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From: Archimedes Plutonium on 2 Jul 2010 04:42


Transfer Principle wrote:
> On Jul 1, 10:50 pm, Archimedes Plutonium
> <plutonium.archime...(a)gmail.com> wrote:
> > Transfer Principle wrote:
> > > Actually, I take that back. I suppose that one could include
> > > 10^500 by stating, "if no odd perfect number less than 10^500
> > > exists, then no odd perfect number exists." As of now, it's
> > > proved that no odd perfect number less than 10^300 exists, so
> > > we still have 200 orders of magnitude left to go before we
> > > reach AP's limit.
> > How far has the Riemann Hypothesis been checked out for? Is it 10^20?
>
> So far, about 10^13 nontrivial zeros of zeta have been confirmed
> to have real part 1/2. The imaginary part of the last known
> zero is also within an order of magnitude of 10^13.
>
> > How far has FLT been checked out? Is it 10^10?
>
> FLT has been completely proved. Therefore, it works for all
> natural exponents, 10^500 and beyond.

Disagree. The Wiles allegedry never distinguishes between a finite-
number and
a infinite-number, as a geometer could never get away with geometry
without
precision defining finite-line versus infinite-line. So Wiles never
proved anything.

FLT is still open to proof and the only proof is to show that it is
true for the first
10^500. There are boatloads of counterexamples in p-adics. I doubt
there is any
counterexample in the first 10^500, but I can be surprized real
easily. Peano
in his axioms never distinguished an infinite-number from a finite-
number and
so all the math proofs prior to a precision definition of infinite-
number versus
finite-number are suspect as not a proof at all.

>
> > How far has Goldbach been checked out? Is it 10^15?
>
> Thereabouts.
>
> > Say, LWalk, can you help me out on public relations? I have used the
> > term "old-math" but such a moniker has been used throughout history.
> > So I need a new moniker. Should I call it the "ill-defined math", or
> > how about "sloth-math" since the community knows they never defined
> > finite number versus infinite number? Or how about "rumdummy math"
> > which has that poetic ring and someone can use it in a song. Can you
> > help me out on this, because math is supposed to be the science of
> > precision but noone seems to care to do their jobs of defining
> > finite-number versus infinite-number. Should I call it rumdummy-
> > math? I like the ring of that.
>
> For some reason, I doubt that the the users of "rundummy-math" would
> like the ring of that name.
>
> I just prefer to call it "standard math," since, as of today, it is
> the standard theory.

I do not know which came first, the physicists calling their particle
physics as the
Standard Model or the mathematicians calling their accepted axioms and
theorems
as the "standard theory". I think a better name would be Accepted
theory. Because
in a hundred years from now, what was standard today will be
trashcanned or modified by the
next century.

The Standard theory of mathematics is missing a precision definition
of finite-number
versus infinite-number. That is a huge gaping hole in all of
mathematics and affects even
geometry. Because you cannot build a infinite line ray out of line-
segments.
You need a infinite-number of line-segments to build a infinite line-
ray.

So the Standard theory of mathematics is a flawed system and this is
very evident in that
we have conjectures dating over 2,000 years old-- perfect numbers and
twin primes. What is
blocking their proofs is the lack of defining finite-number versus
infinite-number. The flaw
of lack of a precision definition is what is backlogging most of those
unproven conjectures.

So to call our present day theory of mathematics the Standard theory
should have a subtraction in it.

Standard Theory of Mathematics minus a precision definition of finite-
number versus infinite number.

That is a whole sentence for a moniker and I need something shorter.
Something like Rumdummy-Math.

Or how about Imprecise Math rather than Standard Math.

Would you accept Imprecise-Math as what you call Standard Math, LWalk?

Imprecise-Math does not offend anyone, LWalk, so I much prefer
Rumdummy Math,
because it gets a better reaction by the listener, to understand that
they never defined
finite-number versus infinite-number.

Perhaps it should have been added into the Peano Axioms of a precision
definition of
finite-number? A new axiom stating that finite-number are all those
numbers less than
10^500.

Of course, if that were tacked on, then all of Cantors nonsense would
be recognized as
nonsense. And that even the proof of Godel's undecidables is further
nonsense since
his proof never recognized finite-number versus infinite-number.

So a precision definition of finite-number versus infinite-number
would sweep clean much
of mathematics as we know it. The Calculus would remain the same but
all that nonsense
about continuity would be thrown out, since the world has no
continuity as imagined by
mathematicians. This is another one of those philosophy or religion
ideas that crept into
mathematics. So there would be a little cleaning up in Calculus as for
the limit concept,
but most of Calculus remains untouched as to its usefulness.

So when mathematicians refuse to recognize their mistake of never
precision defining finite-number versus infinite-number, it is not
proper to call theirs the Standard theory but rather the
Imprecise theory.

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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