Talk:Euclid's proof that there are infinitely many primes

I fixed some instances of strangeness like \text{max} instead of \max.

But a far more substantial edit that I did should expunge something misleading. It said Euclid considered a finite set $\scriptstyle \{p_{1},\ldots ,p_{\max }\}$ of primes. It did not say explicitly that $\scriptstyle p_{\max }$ was to be the largest of those, but the notation certainly suggests it, and it did not say that the the set was to include ALL primes less than or equal to its largest member, but it is in fact a widespread error among mathematicians to think that that is the set that Euclid considered. It is even a widespread error among mathematicians to think that Euclid considered a hypothetical largest prime, and this notation, with "max" could reinforce that. When I say "widespread among mathematicians", I speak as one who has carefully documented the fact that it is widespread in mathematicians' publications; see my paper, which I see somebody cited here.

Later in the article someone considered the case in which $\scriptstyle p_{\max }\,=\,5$, and without saying why, assumed that meant that both 2 and 3 are members of the set of primes considered. That would be true if the set $\scriptstyle \{p_{1},\ldots ,p_{\max }\}$ were taken to contain ALL primes less than or equal to that largest member.

I think this article should avoid tacitly propagating errors that are in fact widespread in the community. Hence my recent edits. Michael J. Hardy 20:25, 10 January 2014 (UTC)

Thank you for your careful corrections. I've approved your edits so all new users should see only that version. (For those not aware, Hardy's article with Dr. Woodgold set the record straight on this matter some years ago.)

Charles R Greathouse IV 21:40, 10 January 2014 (UTC)