Re: Is this proof of infinitely many primes flawed?

quasi <quasi@xxxxxxxx> wrote:
David C. Ullrich <dullrich@xxxxxxxxxxx> wrote:

I didn't make any claims about what it was or was
not "likely" that the OP was asking, just about what
he did in fact ask:

"how can we say p_k  divides evenly (p_1,p_2,...,p_n)?"

There is after all a context.

Yes. The context _seems_ to be that he was confused,
thinking that the answer to his (trivial) question had
something to do with that other assumption, which
it doesn't.

Actually, I think the confusion might in fact stem from the use of
commas instead of a standard product symbol.

Of course, it makes no sense at all to think that p_k would divide
evenly into a _list_ of distinct primes, so _we_ (on sci,math) just
assumed (knowing how the correct proof goes) that the comma was
intended as a product symbol. But the OP (who may simply have copied
it incorrectly off the board in class), may have interpreted the
expression (p_1,p_2,...,p_n) as a list, hence the puzzlement.

That notation might in fact denote the LCM of the p_i
if the teacher attempted to present the proof in a form
somewhat faithful to Euclid's original proof.

--Bill Dubuque
.

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