again, listing the flaws of Wikipedia's Euclid Infinitude of Primes proof Re: Correcting Wikipedia's Euclid's Infinitude of Primes Proof


Mark Nudelman wrote:


The only problem with the wikipedia proof is a slight ambiguity in
language. The first sentence "Suppose you have a finite number of
primes" simply means "take a finite number of primes". It does not mean
"suppose the set of all primes is finite". If you accept the first
interpretation, then the proof is fine. It proves that given any set of

Well that is not the only problem. Just moments ago I corrected Arthur
Rubin's
Wikipedia entry with keeping as much of his wording as possible. So
to
correct his entry you need to omit the "Suppose", which I concur.

But you also need to add a line saying Euclid's proof was Direct
Method
of increasing set cardinality.

But also, you need to correct Rubin's last lines where he has the
example
of 30031 all jumbled around and wrong. For in the Indirect Method,
30031 is
necessarily the new prime which contradicts the Supposition step.



primes, there is another prime not in the set. Therefore, the set of
all primes cannot be finite. This is indeed the way Euclid did it --
see http://farside.ph.utexas.edu/euclid/euclid.pdf proposition 9.20.
Actually Euclid's proof is incomplete because he only proved that given
any set of exactly three primes, there is another prime not in the set.
The proof works only if the set contains any number of primes, but
Euclid apparently assumed the reader would extrapolate from his proof
with three primes. This is a well known failing of Euclid's proof. The
wikipedia proof is an improved version of Euclid's.

--Mark

Wrong, the Wikipedia version is a sloppy mixture of both methods
ending up with a invalid proof.

Archimedes Plutonium
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whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies

.