I don't usually engage the trolls directly. I compile lists of their typical rantings and post them as a warning to others who may be taken in, wasting their valuable time or worse. I don't usually post more than one such warning per thread.
#4#
--- quoting Davidson's attempt at Euclid's IP ---
Iain Davidson wrote:
Posted: Aug 25, 2009 8:43 PM
On 25 Aug, 20:57, Archimedes Plutonium
Here is the Challenge of proving Euclid's Infinitude of Primes. The
challenge is to write both direct and
indirect methods out.
Because of your limited mathematical ability, you forget
to mention that the key theorem for both the "direct method"
and the "indirect method" is
Every integer >1 is divisible by a prime
Direct
Th. 1 Every integer >1 is divisible by a prime
If you can find n primes, then you can find n+1 primes.
Add 1 to the product of the n primes you have found.
The resulting number (>1) is not divisble by any of the
primes that have been found, but by Th.1 this number must have
another prime divisor.
Therefore there is an n+1th prime and this implies the number
of primes is infinite as the process could be repeated
ad infinitum.
Indirect
Th. 1 Every integer >1 is divisible by a prime
Assume that there are only a finite number of primes
Add 1 to the product of all the primes assumed to exist.
The resulting number (>1) is not divisble by any of the primes
assumed to exist, but by Th.1 this number must have a prime divisor.
Contradiction. Therfore, the number of primes is not finite.
--- end quoting Iain Davidson's attempt at Euclid IP, direct and
indirect ---
Davidson makes the same myth-mistake, by believing
that the Direct method can be virtually identical to the Indirect, in
the
mechanism of the proof. The error of running a prime factor search in
both, and failing to recognize that Euclid's Number is necessarily
prime
in the Indirect.
Another major error by Davidson, is the error of
never starting the proof by the definition of prime. When you fail to
start the Euclid IP proof with the definition, then after forming
"multiply the
lot and add 1" you can not have any inspection of that newly formed number, since you have no definition of what is a prime. You easily go astray with not knowing what this new
number
is, for you have no first step of the proof of -- definition-- to
measure this
new number. If Davidson had started his attempts with
the
definition of prime, then after he formed Euclid's Number, he may
have
realized that Euclid's Number is necessarily a new prime in the
Indirect.
So Davidson seems to be unaware of two myths that they
commit. The myth that direct can be identical to indirect, and the
myth that
you can start a proof of mathematics without the vital first step of
the definitions
of the concepts under review.
AP1990s Survey
Many of AP's postings can be safely ignored as well. But once he starts peddling his mathematical snake oil promising an "easier way" for students to do calculus, for example, I think they really ought to be warned about him.
Yeah, I probably have too much time on my hand and should get out more. Sigh...
Dan
Dan seems to have lost sight that sci.math is about math, not about hatred of people and plastering hate-sheets all over the place, but when a person is insane, insanity is where "no reasoning can enter". One can only "use insane people like Dan", like one makes use of horse-manure as a fertilizer for the lawn and grounds.
AP