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From: Archimedes Plutonium on 10 Mar 2010 00:52
Alright, let us look at the Algebra Number Wheel for the numbers from
0 to 99.

We would have 0 as 00 and 1 as 01 and 2 as 02 and further up 99 as 99.

Now we suppose that 99 is the last and final finite number. And that
100 is thus
the start of infinity. But Infinity is the negative numbers and in the
Algebra Number
Wheel the largest Infinity Number is 9999....99999= -1 but in this
model where
99 is the largest finite number and where 100 is infinite then the
largest infinite
number becomes 999 = -1, 998 = -2, on down to 900 which is -99.

That is the Algebra Number Wheel for the case of when 99 is the
largest and last
finite number.

Now let me apply Euler's Identity to this 99 Model. Euler's Identity
of e^(pi)(i) = -1

So we have 2.71^(3.1)(9) = 999 or we have 2.71^(3.14)(3) = 999,
depending on
whether (i) is the 9s pattern or the 3162... pattern:

sqrt9 = 3
sqrt99 = 9.94
sqrt999 = 31.60
sqrt9999 = 99.99
sqrt99999 = 316.22
sqrt999999 = 999.99
sqrt9999999 = 3162.27

Apparently for the 99 Wheel of Numbers (i) is the 3162..... pattern
for it yields
a 9.... result in the Euler Identity

So if 99 were the last and largest finite number then (i) would be
3...

And if there are no fractions in this wheel then all the numbers are
listed
from 0 to 99 with their negative number counterparts. Obviously 3...
is
not amoung those numbers.

So this gives new meaning to what I have been calling the Incognitum
of a vast zone of numbers but which have no reliable algebra or
multiplication.
Nor does the infinity=negativenumbers have an algebra that is
trustworthy.
The only trustworthy zone of numbers for algebra are the finite
positive numbers.

The finite positive numbers occupy 1/2 the wheel of numbers and the
other
hemisphere is the negative numbers corresponding to the positives.

Now I can make an Algebra Wheel of Numbers if the last and largest
finite
number is 10^500 with its inverse of 10^-500.

These wheels of numbers show us for the first time in mathematics what
the
(i) value is in the Euler Identity. And in the past history, we could
never flesh out
what (i) value was. The reason we always failed is because Finite was
not defined
precisely. Once you define finite, there is a last and largest finite
number and its
inverse. This limits or forces a boundary conditions on what pi and e
and (i) are.
In the case of the 10^500 Wheel, we can only use about 10^-100 of
place value
for pi and e, since we cannot go less than 10^-500. So that the Euler
Identity
remits the 99.... for the 9999..99 = -1. We only need several 9s
digits in the
frontview to satisfy the Euler Identity.

The Algebra Number Wheel is new to mathematics. That is a good name
for it,
time being. The Wheel shows us what is trustworthy for Algebra to
handle and
cope with in terms of, especially multiplication.

And the Wheel reminds me of Physics of virtual particles in quantum
mechanics.
A better name for (i) imaginary as square root of -1 would have been a
"virtual number".
In physics, virtual particles come in and out of existence routinely
and they are not
independent existing particles but merely some proton, or electron or
neutron with
more energy than they usually have. Virtual particles are energized
common particles
and they help to balance the laws and forces of physics.

Now someone reading this for the first time may say "why believe in
this wheel?"

And I would retort that old math never precision defined Finite
Number. Math must
precision define finite-number, and that requires a selection of a
last and largest finite
number. So the moment you select the last and largest finite number,
you are forced
and required to accept and use the Algebra Wheel of Numbers. So
mathematics
has no choice about Number Wheels, for everyone in math must have a
precision
definition of finite-number and that leads to a forced acceptance of a
Algebra Wheel
of Numbers. And that forces the recognition that Algebra is only
trustworthy for about
10% of all the numbers that exist.

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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