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From: Archimedes Plutonium on 27 Jan 2010 04:39
This theorem is important in two aspects. One, it changes all of
current math
for it destroys much of what was considered to be math but as it turns
out
was just fiddling idealism such as Cantor transfinites. This theorem
also
places a new method to mathematics such that any conjecture has a
time limit of finding a proof. This theorem solves the Riemann
Hypothesis,
Goldbach Conjecture, Perfect Numbers, Fermat's Last Theorem, and
almost
all other unsolved problems. The new method of mathematics is that
math
is mostly confined to two basic numbers of 10^500 for the large scale
world or macroworld and confined to 10^-500 for the microworld. But
the biggest
change to mathematics and the greatest importance of this theorem
is that for the first time in math history do we actually see that
Physics
is dominate over mathematics and that math is a subset of physics.

Let me comment that I was surprized for in the last few days of
working on
this proof that I thought it was going to be extremely difficult and
that
it would be murky. But just the opposite happened in that it turned
out to
be extremely easy and short and brief.




Theorem: A precision definition of the concept of finite versus
infinite such
as in particular finite-number and infinite-number, and in geometry
finite-line
versus infinite-line require a picking or selection of a member of
those numbers
or line-segments as the end of finitism and as the boundary of
finitism and where
this boundary is the start of infinite entities.


PROOF:

In Numbers there is no precision definition of finite-number versus
infinite-number.
So we turn to geometry where there is a precision definition of finite-
line versus
infinite-line: to wit:

finite-line: is a line-segment meaning that it has two endpoints
infinite-line: is a line-ray meaning it has one endpoint and has a
arrow at the other
end indicating that has no fixed endpoint.

So the proof goes like this-- where I prove that since geometry has a
precision definition
that I show where geometry must have or is forced to have a Selection
of a line-segment
which marks the boundary of finite-line from infinite-line. And once I
show that, I transfer
that to Numbers which must have the same schemata of a Selection of a
number as the
boundary between finite-numbers and infinite-numbers in order for a
precision definition
in Numbers.

Consider this line-ray:


---------------------------------------->
0 1 2 3 . . . . infinity

By logic this line-ray has to yield all the line-segments
and all the line-rays.

Now the above line-ray can be put into a correspondence
of the largest line-ray with the largest line-segment.

The largest line-ray is the above line-ray itself.

Now I seek the largest line-segment.

There has to be a largest line-segment, since by logic there is a
largest line-ray,
and this largest line-segment must be somewhere between 0 and the
arrow that
goes to infinity as depicted above.

Can the largest line-segment be infinitely long? Of course not for it
would
then be a line-ray and not have two endpoints.

Must a largest line-segment exist? Yes of course it must exist
in that it has two endpoints and it cannot be an infinite-ray. And it
must be between 0 and infinity. It must exist since a largest line-ray
exists.


So here is a forced Selection. In that we are required to correspond
the largest line-ray since we do have a largest line-ray, and so, we
must have a largest line-segment.


Hence, we must Pick and Chose and Select a line-segment and call it
the boundary between line-segments and line-rays.


The obvious idea in this proof is that there is a largest Line-ray and
that forces
me to find the largest line-segment to match in a correspondence with
the largest line-ray. If there is no largest line-segment means
that there is a line-segment with is the same as a line-ray, thus a
contradiction.

QED

Now Physics steps into this picture by saying that the only natural
choice or selection
for the finite-number boundary or the line-segment boundary is the
Planck Unit
of 10^500 since physics will never need any number larger than that
since there is
no more physics measurement above 10^500 nor below 10^-500.

So, now, I transfer the above theorem to the Peano axioms and the
Natural Numbers
by saying that finite-numbers stop at 10^500 and that beyond are all
infinite-numbers.

And the last and largest infinite-number, similar to the line-ray in
the proof is the
number 9999....99999. And like in the proof above, the number
9999....9999 as the
last and largest infinite-number would correspond to the last and
largest finite-number
of 10^500. The smallest finite-number is 0 and it would correspond to
the smallest
infinite-number of (10^500) + 1. By the way, this is not a 1 to 1
correspondence but
just a correspondence.


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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