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From: Archimedes Plutonium on 5 Jul 2010 06:53


Archimedes Plutonium wrote:
> A theorem sometimes called "Euclid's first theorem" or Euclid's
> principle states that if is a prime and , then or (where means
> divides). A corollary is that (Conway and Guy 1996). The
> fundamental theorem of arithmetic is another corollary (Hardy and
> Wright 1979).
>

Sorry, that is not my writing, for it is a transmission error. I
wanted to quote Wolfram
on Unique Prime Factorization with Euclid's theorem but it failed to
transmit.

I apologize to Wolfram and have deleted the above in my original post
with a (sic) sign.
I did quote Wolfram in that post with part of that paragraph.

Sorry again for the transmission error.

But let me not spoil a whole post on admitting typing errors. Let me
continue with
the train of thought.

I unfortunately encountered Weil's comment that disparages Euclid, and
ran with it
on the side of Weil, but come to find out that it was Weil that was
clearly wrong.

I guess Weil expected the ancient Greeks to go wiling on page after
page about
the unique prime factor concept, whereas all the Greeks did was prove
it and no
mention thereafter.

What Weil failed to appreciate is that much of the ideas and concepts
of Number
theory depend on this Unique Prime Factorization theorem (UPFAT) and
thus called the Fundamental
Theorem of Arithmetic. So if Weil had stopped for a moment and
thought, "hey, all
we know about Perfect Numbers depends on UPFAT and Euclid spent
considerable time
on perfect numbers.

My concern is the Infinitude of Primes proof and UPFAT is critical for
that proof. Here again,
if Weil had stopped and thought about it, that Euclid could not have
done a valid IP proof
absent of an understanding of UPFAT.

So here we have a case of a famous mathematician Andre Weil, making a
spurious remark
and deprecating remark of ancient mathematicians, which only comes
back to reflect on
Mr Weil himself, that he was not a sharp and first rate mathematician
and that it is likely that
all of his contributions to mathematics were error prone. It is likely
that none of Weil's math
is true.

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
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