Re: essence of the correction Re: corrected Infinitude of Primes proof; both direct and indirect methods

From: Archimedes Plutonium (a_plutonium_at_iw.net)
Date: 03/29/05 

Date: Tue, 29 Mar 2005 14:54:18 -0600

Tue, 29 Mar 2005 15:57:21 +0100 Alec McKenzie wrote:

> Archimedes Plutonium <a_plutonium@iw.net> wrote:
>
> > So the flaws of over 90% of the proofs of Euclid Infinitude of Primes
> > involves the mixing up of "prime factor" in addition to the mixed up claim
> > that Euclid made a indirect proof when there is no evidence that Euclid did
> > such. The evidence suggests that Euclid gave a **direct proof** of
> > Infinitude of Primes.
>
> It's not just that "there is no evidence" -- Euclid could not
> have used an indirect proof because such a concept did not exist
> in his day.
>
> --
> Alec McKenzie
> mckenzie@despammed.com

Yes I believe your statement is true that the concept of Indirect proof method
was unknown at the time of Euclid and of Archimedes. But then we must answer as
to why so many history of mathematics claim that Euclid proved IP indirectly. I
also remember seeing some claims that Archimedes used a
double-reductio-adsurdum. Sounds pitiful to me that any historian would claim
such when none of the Ancients had the Indirect method or ever used it.

The Ancients arrived at proofs via *construction*. Archimedes constructed
geometrical objects and Euclid constructed sets of higher cardinality to prove
Infinitude of Primes.

So there is evidence that Euclid did the IP proof via the "Direct method"
because the language of his proof is set theory with increasing cardinality.
That implies Euclid made a Direct proof of IP.

It would be interesting to look back into history to see where the first time
Euclid's proof of IP was called or named or ascribed with the "Indirect Method".
Who corrupted the history of the Infinitude of Primes proof so that so many
people render an invalid version and so many people come away with a math
education under the falsehood of thinking Euclid did a Indirect proof of
Infinitude of Primes.

So we need to clear up that smudged and tarnished history of the Infinitude of
Primes proof.

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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