Re: Symbolic Logic write-up of Infinitude of Primes, direct & indirect methods; Infinitude of Twin Primes

Nils Borjesson wrote:
You can do abbitary number of assumptions in a proof.
I will give an example where I proof that there
are infinitely many primes that leaves 2 as reaminder
upon division by 3.

A.P. writes:

Well maybe I just did not make myself clear. Today my old textbook of
SYMBOLIC LOGIC Thomason 1970 edition arrived. Thank goodness for
Amazon.com that I can buy old out of print books.

On page 338 of this book is a 26 step proof of a problem and 9 of those
steps were "hypotheses".

Hypotheses are different from a Reductio Ad Absurdum RAA assumption
statement.

You cannot have a double RAA assumption without discharging an earlier
RAA. For you simply just cannot take into account of how one relates to
the other.

Example: Assume the StrongNuclear force did not exist. Then .....

That is okay because we can discuss the physics since the other 3
forces of Nature exist.

But now, Assume the StrongNuclear and WeakNuclear and EM forces do not
exist. Leaving only gravity. Here we cannot do anything because we have
no idea of how they relate.

I am not talking about making numerous hypotheses in a proof argument.
I am talking about making numerous RAA without discharging the first
such RAA.

In the Infinitude of Primes, RAA method, we construct W+1 and it is
necessarily prime. But to consider W+1 as composite with a prime factor
is forbidden for it is a second RAA, without the release and discharge
of the first RAA which said the set of all primes is finite.

Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies

.

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