On Jul 3, 7:25=A0pm, plutonium.archime...@[EMAIL PROTECTED]
wrote:
> 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 =3D (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.
****************************************************************
Nonsense Archie.
First, you have no accomplishment other than the ones your rather wild
and pretty pitiful imagination causes you to believe.
Second, the only huge error is that you believe you can do meaningful
physics and maths instead of making an ass of yourself.
Third: aren't you ashamed of yourself?? I honestly hope you haven't
spawned kids: they'll be laughed and scoffed at badly at school.
Fourth: knock it off, fruitcake!
Regards
Tonio
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