malc...@[EMAIL PROTECTED]
wrote:
>
> Just to put things in order:
>
> I do not hate anyone. I just noted that in normal speech such kind of
> mistakes are common and that it is also normal not to pay much
> attention on them. Certainly one would expect any competent person in
> any field to be able to grasp this kind of mistakes instantly.
> However, as you have come to realize, this simply doesn't happen.
>
When G.H. Hardy writes the Euclid Infinitude of Primes Proof in a book
"A Mathematicians Apology"
and makes the logical mistakes and when Niven, Zuckerman, Montgomery,
in a textbook
AN INTRODUCTION TO THE THEORY OF NUMBERS makes the logical mistakes.
--- quoting from my book Correctiong Euclid's Infinitude of Primes
Proof ---
(#3) --- quoting WHAT IS MATHEMATICS? Richard Courant and Herbert
Robbins
1941 page 22 ---
The proof of the infinitude of the class of primes as given by Euclid
remains a model of mathematical reasoning. It proceeds by the
"indirect
method". We start with the tentative assumption that the theorem is
false. This means that there would be only a finite number of primes,
perhaps very many -- a billion or so -- or, expressed in a general and
non-committal way, n. Using the subscript notation we may denote these
primes by p1, p2, ...,pn. Any other number will be composite, and must
be divisible by at least one of the primes p1,p2,...,pn. We now
produce
a contradiction by constructing a number A which differs from every
one
of the primes p1, p2, ..., pn because it is larger than any of them,
and which nevertheless is not divisible by any of them. This number is
A = (p1xp2x...xpn) +1, i.e. 1 plus the product of what we supposed to
be all the primes. A is larger than any of the p's as a divisor. Since
our initial assumption that there is only a finite number of primes
leads to this contradiction, the assumption is seen to be absurd, and
hence its contrary must be true. This proves the theorem.
--- end quoting WHAT IS MATHEMATICS? Courant and Robbins ---
One thing that Courant and Robbins do that is really good is clearly
state what they thought Euclid method was.
But then their proof pretty much dissolves away or
collapses. For they did not fetch a new prime to ever warrant them
saying
they reached a contradiction. They say that A is different and A is
absurd,
but why were they never able to say that A is necessarily a new prime.
Like the other authors listed before, if Courant and Robbins had had
to
provide
both a indirect and direct method proof, perhaps they would have
delivered
a clear and valid result instead of this incomplete attempt.
--- end quoting ---
I would say those books are serious books and if they cannot give a
waterproof proof of
Euclid IP without huge error, then Malcolm is a hatemonger that trys
to diminish and belittle
the accomplishments of Archimedes Plutonium.
In my example of the Grade Schoolers Analogy:
Add this column:
3
5
10
9
____
And if thirty Grade school children handed in their answer and twenty-
eight of them
summed to 18
while two of the children summed to 27.
Then Malcolm is going to say that all thirty had it correct and that
their mistakes were
minor language mistakes.
This is where people in academics and education no longer belong in
those fields, where
they continue to make excuses and continue to not recognize
achievement.
When we ask the question of 30 professors of mathematics about their
published "alleged"
proof of Euclid Infinitude of Primes (of course Hardy and Courant and
Polya are dead) but
of those 30 professors who are living who made the mistakes. If you
ask them this question:
If the Universe of "all the primes" were merely the set of 3 and 5,
then (3x5) + 1 = 16
then the 16 is
necessarily a new prime in that universe, and the reason for the
contradiction is because
of the starting off definition of prime. If you ask those of the
thirty who got it wrong, whether
they can agree and understand that 16 is a new prime number, then they
are admitting to
their big mistake.
Likewise, if we were to question the two Grade Schoolers why they
added 10 as 10 and not as
1 and they are able to tell you that 10 is the number after 9 while
the twenty eight kids with the
wrong answer see 10 as 1 and 0.
> I think that the matter on how horrible the mistake is, is a bit
> subjective. For me it is a curiosity, and I believe that it is due to
> a confusion of two very similar proofs. I do not think any of those
> mathematicians, Hardy included, would not have corrected their proofs
> as soon as anyone would have made them note that.
>
A mistake is a mistake. If you answer that 3 + 5 + 10 + 9 = 18, then
do not
cover up your mistake. Likewise, if you claim to be giving a valid
Euclid Infinitude of Primes
Proof such as Niven, Zuckerman, Montgomery or Courant and Robbins or
Polya or Hardy,
then do not try to be making excuses for your big mistake. Come forth
and admit the
mistake is big.
> I am sorry that you have felt my discussion as an attack.
>
You suffer the same disease of hatred that Jesse Hughes suffers. You
see someone you
hate, and then you make all sorts of excuses. You cannot admit that
Archimedes Plutonium corrected a
big mistake made by mathematics professors in delivering a valid proof
of Infinitude of Primes.
The moment that a person such as you, cannot admit to the
accomplishments and
achievements by others then you should depart education and science.
> The question about the primeness of the strange looking ......
> 13121110987654321 was serious. Is there anything similar to the
> fundamental theorem of arithmetic for your AP-adics?
>
> Cheers.
I wrote a very long book recently called AP-adics primer, where your
question is answered. That
answer is too long to get started here. The above is a prime number
for it is Champernowne's (spelling)
number attached to the primes 11 and 13 or any other pair of primes.
In that book I argue that
this set of numbers 1,2,3,.... the Counting Numbers are fictional.
Again, too long to start a discussion
here.
Archimedes Plutonium
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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