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From: Archimedes Plutonium on 4 Jul 2010 03:03

Now, curiously enough, this new axiom appended to the existing Peano
Axioms strengthens
the Natural Numbers as defined by those axioms.

New Axiom: define finite-Natural Number as all less than 10^500 (the
largest meaningful
number in physics) and define infinite Natural Number as all those
equal to or larger than
10^500.

So curiously, we find that this new axiom when appended to the old
Peano axioms does
not upset or disturb the existing lot. However, in the program of
building the Rationals and
then the Reals, well, we get into a huge fight because many of the
concepts in the Rationals
and Reals are untenable.

Perhaps the best news of this new axiom is that of our methods of
proof in mathematics
hinges more on brute calculations rather than some clever trick such
as "multiply the lot
and add 1" in infinitude of primes. That is where Perfect Numbers,
Twin Primes, Goldbach,
FLT, Riemann Hypothesis will be proven in going through all the
numbers to 10^500.

Beyond 10^500 is meaningless in physics. You cannot measure beyond it;
you cannot count
to it; you cannot experiment beyond it. So if physics can never do
anything with numbers larger than 10^500, it is rather absurd to think
that some mathematician sipping coffee in
ivory towers has meaning for numbers larger than 10^500.


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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