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From: Archimedes Plutonium on 10 Aug 2010 12:32
Please note Julia F. Knight and Chandler Davis, you really cannot
ignore this post as asking you to provide your own proofs of Euclid's
IP, indirect. Both of you said mine proof was "not acceptable". If you
continue to ignore, then I will press that both of you be relieved as
math journal editors. Students at both Notre Dame University and
University of Toronto cannot tolerate those in a position that "say
this and this is wrong, whilst they themselves never provide a proof"

Neither Julia nor Chandler can hide from this but must
provide their own Euclid Infinitude of Primes proof of
Indirect Method.

As Julia's letter stated words to the effect: every working
mathematician worth their weight in salt knows
a Euclid proof.


The date on the below message from Notre Dame Univ began bothering me
for it has
no year, so I took the trouble to go through my old records and found
it to be year 1993. Also, I included the year with a "sic"
sign.
And why in the world bother to date a letter absent of the year,
Julia
Knight? I mean, you
are in charge of a journal of logic and something as simple as a
complete date is not
indicative of a person with a high logic mind. Also I was skimming
through the file and
noticed that I had some posters of speakers of physics and
mathematics, and here too,
I should have marked down the year in which those speakers spoke,
because posters
usually do not bother with a year. So if anyone wants to keep posters
for posterity, should
write down the year somewhere -- perhaps on a back corner.




- Show quoted text -
















































Now every math journal editor in the entire world, feels that a proof
of infinitude of twin
primes is going to be some very long expose of 100 pages bearing all
sorts of
detailed arcane subjects of mathematics and which is going to take a
long time to
search through to see if a valid proof.


Not a single math journal editor in the world expects that the proof
of the Infinitude of Twin Primes is as easy as the Euclid proof of
Regular Primes. No-one, not Julia F. Knight nor
Chandler Davis. But the truth of it is that Infinitude of Twin Primes
is as easy as Euclid's proof of Infinitude of Regular Primes if one
uses the Indirect Method. Euclid used the Direct method
of construction. And during the long history of this proof, it became
corrupted of its logic.
We still see more than 50% of the textbooks in math stating that
Euclid did a Indirect method,
when in fact he did a Direct method.


What that means is that no-one in the history of mathematics ever
gave
a full valid Indirect
method of Euclid's Infinitude of Regular Primes proof. Here is the
proof below:


So in words, the Euclid Infinitude of Primes proof, Indirect in
  short-
   form goes like this:


1) Definition of prime
   2) Hypothetical assumption, suppose set of primes 2,3,5,7,.. is
   finite with P_k the last and final prime
   3) Multiply the lot and add 1 (Euclid's number) which I call W+1
   4) W+1 is necessarily prime
   5) contradiction to P_k as the last and largest prime
   6) set of primes is infinite.


That proof immediately is able to prove the Infinitude of Twin Primes
since W-1 and
W+1 are necessarily two new primes which can thence be recursively
repeated in
the Euclid Number for a Y-1, Y+1 ad infinitum.


So what I am saying is that Julia F. Knight and Chandler Davis are
expecting a Infinitude
of Twin Primes proof to be long and hard and dabbling in all sorts of
remote math. When in fact
the Twin Primes proof is all about being able to write a valid Euclid
Infinitude of Regular Primes Indirect.


So, can Julia and Chandler write out a valid Euclid Infinitude of
Primes Indirect? Apparently not so far, because if they can do that
task, they can also prove the Infinitude of Twin Primes.


Both Julia and Chandler, in their communications with me feel that
the
subject of Euclid's Infinitude of Primes proof is a closed field of
study:


Julia F. Knight -- (referee) : "Every working mathematician knows a
correct proof that there
are infinitely many primes"


Apparently Julia is completely and oppositely wrong on that claim,
because if one single person knew of a valid Indirect method of
Euclid
IP, then they would have discovered the proof of Infinitude of Twin
Primes.


Chandler Davis:   "The Infinitude of Primes is not a good field of
study any
  more, evidently."


Here Chandler is being illogical, for on the one hand he issues a
article of "Prime Simplicity" for the Fall of 2009 in Mathematical
Intelligencer over Euclid corrections and here he tells me
words to the effect that the subject field is dead.


But worst of all is that if Chandler Davis could ever pen a valid
Euclid IP, indirect method, if he
could muster the energy to pen a valid Euclid IP indirect, he would
see that he could immediately pen a proof of the Infinitude of Twin
Primes.


So I would call Chandler Davis's assessment of Euclid's proof far
from
being a dead field of study.


And it is rather ridiculous of Davis, Hardy, Woodgold of that Fall
2009 article to excoriate Devlin over his Indirect method, yet where
Davis/Hardy/Woodgold never display their own
Indirect Euclid Infinitude of Primes proof. Is it because neither
Davis, Hardy, Woodgold have
enough math acumen to even attempt to do a Euclid IP, indirect.
Apparently that is the truth.
They cannot, because they have not.


I was looking into the history of Chandler Davis and apparently he
fled from the USA because of some legal issues and fled to Canada. So
is Davis also fleeing from ever showing whether
he can do a valid Euclid Indirect method of Infinitude of Primes? Can
Davis only write nastily
of Devlin over his Indirect, but Davis never able to even do a
Indirect? Maybe the only thing
Davis knows how to do is flee.


I am posting this to sci.edu, because I want colleges, universities
and High Schools and libraries across the world to consider "dropping
the magazine Mathematical Intelligencer"
for the reason that it is a poor magazine about math for it is
lopsided, full of mistakes
and where the editor in chief refuses to reference electronic
newsgroups of sci.math.


I have repeatedly asked for Chandler Davis to include a reference
citation over Euclid's proof
of the Hardy/Woodgold article since I take precedence over them, yet
Davis increasingly refuses to acknowledge the sci.math newsgroups. I
feel Davis and his magazine has "stolen
some of my work."


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: OwlHoot on 10 Aug 2010 14:22
On Aug 10, 5:32 pm, Archimedes Plutonium
<plutonium.archime...(a)gmail.com> wrote:
>
> So in words, the Euclid Infinitude of Primes proof, Indirect in
>   short-
>    form goes like this:
>
> 1) Definition of prime
>    2) Hypothetical assumption, suppose set of primes 2,3,5,7,.. is
>    finite with P_k the last and final prime
>    3) Multiply the lot and add 1 (Euclid's number) which I call W+1
>    4) W+1 is necessarily prime

Not necessarily: W + 1 and W - 1, and for that matter any
integer V +/- W where V and W are any integers whose product
is divisible by all of 2, 3, 5, 7, .., P_k must be divisible
only by primes larger than P_k.

But these "new" primes can divide those integers V +/- W to
a degree greater than 1, and there can be more than one of
them.

The rest of the proof works in the same way though:

>    5) contradiction to P_k as the last and largest prime
>    6) set of primes is infinite.


Cheers

John Ramsden
From: OwlHoot on 10 Aug 2010 14:25
On Aug 10, 7:22 pm, OwlHoot <ravensd...(a)googlemail.com> wrote:
>
> Not necessarily: W + 1 and W - 1, and for that matter any
> integer V +/- W where V and W are any integers whose product

Niggle:

... V and W are any _coprime_ integers whose product ...

In other words, each prime 2, 3, 5, .. P_k divides exactly
one of them to some positive power.

From: Jacko on 10 Aug 2010 18:36
Don't for get to prove that {prime, not prime} or {finite, infinite}
are trivially complete sets. Otherwise the contradiction may lead to a
multitude of possible counter assumptions, and it would not be sound
logic.

not(red) = blue => no green.
not(not(red)) = red or blue or green.
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