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From: Archimedes Plutonium on 17 Sep 2009 17:16

Bill Dubuque wrote on Sep 17, 2009 12:39 PM
> juandiego <sttscitrans(a)tesco.net> wrote:
> >
> > depending on how you formulate the argument
> > you can derive different contradictions ?
> >
> > 1) A natural >1 is prime iff it has no proper
> divisors
> > 2) Every n > 1 has a prime divisor
> > 3) assume a <b <c are the only primes
> > 4) z = abc+1 > c => z composite
> > 5) z has no prime divisors
> > 6) z is composite contra z has no prime
> divisors
> > or 6') z = 1 contra z > 1
>
> I've emphasized this and many other variations since
> at
> least 2003, e.g. see [1], [2], [3]. This has not
> convinced
> AP yet. So why do you think that merely repeating
> exactly
> the same old arguments will have any success? There
> is
> nothing in this thread that hasn't already been said
> many
> times before. You are severely beating a dead horse.
> Please TTTTT (terminate tickling the troll's tail)
> http://google.com/search?q=tickling+the+dragon%27s+tai
> l
>
> --BD
>


I should pause here and dwell on the above misconception of Bill
Dubuque about mathematical proofs and the Indirect method especially.
For it is
BD's misconception that fans others like Iain Davidson
in never a understanding.

The most worrisome misconceptions of BD is his statements such as "any
contradiction works" and
Euclid's IP proof has numerous valid variations. Another one of his
misconceptions is that W+1 as
necessarily prime is only one of many organized
variations.

So let me dive into this BD list of misconceptions with
some detail.

First of all, it is a poor mathematical judgement call on
the part of BD to think there are a numerous valid variations of a
mathematical proof of a statement. If one reflects for a moment on how
math is constructed,
its foundation and structure, that there should be only
one valid proof of a statement given a fixed set of
elements of that statement. And that variations are not
independent valid proofs but merely tacked on irrelevancies.

So for example, BD believes that Euclid IP with its fixed element of
construct W+1 has a dozen or more
valid Indirect proofs. AP believes that this Euclid IP
has only one valid proof and that any variation is just
added on irrelevant nonsense which when trimmed away, leaves only the
one valid proof.

So that when Iain Davidson comes running in with his
prime divisor theorem, he fails to discharge the reductio
ad absurdum step and he adds on the irrelevancies of
that theorem. So that BD would say that Davidson had
a independent and valid proof of IP indirect, whereas
AP would say that Davidson had a invalid proof because he failed to
properly do the logic to discharge the assumption.

So it all boils down to that BD thinks Euclid's IP indirect has a
dozen or thousands of independent and
valid proofs. AP would counter, and say that there exists only one
valid proof, and if someone varies from
that valid proof by tacking on irrelevancies, it makes the proof
longer, but if they fail to put together the logical steps, then their
attempt is invalid.

So AP says that there is only one valid proof without
irrelevancies. There can be other valid proofs but they are longer
since they have irrelevancies. But that most
proof attempts such as Davidson or Dubuque's fail to
have the correct steps of logic and thus are invalid.

Now why BD believes there are numerous valid and independent proofs of
Euclid IP indirect is beyond my reasoning. My reasoning follows from
my familarity of
mathematics in whole and such as the Hardy statement in his book A
Mathematician's Apology. Hardy remarked with words to the effect that
Reductio
ad Absurdum is the ultimate gambit where you offer up
the total subject of mathematics to squeeze out a contradiction.

Now if anyone pauses and reflects on that Hardy evaluation of
mathematics and has spent any time
in math making Indirect proofs, would instantly recognize that
Euclid's IP should not have a dozen or
more independent valid indirect proofs. That Euclid's
IP indirect should have only one narrowly constrained and confined
valid proof given W+1. That math is not
built so wide open and sloppy as to offer itself up in a
gambit where a dozen or more independent and valid IP
indirect exist.

As I said, there can be alot of offerings where irrelevant
garbage is packed into the offering, and although excessively long
when it can be shortened does not invalidate it. But as the case of
most of these irrelevant
packed offerings, it is the lack of logical inferences and
discharging of previous steps that makes their garbage
filled attempt invalid.

Neither Davidson nor Dubuque, as far as I have seen
on sci.math, deliver a LongForm of Euclid's IP direct
and indirect. Theirs has always been abbreviated steps
and steps in midair. Without the LongForm, noone can
assess that they ever reached a valid proof, but only a
invalid proof.

In the world of mathematics, it is wrapped around so tightly of its
structure, that there is only one valid proof
of Euclid IP. There can be tacked on irrelevancies that
makes the valid proof longer, but still valid. But there are no other
independent and valid proofs of Euclid IP
indirect. The offerings given by Dubuque and Davidson
have not been valid because of lack of proper logical
inferences-- they fail to discharge the assumption step.
Their attempts are not invalid because they tack on superfluous
irrelevancies, but invalid because they never have the proper sequence
of steps to prove the
problem.

Maybe BD is confused about mathematics proof because he sees a
topological Euclid Infinitude of Primes proof or some other area of
math that has
a proof of Euclid IP. If anyone stopped to think about
it, there are no dozen or so independent topological
proofs of Euclid IP, there is just one, and someone
can add irrelevancies to the topology IP that is still valid, but if
one were to omit key steps, then the topology proof is also invalid.

So it is about time that BD stops fanning his misconceptions for it
only further buries Iain Davidson
with his misconceptions.


Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
From: juandiego on 18 Sep 2009 13:02
On 18 Sep, 04:48, Owen Jacobson <angrybald...(a)gmail.com> wrote:
> On 2009-09-17 17:16:26 -0400, Archimedes Plutonium
> <plutonium.archime...(a)gmail.com> said:
>
> [snipped]
>
> Essentially, your point is given a finite set of primes p, then ∏p + 1
> is also prime, yes? And that any proof that talks about cases where ∏p
> + 1 is not prime are "unnecessarily" adding "irrelevant" details?
>
> Consider the case where the set of primes is p = {2, 3, 5, 7, 11, 13}.
> Therefore,
>   ∏p + 1
>  = (2 * 3 * 5 * 7 * 11 * 13) + 1
>  = 30030 + 1
>  = 30031
>
> Note also that 59 * 509 = 30031, so 30031 is /not prime[0]/.
>
> I know this has been raised to you before; if you addressed it, I
> must've missed it and I'd appreciate a message-id so I can look it up.
>
> -o
>
> [0] given that a number is prime if and only if its only divisors are
> itself and 1.

This, of course means.
that 1 is prime (iself (1) divides 1 and 1 divides 1)

z =(1 * 2 * 3 * 5 * 7 * 11 * 13) + 1

1 divides z so the claim that none of the primes that
are assumed to exist divide z is false. z is necessarily
composite.
Of course. if you are AP you can accommodate the
idea that 1 is both prime ans not-prime in the
AP-exrectolocutionary domain of copristic numbers.
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