Eucl Geom = Ellip + Hyperb, or, | = )+( #260; Correcting Math - sci.math

Message from discussion Eucl Geom = Ellip + Hyperb, or, | = )+( #260; Correcting Math

Archimedes Plutonium

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More options Nov 3 2009, 7:25 pm

Newsgroups: sci.math, sci.physics, sci.logic

From: Archimedes Plutonium <plutonium.archime...@gmail.com>

Date: Tue, 3 Nov 2009 11:25:37 -0800 (PST)

Local: Tues, Nov 3 2009 7:25 pm

Subject: Eucl Geom = Ellip + Hyperb, or, | = )+( #260; Correcting Math

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Archimedes Plutonium wrote:

(snipped)

> When I wrote the AP-adics book, I was attacking two
> math ideas. One was a better formulation of P-adics from Hensel's p-
> adics and so I came up with the AP-adics. But a second attack was to
> further the idea that
> Geometry was this:

> Euclidean Geometry = Elliptic unioned to Hyperbolic Geometries

> Written in short: Eucl = Elliptic + Hyperbolic

Having all the numbers finite is neat because I can rewrite that
equation in
symbol form as this:

| = ) + (

The idea is that the Elliptic geometry is the inverse of Hyperbolic
geometry
and where the application of a curve ) on another curve ( ends up with
a
straight line segment.

Now to translate that into number algebra we simply go to inverses
where +2 is the inverse of -2. So if we have a curve ) that is all
positive
finite numbers applied to a curve ( of all negative finite numbers,
they
cancel leaving behind a straight line segment.

Or, we can do the transform via multiplication inverse where curve )
is positive integers and curve ( is multiplicative inverses cancelling
to form a straight line segment.

> And where I use the three and only three number-systems as native to
> one of those geometries such as this:

> Doubly Infinites = +AP-adics unioned -AP-adics

> But with this book of Correcting Math, I have run into
> a serious problem. In the AP-adics book, those numbers are defined as
> having a infinite-component
> and in Doubly Infinites there is no finite-component.

> In this book, I define Finite as 10^500 or less (inverse
> included). And I throw out as meaningless the infinity
> or infinite-numbers.

> So this book of Correcting Math ruins my previous book of AP-adics.

> But I can salvage the AP-adics book.

> I simply retitle it as Eucl Geom. = Ellipt unioned Hyperbolic. So I
> switch the emphasis to the geometry
> aspect of that previous book.

Actually it appears that all finite numbers makes my other book
easier. I now
can see that the finite numbers from 0 to 10^500 cover a hemisphere
and where
the South Pole becomes the number 10^500 and then returning to the
North Pole
of 0, we have negative numbers in the return and where we consider the
point one
unit shy of the North Pole as (-)999..99 where that is one less than
(-)10^500

And I set up Euclidean geometry as a finite geometry going from one
extreme end of
(-)10^500 to the other extreme end of 10^500

Both the Elliptic and Hyperbolic geometry can be represented by a
sphere and where
one is concave outwards, the other is concave inwards and putting the
two together
they cancel one another yielding a Euclidean straight line segment.

> Then I go ahead and define all the integers to 10^500
> as the AP-adics

> I define the Hyperbolic geometry numbers as the negative integers to
> (-)10^500

> For the numbers native to Euclidean Geometry I define
> them as the Doubly Finites rather than the Doubly Infinites which has
> numbers such as this:

> 333..33d999..99 where the symbol .. signifies the
> upper bound of 10^500 (and inverse).

> Simply put, I erase all infinite numbers and provide
> only finite numbers defined as 10^500 upper bound.

> The beauty of all numbers as finite, is a relief to Calculus, which
> works as old Calculus but there is
> never any problems of discontinuities, since there
> never was any continuity to begin with. All of geometry
> is discontinuous with holes in between all numbers.

> So math becomes what Feynman became used to
> in his old age with Quantum Electrodynamics of getting
> rid of the infinites with renormalization procedures.

> So in effect, I, Archimedes Plutonium, is not improving
> Quantum Electrodynamics by renormalizing, but rather,
> I am improving all of mathematics by renormalizing all of mathematics
> and throwing out infinities.

> So by defining Finite in mathematics as 10^500 or below, what I have
> thus done is similar to what Feynman did for Quantum Electrodynamics--
> renormalized.

> But, also, now, I have to correct my previous book of its Geometry
> with the concept of finite.

> Since there are no infinities in mathematics because there are none in
> physics, then we cannot have an
> infinite line, afterall. That means all lines in Geometry
> are finite and can go to the extreme of (-)10^500
> endpoint to 10^500 endpoint. I spoke of a Euclidean
> Geometry as an all finite geometry already and see no
> problems in replacing out the old with the new.

> But I do see some problems in defining a finite line in
> Elliptic and Hyperbolic geometry. So it may be years
> before I get back to that new edition and in the meantime can
> anticipate those changes.

So rather than harming my previous work of Eucl = Ellipt + Hyperb,
it appears that as I make all the numbers Finite, that it helps the
program and it gives more clarity.

Archimedes Plutonium
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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