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From: Archimedes Plutonium on 13 Jul 2010 02:16
Now here is a very nice place to talk about if mathematics had a
precision definition
of finite-number versus infinite-number as that of 10^500. And we
should take a peek
of the numbers above 10^500 and feel assured that Twin Primes, Quad
Primes, N+6
primes are all to be found for numbers beyond 10^500 and thus proofs
that Even N
Primes are each infinite sets.

Another nice benefit of 10^500 is that if one detests Indirect method,
well, dispense
with it entirely for every proof can be followed into 10^500 where
mathematics domain
lies and no further.

In philosophy of old, they used to talk about "the present bald king
of France." Sort of
a joke you see, because France has no more kings, so the whole thing
is a piece of
fiction imagination. But it still conjures up a image in people's
minds.

Same thing is true if you say Primes are infinite where there is no
10^500 boundary.
And so we have numbers such as "pi" without decimal points going like
this
314159........ and if we turned it around like this ......951413, and
we know pi is
irrational, even transcendental, and would this number have those
features ....951413
and would .....951411 be twin primes? Or Champernownes number of
123456789101112....
turned around as .....211101987654321 and would .....211101987654323
be twin primes?

You see, when math does not well define what is infinite-number, it is
no wonder that
it gets into trouble with almost every conjecture that deals with
infinity.

If math defined infinite-number as 10^500, twin primes, quad primes,
perfect numbers,
Goldbach conjecture, FLT, Riemann Hypothesis would not be horrible
unproven problems,
for they would be understandably true since numbers beyond 10^500
confirms all those
problems. Confirmation is not a proof, for we would actually have to
go through every number from 0 to 10^500 to prove say FLT or RH or
Goldbach, but confirmation is that if we see
solutions for RH or Goldbach or FLT holding true at 10^600 then we
would say "tentative proof"
and that all proofs are Direct Method, construction.

You see, when math has an Indirect proof method, means that math pits
all the axioms and
theorems against a supposition. Hardy in his book A Mathematician's
Apology describes this
gambit more poetically than I am describing it. There is a problem
with Indirect, in that you cannot be sure that the axioms of math and
consequent theorems are a consistent set, and
another problem is that you cannot be sure that Mathematics is only
linear logic, for it probably
is duality logic like physics, and so, the Indirect Method is a very
erroneous method to attain
knowledge. Physics does not use Reductio Ad Absurdum to base physics
knowledge upon. Physics rests solely on Experimental Knowledge, some
Observational Knowledge, but nowhere in physics is there this reliance
on a reductio ad absurdum for which mathematics
rests much of math knowledge upon.

So you see, if math defines infinite-number as 10^500 and beyond, all
of a sudden, mathematics is all Direct Proof Method. All of a sudden
we can determine if Twin Primes
and Quad Primes are infinite just by looking to see if they continue
beyond 10^500. We
can confirm that FLT, Goldbach and RH are true by sneeking a peek
beyond 10^500 if
they hold. We would instantly know that the Poincare Conjecture is
false and never was
true, even though some recent blabbering and blubbering of alleged
proof. PC is false because
the world does not have absolute-continuity. Continuity breaks down at
10^-500 when
10^500 is infinity. In the microworld, there are holes between
numbers. So the reason
PC was never proven is because the fabric of space was never absolute-
continuity.
The betweeness axiom in Euclidean geometry is inconsistent with the
parallel axiom
of geometry.

Now you can make a modified Poincare Conjecture and easily prove it,
by saying that
all closed loops can be shrunk to a point of 10^-500 or larger but not
below that point.

You see how much easier the world would be, would be for mathematics
if they precision
defined finite-number versus infinite-number. Overnight, mathematics
would be a cleaned up
house, rather than a house of grime and mess.

No longer would there be a need for the Indirect Proof method. All
proofs of mathematics would be Direct construction. If all even
numbers from 0 to 10^500 obey Goldbach conjecture
then it is proven true. Since our computers cannot do that, we can
estimate or confirm that
Goldbach holds true for numbers beyond 10^500 and is thus likely to be
true.

Now some may complain that 10^500 is a artificial boundary. But they
do not know much
of anything about the world. That number is so large that there is
nothing in physics beyond
it. That number covers all of physics, and since physics is above
mathematics, then anything
that mathematicians do that is beyond 10^500 is just purely their
imagination run amok.

When I did the AP-adics and was talking about numbers like these:

99999.....99999, and 99999.....999998, and 999999.....999997, and
wondering if
9999.....99997 was the worlds largest prime number. And whether
99999....999991
with 99999....9999989 was the worlds largest twin primes. With these
infinite integers
we get a sense of a vast world that where all the definitions of math
can be turned topsy turvy.
One can create numbers that are neither composite nor prime. One can
create an integer that
is transcendental. Another that is neither rational nor irrational.
All because infinite-number
is not precisely defined.

Ironic that in year 2010, the only human to voice a complaint that all
the sciences from
astronomy to physics, to chemistry to biology solved all their
problems that were started
in Ancient Greek times, except for one science -- mathematics. The
science that is supposed
to be the science of precision still has Perfect Numbers and
Infinitude of 2N Primes unsolved. Reason for this is really quite
simple. Math refuses to precision define finite-number
versus infinite-number.

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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