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From: Archimedes Plutonium on 28 Jun 2010 15:15


David Bernier wrote:
> Archimedes Plutonium wrote:
> >> [0] Michael *Hardy* and Catherine Woodgold,
> >> "*Prime* *Simplicity*", *Mathematical
> >> Intelligencer<https://mail.google.com/wiki/Mathematical_Intelligencer>
> >
> >
> > I was contacted that the above has Archimedes Plutonium's ideas
> > published in Mathematical Intelligencer.
>
>
> The authors write that Euclid's proof that there is no largest
> prime number is a constructive one. They mention several
> forms of distortions that misrepresent the proof, for example
> those who say that Euclid's proof was a proof by contradiction.
>
> Harold Edwards wrote a letter to the Editors showing his
> enthusiasm at having the proof presented as it appears
> in the Elements.
>
> Cf.:
> < http://www.springerlink.com/content/m0t8727288823ug5/ >
>
>
> [first page only to non-subscribers].
>
> David Bernier

Funny how they say get your information faster on the Internet. But
when it comes to basics such as a mailing address for Mathematical
Intelligencer MI, one has to run to an actual
hardcopy.

Hard for me to understand Harold Edwards enthusiasm for finally
exposing the truth about
whether Euclid's Infinitude of Primes (IP) proof was direct or
indirect, when according to Wikipedia that Mr. Edwards had
enthusiasm for the fake proof of Fermat's Last Theorem of Wiles,
considering it is a fake proof because Wiles never defines what is the
difference between a finite number and an
infinite number. You see, in mathematics, if you leave the question
unanswered as to when
numbers become infinite numbers and no longer are finite numbers, then
you end up with a
whole gaggle of statements that can never be proven true or false. I
am not talking about
undecidability, but am talking about, simply precision of definition
which is the main job of
mathematics in the first place.

Fermat's Last Theorem has boatloads of numbers that satisfy
a^n + b^n = c^n to any exponent when a number is ambiguous as to
whether it is finite or infinite. The Peano Axioms never well-defines
the difference between a finite number and
an infinite number. Ask anyone what finite number means and then ask
them whether
.....33333 is finite. According to Peano axioms and Fermat's Last
Theorem the number
.....33333 is as finite as the number 3 because the Peano axioms never
tells us where
finite ends and infinite begins. And this is the reason Goldbach
Conjecture, Fermat's Last Theorem, Twin Primes, Riemann Hypothesis
have no proof, nor will they ever be proven so long as noone
in math gives a **precision definition of finite versus infinite
number**. Some people may
think, oh well AP is just complaining, but then look at geometry where
they do well-define
a finite line as a line segment and a infinite line as a line ray or a
ray infinite in both directions.
If Geometry is wise enough to well define finite line from infinite
line, then why is number
theorists too dumb and too stupid to well define finite number from
infinite number? Is it because, well, too many mathematicians will
have the shame of pie in their face?


Now I did give a precision
definition of finite number versus infinite number and it is the only
way to go on this chore.
I used the king of science-- physics, because physics contains all of
mathematics as a tiny
subset of itself. In physics, numbers give out at 10^500 for integers.
That number is so huge,
that their is nothing in physics of the Planck Units that makes any
physical sense. But mathematicians are really not very bright and not
very smart of a class of people. Mathematicians in large part are
lemmings and parrots who follow fashion trends of any
given century rather than follow Physics and Logic. If you define
Finite as all the numbers
smaller than 10^500, you instantly clear out all of those Number
theory problems unsolved
and unsolvable.

Now it sounds as though I am pretty harsh on mathematicians and on
Harold Edwards,
which according to Wikipedia Mr. Edwards is a founder of the magazine
Mathematical Intelligencer.

But I am not harsh enough, because mathematics has progressed so far,
so fast, but
it cannot even address and correct something as old as Euclid's
Infinitude of Primes proof
when such is under scrutiny. Mathematics is too much of a old man's
clubhouse that
entrenches fake math. And Mr. Edwards is part of that problem itself.

Did Edwards ever write out a Euclid Infinitude of Primes proof in one
of his books? I would
guess he did. And I would further guess that Edwards was never bright
enough to do both the
direct and indirect method of proof. No, I would guess that Edwards,
as a founder of MI,
was not even bright enough to ask some writer to expose both a valid
direct and valid indirect
proof of IP in a MI issue. About the only brightness of Edwards
concerning Euclid's IP is to
get some authors to talk about a statistics of how many thought
Euclid's IP was constructive
or contradiction. A statistical expose of how many mathematicians
voted constructive rather
than contradiction. That is not really much progress but it is snail's
pace progress.

A bright editor, on the other hand would have summoned someone to
write a article exposing what the valid Euclid IP constructive versus
the valid Euclid IP contradiction methods looked like. Edwards was not
bright enough for such a project, because, probably, Edwards was never
able to give a valid Euclid contradiction proof himself.

To give a valid Euclid contradiction method proof means you must say
in the proof that the
Euclid Number is necessarily prime, otherwise your attempt is an
invalid proof. Edwards probably never could see that, and so we have
at best from MI a statistical article, or a roll-call
of how many mathematicians think Euclid IP is constructive "please
raise your hands".

We don't have an Edwards in control of the situation. An Edwards who
wants the "real and whole truth" about Euclid's Infinitude of Primes,
who is not a scaredy-cat about printing a valid direct alongside a
valid indirect.

Why do we not have that? Because obviously, about 90% of all those
mathematicians who
ever wrote down a Euclid IP in book or print form, have a mangled and
garbled mess and invalid proof. Imagine that, 90%
flunking in a Euclid IP proof. That is worse, by far than a freshman
Calculus class on a surprize quiz.

The Internet and newsgroups such as sci.math is helping mathematics by
training our focus
away from magazines and publications, which is a good thing. Because
the major reason that
math is so slow in correcting itself and why math has fakeries such as
Cantor infinities and
Godel nonsense and Wiles FLT, is that fakeries can hide behind
entrenched math publications. The Internet is "open to all" and
admittedly most of the Internet is worthless nonsense, but the small
percentage of the best of the Internet quickens the pace of fake
math being exposed. Fake math that hides behind entrenched journal
writings.

We now have the question of whether Euclid IP is direct or indirect by
this article of
Hardy/Woodgold/MI. But the deeper question as to "could any
mathematician prior to
1993, ever give a valid Euclid IP indirect?" I say noone prior to
1993, realized that
Euclid's Number must necessarily be prime for the proof to be valid.

So, does Edwards have the audacity, the integrity to have a writeup in
Mathematical
Intelligencer exposing the fact, the idea that only when Euclid's
Number is necessarily
prime that you have a valid reductio ad absurdum proof of Infinitude
of Primes? Does Edwards
measure up to the contest of valid indirect method?

Can someone please post the mailing address of Mathematical
Intelligencer.

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
From: sttscitrans on 28 Jun 2010 15:37
On 28 June, 20:15, Archimedes Plutonium
<plutonium.archime...(a)gmail.com> wrote:
> David Bernier wrote:
> > Archimedes Plutonium wrote:
> > >> [0] Michael *Hardy* and Catherine Woodgold,
> > >> "*Prime* *Simplicity*",  *Mathematical

> To give a valid Euclid contradiction method proof means you must say
> in the proof that the
> Euclid Number is necessarily prime, otherwise your attempt is an
> invalid proof.

I see you still have not grasped a few simple ideas.

1) Every natural greater than 1 has a prime divisor
2) GCD(n,n+1) = 1

3) If there is a last prime then GCD(w,w+1) <> 1
Contradiction.

Therefore, the number of primes is infinite

Presumably even you can see that 1) and 2) are true statements
and that the assumption that primes are finite in number leads
to the contradiction GCD(w,w+1) <> 1

The necessity of "necessary primes" is simply
a delusion on your part
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