It is typical to find a corollary that following theorems, but is it right to use the word corollary for a statement following a conjecture, where the statement is true only if the unproven conjecture is true? Answer I think it’s generally bad form to have a corollary dependent on an earlier conjecture. I recommend … Read more
EDIT: Part of the community has decided on a less catchy and more representative title than “Socially acceptable plagiarism (with regards to translation)”. Let’s run with that for a while. GRP.10.27 END EDIT. The catchy part of the title refers to reusing words or ideas without permission, but without ‘rocking the boat’. In mathematics, this … Read more
It strikes me that there is no widely accepted symbol to denote the set of usual prime numbers in N. Look: ζ(s)=∏p∈?1(1−p−s) Wouldn’t it be nicer to have a standard symbol to put in place of the “?” instead of writing just Πp and specifying by words “where p ranges in the set of prime … Read more
This is a boring, technical question that I stumbled upon while making a contribution to Sage. I would still like to hear a constructive answer so hopefully the question does not get closed. The question is the following. How many spanning trees does the empty graph $E$ have? According to Sage it has 1, while … Read more
It seems in writing math papers collaborators put their names in the alphabetical order of their last name. Is this a universal accepted norm? I could not find a place putting this down formally. Answer This tendency of mathematicians is so well-known and universal that it has been taken as an axiom. See Andrew Appel’s … Read more
I think we all occasionally come across terminology that we’d like to see supplanted (e.g. by something more systematic). What I’d like to know is, under what circumstances is it reasonable to believe that such a fight is winnable? Question. What recent programmes to alter highly-entrenched mathematical terminology have succeeded, and under what conditions do … Read more
Many mathematical definitions almost used $\epsilon >0$ to define any mathematical notion, for example if we want to give definition to the convergence of sequence we say ” $\forall \epsilon >0 , \cdots $ which means $\epsilon \in (0,\infty)$ than $\epsilon$ can take any large value since its belong to this domain $(0,\infty)$ , I … Read more
I’ve seen the notation $\mp$ to contrast with $\pm$ to indicate “Yes there are only two cases and these guys must be opposite signs”. So something like $(\pm2, \mp3)$ would just be $\{(2, -3), (-2, 3) \}$. But if I write $(\pm 3, \pm 4)$, does this refer to $\{(3,4), (-3, -4)\}$, or $\{(3,4), (-3, … Read more
Closed. This question does not meet Mathematics Stack Exchange guidelines. It is not currently accepting answers. Want to improve this question? Update the question so it’s on-topic for Mathematics Stack Exchange. Closed 6 years ago. Improve this question In books the cardinal numbers are usually written with a gothic font. Is there any convention how … Read more
I’m currently reading Lee’s Introduction to Smooth Manifolds, in which he makes a remark along the following lines: “The next corollary can be viewed as a more invariant version of the rank theorem.” My question isn’t about the corollary or the rank theorem itself, but about Lee’s use of the word “invariant.” This word is … Read more
