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From: Archimedes Plutonium on 4 Mar 2010 02:46
I am going to have to address this issue before leaving this book. The
most
recent latest information on Algebra was that I said that Algebra
falls apart
or breaks down at about 10% of all the numbers that exist. And I
fetched that
conclusion from the Luminet-Poincare Dodecahedral Space in conjunction
with
the boundary of arcs forming triangles and rectangles in Elliptic and
Hyperbolic
Geometry. That boundary is a 10% of a great-circle and the 100-Model
that if
100 was the last number then multiplication is only good to 10 x 10
and fails
with 11x10.

But all of those conclusions preceded the revelation that Infinity =
negative numbers.

So is Algebra as good as the old Algebra? I would say no. I would say
that Elliptic
geometry reminds us that we cannot multiply on large sized triangles
or rectangles
in Elliptic geometry. In Euclidean geometry we an multiply without
limitations of a
length by width. But in Elliptic geometry we cannot multiply a length
by width with
no limitations. Multiplying the Equator by a longitude has no
geometrical meaning.
So it appears that the limitations still are intrinsic to Elliptic
geometry that concavity
combined with rectangles are good for 10% of the length of a great
circle.

So it appears that Algebra is no longer as comprehensive and broad of
a subject
but has been trimmed of its validity. We used to think that Algebra
was all
encompassing of geometry and that we just revise definitions to
accomodate Algebra
in Elliptic geometry. But nowadays, we see Geometry as the bigger
subject and
Algebra as the lesser subject. So that we cannot have a huge sized
rectangle on
sphere model of Elliptic Geometry, means that we are restricted in
multiplication
and that Algebra is only good for about 10% of Elliptic geometry.

So that if 10^500 is the last and largest finite number as is the
South Pole number
then what the boundaries of having algebra of multiplication? Since
the square root
of 100 is 10 and 10x10 is the limitations of multiplication when 100
is the last and
largest number, so is 10^250 the limit of multiplication for Algebra
in mathematics?

So I am afraid, and it looks as though the answer is that Algebra has
become a
smaller subject in mathematics with these revelations.

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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