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From: Archimedes Plutonium on 24 Jul 2010 17:09


Archimedes Plutonium wrote:
> sttscitrans(a)tesco.net wrote:

LWalk, according to Math Forum that site---sttsc is registered to a
Iain Davidson.
But the trouble with that is there is no Iain Davidson showing up as
ever being a
mathematician in the UK, or graduated with a math degree. So whether
he is using
a fake name also is an open question.

LWalk, do you see the flaws of the below Iain Davidson offering. And
Davidson misnumbered
his offering with two steps numbered 3).

His first big mistake is that his Lemma deletes the important
characteristic that all Natural numbers are divisible by themselves.
That mistake would be akin to me saying that a prime
number is divisible by 1 but omitting the fact that it is divisible by
itself. Davidson's half baked
lemma in 2) is the fatal flaw for it should read "Every natural >1 is
divisible by itself and by at
least one prime divisor. So that when Davidson forms W+1, it is
divisible by W+1 and divisible by 1 and hence by Davidson's step 1),
the newly formed number W+1 is a prime
natural number. So Davidson has no contradiction and must add on about
three more steps
in order to have a valid Indirect. Already, Davidson's offering is
seven steps long and adding
three more to make it a proof would be ten step proof.

--- Iain Davidson offering which really has seven steps, not six ---

> 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


LWalk, here is my proof:

short form Indirect
(1) definition of prime number
(2) hypothetical assumption, assume the primes are finite and that
the sequence list is 2,3, 5, 7, 11, . . , p_k
(3) multiply the lot and add 1, calling it W+1
(4) W+1 is necessarily a new prime because of definition in (1)
joining with the fact that
division of W+1 by all the primes that exist in (2) leave a
remainder
(5) contradiction to (2) that p_k is the largest and last prime, for
W
 +1 is now the largest prime
(6) reverse supposition step (2) and primes are infinite

Notice, LWalk it takes me six steps in all for a complete proof. It
took me only two
steps to conclude that W+1 was prime. It took Davidson seven steps
which is an
incomplete proof and which only establishes that W+1 is a prime
number. Yet, LWalk
and Davidson were thinking that W+1 was not a prime.

Davidson's is not a proof but the mere establishing that W+1 is a
prime number, and this is
established because W+1 is divisible by itself and divisible by 1 so
that W+1 has precisely two distinct divisors in Davidson's convoluted
step 1) of the definition of prime.

I have found always in life as in math, use the most direct
definition, not some convoluted piece.

So Davidson has no proof, but only a seven step argument that leads to
the conclusion that
W+1 is a prime number. And Davidson never admits that W+1 is a prime.
And LWalk became
interested in Davidson's argument because he proclaims that W+1 cannot
be prime.

And Davidson's last step which he misnumbered as 6) when it is 7) is
utterly false given
the prior six steps because Davidson never admits that W+1 is prime
and so it cannot be a
prime larger than pn; who knows what he was thinking. For anyone who
cannot even give a
accurate Lemma of all its parts, rather than deleting half the Lemma,
we cannot expect to
assemble a valid proof, nor understand his mistakes.

So it takes Davidson seven steps to find out W+1 is a prime number,
for which he insists is never a prime.

LWalk, please reconsider your evaluation of Davidson's offering and
criticism. He is messy, sloppy, posts only half of what a Lemma really
is, and worst of all, lacking of any manners
or politeness. Somewhere along the line, he never learned the basic
core teaching that every
human must have-- being courteous, being polite and full of good
manners and cheer.

Please reconsider your judgement, LWalk. I know Davidson can never
admit wrong. But I expect it is easy for you, LWalk to admit to your
mistake. LWalk, you do not want to be seen as endorsing the deletion
or lopping off of a Lemma.

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 24 Jul 2010 18:09
On 24 July, 22:09, Archimedes Plutonium
<plutonium.archime...(a)gmail.com> wrote:
> Archimedes Plutonium wrote:
> > sttscitr...(a)tesco.net wrote:
> n question.
>
> His first big mistake is that his Lemma deletes the important
> characteristic that all Natural numbers are divisible by themselves.

If the lemma is false state an n for which
it is false.

Otherwise you are just passing wind and
pretending you know something about maths.

> That mistake would be akin to me saying that a prime
> number is divisible by 1 but omitting the fact that it is divisible by
> itself.

Poor Archie, you really are completely clueless.
Everyone knows that the trivial divisors of
n are 1 and n.

1) n is divisible by 1
2) n is divisible by n


So that when Davidson forms W+1, it is
> divisible by W+1 and divisible by 1 and hence by Davidson's step 1),
> the newly formed number W+1 is a prime
> natural number.

You have no idea what you are talking about.

So Davidson has no contradiction

Of course there is a contradiction.

"Every n>1 has a prime divisor"
and "w+1 has no prime divisors"

cannot both be true.

Maybe you simply don't understand what
a contradiction is.

In fact, I'm beginning to think that you have
no idea what any mathematical term means and that
you are incapable of understanding any mathematical
concept.

It is as if your mathematical outpourings
were being produced by a computer that was running
a simple generative grammar with a mathematical lexicon.
At first glance, what you write looks like
maths, but if you look at it again, it is merely
gibberish.


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