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From: juandiego on 27 Sep 2009 13:41

> 1) Definition of prime
Haven't you found a definition of prime you can
understand yet ?

> 2) Hypothetical assumption, suppose set of primes 2,3,5,7,.. is
> finite with P_k the last and final prime
finite => last => final => finite
hypothesis => assumption => hypothesis

> 3) Multiply the lot and add 1 (Euclid's number) which I call W+1
> 4) W+1 is necessarily prime

4 is divisible by 1 and 4 is divisible by 4
this deduction does not make 4 necessarily prime.
4 is not prime because it has at least one proper divisor,
i.e. 2 with 1<2<4
You seem to grasp that none of the proper divisors
of w+1 is a prime assumed to exist,
but you need to prove that w+1 has no other
proper divisors, say some number a
p5 <a< p6.
w+1 = am
Only then can you correctly claim that w+1 is prime.

If w+1 has proper divisors that are not prime divisors
and w+1 has no prime divisors then no contradiction is found and the
proof does not go through.


> 5) contradiction to P_k as the last and largest prime
> 6) set of primes is infinite.
>
> What the Fitch Symbolic Logic format does is eliminate the sloppy
> errors of a Misplaced or Disconnected contradiction.

It is logically impossible to correctly deduce a false statement
from true premises. A contrdiction is a false statement.
So if you deduce C and -C from an assupmtion A (assumed true)
and premises which are true, the only possibility is
that A is false.

You have not read the section in your book on valid
inferences.
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