Re: ** says: Definition: sum{i in N} i = 0

On Sun, 08 Jul 2007 11:38:11 -0700, hagman <google@xxxxxxxxxxxxx>
wrote:


but I know that his proofs usually showed only the case n=3
when one would use [indexes] today,

Yes. But it's clear that his proof (i.e. the proof idea) works for any
number n of "assigned primes".


he did not prove that there are infinitely many primes but rather
that there are more than three primes.

Exactly. Or (see comment above) that there given n primes there is
always (at least) one more.


Any proper interpretation will however reveal that this can be
translated to "There are infinitely many primes".

Right.


He used a proof by contradiction. [WM]

The usual crackpot nonsense of WM.


Euclid's proof is/was a /direct/ proof, even "constructive".


F.

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