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From: Archimedes Plutonium on 11 Aug 2010 12:02


sttscitrans(a)tesco.net wrote:
> On 11 Aug, 04:37, Transfer Principle <lwal...(a)lausd.net> wrote:
> > On Aug 8, 4:37 pm, Archimedes Plutonium

>
> If Davidson is false then AP is also false
> If Davidson is true then AP is true.
>

Mr. L. Walker, the below is a true proof, because in step 4) W+1 is
recognized as being
necessarily prime since it is divisible by itself and by 1 and that
none of the finite list of
primes divides into W+1, so by definition W+1 is necessarily a new
prime not on the finite list.

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.


Mr. L. Walker, and here is Iain Davidson's attempt that you endorsed
as true:
sttscitr...(a)tesco.net wrote:

 > 1) A natural is prime if it has preceisly two distinct divisors
 > 2) Every natural >1 has at least one prime divisor
    > 3) GCD(m,m+1) = 1, for any natural m
    > 3) Assume pn is the last prime
    > 4) w = the product of all primes
    > 5) 3) => gcd(w,w+1) =1 => no prime divides w+1
    >    This contradicts 2)
    > 6) Therefore: Assumption 3 is false
    >   - pn is not last prime

It is not a proof because it has no contradiction. All that Davidson
achieved in seven steps
(he miscounted the steps) is that W+1 is a prime number. He has not
contradicted 2) because
Davidson fails to realize that W+1/W+1 and is divisible by 1 so that W
+1 is a prime number. So he has no proof and he has no contradiction.

So Mr. L. Walker, you are responsible for having encouraged Davidson
into believing his misguided steps and his convoluted use of half of a
theorem. And L. Walker needs to
state that Davidson is wrong.

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 11 Aug 2010 13:40
On 11 Aug, 17:02, Archimedes Plutonium
<plutonium.archime...(a)gmail.com> wrote:
> sttscitr...(a)tesco.net wrote:
> > On 11 Aug, 04:37, Transfer Principle <lwal...(a)lausd.net> wrote:
> > > On Aug 8, 4:37 pm, Archimedes Plutonium
>
> > If Davidson is false then AP is also false
> > If Davidson is true then AP is true.

I see you have still not answered my question.

Is
"Every natural >1 has at least one prime divisor"
a true statement or a false statement.

Your bizarre idea that the statement is "incomplete"
shows how primitive and confused your thinking on these matters is.

By Archie Poo "logic" every theorem would be incomplete
as you could always AND it with some another theorem
or theorems.

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