On 3 jul, 18:25, 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.
>
> 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 =3D 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 =3D 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 Plutoniumwww.iw.net/~a_plutonium
> whole entire Universe is just one big atom
> where dots of the electron-dot-cloud are galaxies
Hi,
You say my synopsis is wrong as a whole? Please, explain.
It also seems you want me to provide a proof... Ok, here it goes.
We say a natural number is prime iff it is greater than 1 and doesn't
have any divisor other than 1 and itself.
By the fundamental theorem of arithmetic, every number greater than 1
has a prime divisor.
Let us suppose that the subset of all prime numbers is finite.
Then the product of all primes plus one, since it doesn't belong to
the subset of all prime numbers (it is greater than any of them) is
not a prime, but it has a prime divisor, since it is greater than 1.
But in fact, it doesn't have any divisor from the list of all primes.
Contradiction.
I keep on believing that the key idea in this proof is the
construction of the number "the product of all primes plus one", and
not the strict application of the rules of logic, which are supposed
to work when applied correctly.
For some other proofs of the infinitude of primes I recommend:
Number Theory. An Introduction via the Distribution of Primes
Benjamin Fine
Gerhard Rosenberger
Birkh=E4user
Cheers.
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