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Jul 13, 2011 at 23:12 comment added user9072 @Michael, my point was only that the suggested notation is not a true substitute for having a notation for the set of prime numbers. This is perhaps a bit pedantic. In general, both the originally suggested notation as well as all kinds of other things can be useful. Typically , I do not use 'voluminous' sub- and superscripts but this is I would say to a large extent a matter of personal taste.
Jul 12, 2011 at 20:11 comment added Qiaochu Yuan @Michael: then I might write $\displaystyle \prod_{p \text{ prime in Foo}}$. I am not averse to writing long conditions in my sums...
Jul 12, 2011 at 19:34 comment added Michael Hardy @quid & @Qiaochu: Maybe there are times when you want to say $\prod_{p\text{ prime}} s_p =\text{something that depends on which structure it is}$. (But maybe I'm also taking this more seriously than I could have......)
Jul 12, 2011 at 19:31 comment added Michael Hardy ....and sometimes it is more convenient to write $\sum_{\text{even }n\ge 0} s_n$ than $\sum_{n=0}^\infty s_{2n}$.
Jul 11, 2011 at 19:25 comment added user9072 I did not mean it that seriously, which I even tried to signal. In case you dislike the comment, I'll delete it (and then this one too of course).
Jul 11, 2011 at 19:08 comment added Qiaochu Yuan @quid: well, presumably there are words before and after this and it should be clear from context. As a mild extension if I am talking about a fixed ring $R$ I think I could safely write "P a prime ideal" instead.
Jul 11, 2011 at 19:06 comment added user9072 Leaves the question: 'prime' in which structure? :) [Sorry could not resist.]
Jul 11, 2011 at 18:35 history answered Qiaochu Yuan CC BY-SA 3.0