And I have often written that the longer one spends
in science, that science has a nasty habit of falsifying
your earlier work. I think it was Frege or Russell or
someone spent years on writing a book when it was
obsolete just before the publishing date from some
new results.

Anyway, the history of science shows us that even some of the most
"indubitable knowledge" some of the
most closely held beliefs turn out to be falsified by future science
discoveries. There was a time when it
was believed that Newton's physics would be everlasting, just as
absolute space and absolute time.

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

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.

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.