Timeline for A symbol to denote the set of prime numbers ?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 12, 2019 at 7:43 | comment | added | SasQ | There would be no problems with single-letter symbols, nor with agreeing upon their meaning, if only math had some syntax for DECLARATIONS, as in programming languages. Then you could introduce whatever symbol you like by declaring its name and type, and from then on, you could use that symbol (even a one-letter one) in the rest of the formulas. Isn't that what Alonzo Church tried to accomplish with his Lambda Calculus? (To get rid of "undefined symbols" from mathematical symbolic notation.) | |
| Jan 25, 2019 at 2:13 | comment | added | Douglas Sirk | $\mathbb P$ is used for the set of irrationals by many topologists | |
| Jan 24, 2019 at 23:53 | comment | added | Jules Lamers | I'm a bit late to the party, but if you're willing to write $p \in \texttt{PRIMES}$ then why not just $p: \text{prime}$ as in Qiaochu Yuan's answer? That's as clear yet shorter (and I personally find it a bit less ugly). | |
| Jun 16, 2017 at 23:02 | comment | added | Stephen | I still want to use $\mathbb{P}$. | |
| Feb 25, 2017 at 13:06 | comment | added | Gerald Edgar | Mostly I don't like this. I guess use $\mathtt{PRIMES}$ only if you also use $\mathtt{INTEGERS}$, $\mathtt{RATIONALS}$, and $\mathtt{REALS}$ . That is, in a computer program. | |
| Jul 12, 2011 at 14:31 | comment | added | user9072 | And, before someone reminds me of Hom, Ker, Ext, Tor, sin, or whatnot, let me add that these are already standards, are typically primted in standard font, and are in some (vague) sense notations of a different form. | |
| Jul 12, 2011 at 14:20 | comment | added | user9072 | unknowngoogle, what about the variants based on just P to waste even less space? ;) More seriously, while at least in theory I have some sympathy for the idea of writing-things-out, it is excessively hard for me to imagine that a half-way solution like PRM will be useful, in the spirit of the answer 'opening up a paper in the middle.' Quick question: Who will see PRM written somewhere in the middle of a paper and default to thinking this is the set of prime numbers, and who it is something defined earlier in the paper? (Except context is so clear that nothing is required, cf GH.) | |
| Jul 12, 2011 at 10:18 | comment | added | Qfwfq | What about $\mathtt{PRM}$ (to not waste too much space...) ? | |
| Jul 12, 2011 at 10:16 | comment | added | Qfwfq | @David: $\mathtt{PRIMES}\setminus\{2,3\}$ could be an instance. | |
| Jul 11, 2011 at 22:43 | comment | added | Suvrit | although I find the argument to avoid "font / symbol overload" of the letter 'p' fairly compelling, I also wonder why a concept of such high importance does not yet have its own symbol. I guess, once more number theory is taught at grade-school level..... | |
| Jul 11, 2011 at 21:17 | comment | added | David E Speyer | Yeah, agreed. I'd have to think a little to come up with an example where using a notation for the set of primes itself was the best option. | |
| Jul 11, 2011 at 20:58 | comment | added | Martin Brandenburg | This sounds reasonable. For the same reason, we should probably write for instance (Groups) for the category of groups instead of (Grp) or even more confusing abbreviations such as (Gp) or (Gps) (which I have all seen so far). But maybe it is a bit redundant to write such a long technical formula $p \in \mathtt{PRIMES}$ if you are not really interested in this set of all prime numbers and manipulate it by set-theoretic means. In the case of a simple product which runs over the primes, then I would prefer the notation proposed by Qiaochu (which is, of course, very popular). | |
| Jul 11, 2011 at 18:29 | history | answered | David E Speyer | CC BY-SA 3.0 |