Prev: HISTORIC SPECIFIC MATHEMATICAL PROOF AGAINST CURRENT MATHEMATICS GIVEN TO PROFESSOR EDDIE ESCULTURA BELOW
Next: deriving speed of light out of raw pure math Chapt 19 #206; ATOM TOTALITY
From: Archimedes Plutonium on 27 Jun 2010 16:25
> [0] Michael *Hardy* and Catherine Woodgold,
> "*Prime* *Simplicity*",  *Mathematical
> Intelligencer<https://mail.google.com/wiki/
Mathematical_Intelligencer>

First off, let me apologize to Catherine Woodgold, for I mistakenly
somehow
typed in Moongold and that word seemed to have electronically
increased,
and where that came from, I have no idea other than in the
heat of anger of seeing part of my work printed without any
attribution towards
my long hours of work.

In that Mathematical Intelligencer (MI) article, I see now that Hardy/
Woodgold
and MI editors are complaining only about whether mathematicians saw
Euclid's IP
as either direct-constructive or as a indirect-contradiction proof and
were lambasting
those that figured Euclid's IP was indirect. I too, was lambasting all
those who
thought Euclid's IP was indirect.

But the major difference between me and the MI/Hardy/Woodgold, is that
I posted
from 1993 to present that few if any mathematicians had a valid proof
argument for
the indirect Euclid IP. So I lambasted the mathematics community for
two things--
(a) Euclid's IP was direct-constructive and not indirect-contradiction
(b) few if any
mathematician ever did a valid indirect-contradiction method proof.
Whereas MI/Hardy
/Woodgold is lambasting for one thing-- that Euclid's IP is direct
contructive.

So it is on the (b) feature that MI/Hardy/Woodgold are silent about in
their MI article
and for which in that article, one can see that the editors of MI and
Hardy and Woodgold
would not be able to do a valid Euclid Infinitude of Primes proof
indirect-contradiction
based on the fact that in their opening paragraphs MI/Hardy/Woodgold
write this:

--- quoting from Mathematical Intelligencer their article ---
Then he said, ‘‘By our assumption, no
other primes than those exist. This number is therefore not
divisible by any primes. Since it is not divisible by any
primes, it must itself be prime. But that contradicts our initial
assumption that no other primes than p exist.’’
We shall see that this account of what Euclid did in his
famous proof of the infinitude of primes is commonplace
among some (not all) of the best number-theorists and
among a broad cross-section of mathematicians and others,
and that it is historically wrong.

--- end quoting ---

--- quoting MI ---
Only the premise that a set contains all prime numbers could
make one conclude that if a number is not divisible by any
primes in that set, then it is not divisible by any primes.
Only the statement that p is not divisible by any
primes makes anyone conclude that that number ‘‘is therefore
itself prime’’, to quote no less a number-theorist than G. H.
Hardy
--- end quoting MI ---

MI/Hardy/Woodgold are wrong on those ideas quoted. And those quotes
evinces me, at least me, that MI/Hardy/Woodgold could not do a valid
Euclid Infinitude of Primes proof because they could never stomach a
step in which it says "Euclid's number is necessarily a prime number".

You see, the editors of MI, and Hardy and Woodgold have that all
wrong.
The above is actually the valid proof of Euclid IP indirect-
contradiction. Provided
the definition was the first step in the proof which would force
Euclid's number
to be necessarily prime.

That Euclid's number is indeed a necessarily prime number given the
assumption
space ordered up by the reductio ad absurdum method. Under that
assumption,
if 3 and 5 were the only primes in existence, then Euclid's number 16
would be a
prime number in that assumptive space. What the editors of MI and
Hardy and
Woodgold fail to understand is that the only valid contradiction proof
has Euclid's
number a "necessarily prime number".

It is due to this confusion, that many thought that Euclid's IP could
be either constructive
or contradiction. But when you realize that Euclid's number is
necessarily prime in the
contradiction method, then you realize that Euclid's IP proof could
only have been
constructive increasing set cardinality, for Euclid never states that P
+1 was necessarily
prime.

So I should include this MI article with the editors of MI and Hardy/
Woodgold as unable
to deliver a valid contradiction proof of Euclid's Infinitude of
Primes proof. And although
this article does point out one truth-- Euclid's proof was direct
construction. This article
only contributes far more confusion to the issue than what it is worth
to have in
print.

One of the main reasons that there is so much confusion and mistakes
over the
Euclid infinitude of primes proof is because of lack of logic. Lack of
logic to list
both methods, up front in the first paragraph. Why chitter chatter
around with
a metaphorical classroom teacher.

For anyone to clear the confusion would have to be able to submit both
the methods of
proof to contrast one another and that is where MI/Hardy/Woodgold have
failed miserably
and have only added to the confusion.

In as few of words as possible the mistakes made are these when doing
both methods
simultaneously:
(a) most people forget that the definition of primes is the first
statement
(b) set cardinality increase to any finite set is the constructive
method and it
may have a lemma in there about fetching the new prime, but the fact
that you
are increasing set cardinality makes the method, unmistakeably
constructive.
And in fact, no lemmas are needed, but when a confused lad or lassy
enter
a lemma, well, its excess baggage
(c) the most often occurring error in Euclid IP and which has tripped
up most
mathematicians doing it, is that in the contradiction method, Euclid's
number
is necessarily a new prime. Most people trip up on this because they
forget that the
reductio ad absurdum structure demands P+1 to be prime, and in their
tripping up,
they cite goofball examples such a 2x3x5x7x11x13 (+1) has prime
factors. This is
goofball logic because under the assumptive space of reductio ad
absurdum that
those primes were all the primes that existed and hence P+1 is
necessarily prime
no matter what examples you pull out of your hat, for when you assume
that 3 and
5 are the only primes that exist in contradiction method, then 16 is a
new prime in that
space. This is very hard for even top mathematicians, let alone the
general public
or MI editors or Hardy and Woodgold to understand.

The formal LOGIC demands that Euclid's number P+1 is necessarily prime
in
the contradiction method.

But I still will send a letter to MI editors, scolding them for their
lack of attribution
for my 16 years of hard work and postings to sci.math for which that
article lifted
much of their conclusions, although not their mistakes, from my
postings.

I will ask MI editors to include my name with attributions to that
article of Hardy and
Woodgold in a future issue correction page, citing Archimedes
Plutonium's sci.math
postings on the subject of Euclid's Infinitude of Primes proof from
1993 to 2009.

It is about time that magazines and news outlets stop stealing from
the electronic
media without attribution. Sci.math is not a place to freely steal
ideas and pretend as
if they are your own original ideas, and if you see someone making the
same arguments
over whether Euclid IP was direct or indirect and has an earlier date
of claim, you should
not publish an article without attribution.

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 27 Jun 2010 21:38
I see you are still having problems with numbers and simple logic.

> no matter what examples you pull out of your hat, for when you assume
> that 3 and
> 5 are the only primes that exist in contradiction method, then 16 is
> a prime

Perhaps you will find a simple argument with strings easier to follow.

If say a,b,c are string "primes" then you can form an infinite number
of strings of the form a, b, c, aaa, ab, aab, aaaacc etc.

But can you order all of them so that no two consecutive strings
share a common "prime".
a,b,c,ab,cc,aab,ccc, bb, etc.

Obviously not. The string "abc" must occur somewhere in the
ordering and any string that follows must share some "prime"
with "abc".

The analogy with natural numbers is obvious.

No two consecutive naturals share a prime divisor.
If you assume there is a finite number
of primes w amd w+1 must share a prime divisor. A contradiction.

Whatever "comes immediately after" abc shares a prime
factor with it whether it is prime or not a,b,c, aaabbc, etc.

In the case of the naturals all primes assumed to exust
precede w, every number after the largest prime is therefore
composite.

From: porky_pig_jr on 27 Jun 2010 22:17
On Jun 27, 9:38 pm, "sttscitr...(a)tesco.net" <sttscitr...(a)tesco.net>
wrote:
> I see you are still having problems with numbers and simple logic.
>
Tsk, tsk. Be nice to Archie Poo. Archie is our village idiot.
 | 
Pages: 1
Prev: HISTORIC SPECIFIC MATHEMATICAL PROOF AGAINST CURRENT MATHEMATICS GIVEN TO PROFESSOR EDDIE ESCULTURA BELOW
Next: deriving speed of light out of raw pure math Chapt 19 #206; ATOM TOTALITY