why Davidson cannot learn from Flath -- Euclid's IP proof #5.04 Correcting Math
in [Logic]
|
Prev: what Julia F. Knight (Journal of Logic) has in common with Chandler Davis (Mathematical Intelligencer) #5.03 Correcting Math
Next: why Davidson cannot learn from Flath -- Euclid's IP proof #5.05 Correcting Math
From: Archimedes Plutonium on 8 Aug 2010 17:26 Iain Davidson sttscitrans(a)tesco.net wrote: > > "Every natural >1 has at least one prime divisor" > Here we see and compare the incompetence of Iain Davidson with that of Flath. (# 9) --- quoting Daniel E. Flath INTRODUCTION TO NUMBER THEORY, 1989 page 2 --- Theorem 2.2 Euclid. There are infinitely many primes. Proof. We shall show that every finite set of primes omits at least one prime. It will follow that no finite set can contain all the primes. Let {p_1,p_2,...,p_r} be a finite set of prime numbers. By Theorem 2.1, (Every positive integer n greater than 1 is a product of prime number.) , there is a prime divisor q of N = p_1*p_2*..*p_r +1. Because q divide into N but p_i does not divide into N, the prime q must be different from p_1,p_2,...,p_r. --- end quoting INTRODUCTION TO NUMBER THEORY, Flath --- Flath did a Direct method using that Lemma -- Every positive integer n greater than 1 is a product of prime number. Flath recognizes that W+1 is divisible by W+1 and so by definition of prime, W+1 is prime. For some reason Davidson is never able to recognize his half-baked lemma-- "Every natural >1 has at least one prime divisor" where he forgets to include that **Every natural >1 has at least one prime divisor and is divisible by itself** So where Flath uses the correct lemma in a Direct proof, Davidson uses a half-baked lemma and jumps into a error filled proof. He commits the error of thinking he attained a contradiction, when all he did was reach the fact that W+1 is necessarily a prime number and thus has further steps to go to reach a contradiction. 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 8 Aug 2010 17:37
On 8 Aug, 22:26, Archimedes Plutonium <plutonium.archime...(a)gmail.com> wrote: > Iain Davidson > > sttscitr...(a)tesco.net wrote: (mindless prevarication deleted) > > "Every natural >1 has at least one prime divisor" Is the statement true or false ? Do you have a counterexample ? Do you understand what the statement says ? Will you continue to talk out of your rectum ? |