + 1/4 +...
The fact that pi and e are able to be written as Continued
Fractions should have alerted at least one or two smart and
savvy mathematicians of the last several centuries. Alerted
them into realizing that pi and e cannot be transcendental
and both most be Algebraic because a Continued Fraction
is a Algebraic Number.
And this is probably the easiest mathematical proof that pi
and e are Algebraic and that no transcendental number exists
and that the Old Reals are a fake set.
The Old Reals are begotten like this:
(1) start with Naturals
(2) construct Rationals
(3) construct Irrationals
(4) put all previous together in one pile and call them Reals
The AP-Reals are begotten like this:
(1) start with AP-Reals
(2) construct AP-Reals-Rationals
(3) construct AP-Reals-Rationals-Irrationals
(4) nothing more is possible to construct
The Continued Fraction is the end of the line in Algebra.
You cannot construct any number that is beyond a
Continued Fraction and still have Algebra.
So a smart and savvy mathematician of the last centuries
should have noticed this fact. Obviously, none did.
Instead, what mathematicians of the past did was the
exact wrong thing to do-- they dreamed up a new class
of numbers and called them Transcendental.
What they should have called "pi and e" in Euclidean geometry
was "imaginary numbers"
The AP-Reals-Rationals-Irrationals are constructed as Continued
Fractions. We run out of construction programs. That was the
end of the line in construction. But we have all the numbers
in the form of Continued Fractions, so we need not worry.
But why were there so many mathematicians running around
without a head on their shoulder over Transcendental?
Pi is Algebraic in Elliptic Geometry. Pi varies from 2 to
3.14159..... in Elliptic Geometry. That variation allows for
a pi to all circles in Elliptic Geometry. Now we go to Euclidean
Geometry and we have all sizes of circles, we have big circles
and we have little circles. Do we have numbers in AP-Reals
to *cover all those circles*? We do not! It is for that reason
that mathematicians of the past thought that pi was
transcendental.
We have only one circle in all of Euclidean Geometry that has
the numbers that fulfill that circle in Euclidean Geometry and all
the other circles are lacking in numbers to make up a circle.
In Elliptic Geometry, pi varies infinitely in value and so all
circles in Elliptic are covered by AP-adic numbers. But in
Euclidean, the numbers of AP-Reals can only cover one
full circle, and then all the other circles have to use that
"pi constant" as a vector basis to cover the numbers to compose
those circles.
Let me state it geometrically, in Elliptic Geometry all circles
have a pi value and it varies due to size of the circle and that
is because the AP-adics bends and curves as numbers, helping
out the circles formed and causing variable values for pi. But
in Euclidean geometry all circles are in a flat plane where the
AP-Reals do not bend or curve and thus never help out. Yet one
number "pi" at 3.14159.... is supposed to cover all these various
sized circles. It is impossible of a task because it then requires
the existence of numbers in the AP-Reals that cannot exist.
That is why mathematicians of the past dreamed up Transcendental
to cover this situation of pi a constant yet not having "numbers that
exist" to cover all those different sized circles.
The solution? The remedy? Is simple. "Pi" in Euclidean is
3.14159...... and is a constant but for only one circle and
is imaginary-number for all other circles where the "pi" is
used as a vector basis for all the other circles.
Same thing goes for "e".
Continued Fraction is the end of the line for numbers and for
Algebra. Continued Fraction is a Topologically connected, dense,
closed Algebraic Field. There is nothing beyond Continued-Fraction.
And mathematicians of the past, tacitly implied that their
Transcendental
was beyond Continued Fraction.
Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
you make 4 mistake above, please fix and I correct you again.
a good learning lesson for you
Ignorance is educable, stupidity is forever.
I cannot believe how incredibly stupid Archie-Poo is. I mean
rock-hard stupid. Blazing hot mid-day sun on Mercury stupid. Surface
of Venus under 80 atmospheres of red hot carbon dioxide and sulfuric
acid vapor dehydrated for 300 million years rock-hard stupid. Stupid
so stupid that it goes way beyond the stupid we know into a whole
different sensorium of stupid. Archie-Poo is trans-stupid stupid.
Meta-stupid. Stupid so collapsed upon itself that it is within its
own Schwarzschild radius. Black hole stupid. Stupid gotten so dense
and massive that no intellect can escape. Singularity stupid.
Archie-Poo emits more stupid/second than our entire galaxy otherwise
emits stupid/year. Quasar stupid. Nothing else in the universe can
be this stupid. Archie-Poo is an oozingly putrescent primordial
fragment from the original Big Bang of Stupid, a pure essence of
stupid so uncontaminated by anything else as to be beyond the laws of
physics that define maximally extrapolated hypergeometric
n-dimensional backgroundless stupid as we can imagine it. Archie-Poo
is Planck stupid, a quantum foam of stupid, a vacuum decay of stupid,
a grand unified theory of stupid.
Archie-Poo is the epitome of stupid, the epiphany of stupid, the
apotheosis of stupid. Archie-poo is stooopid.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2