TITLE: Are there rules in the useage of prepositions in Math?
QUESTION [6 upvotes]: It is often to use prepositions in various expressions. 
E.g.

$2$ is in the set of natural numbers $\mathbb N$ 
The symmetric group on 3 letters $S_3$ is the group consisting of all possible orderings of the three letters ABC i.e. contains the elements ABC, ACB, ..., up to CBA, in total 6 elements. 
The group of integers modulo $n$ is written $Z_n$ or $Z/nZ$
If $R$ is a binary relation over $X$ and $Y$, then $R^{-1}$ is a binary relation over $Y$ and $X$.

However, it's perhaps a bit dazzling for someone who is not quite familiar to the syntax of English. So my question: Are there some rules in the useage of prepositions such as 'at', 'in', 'on', 'over', 'under', 'of', 'for' and 'from' in Math? Or everything is just a convention?

REPLY [2 votes]: The short answer is that you should speak and write the way that a native speaker of the language does. If you’re uncertain, ask a native speaker. Note that this is true for all languages, not just English.
The long answer is that English is one of the Indo-European languages, which all (as far as I know) put a very great weight on the preposition. And the wrong preposition can change the meaning of a sentence disastrously, or merely make the sentence sound clumsy. Furthermore, which preposition is the right one can be entirely different not merely from language to language (in English, $x^3$ is “$x$ to the third”, but in Danish it’s “$x$ in third”) but from dialect to dialect within a language (among Americans, $x/y$ ix “$x$ over $y$”, but among Britons it’s “$x$ on $y$”, as I recall). In short, then, see the paragraph preceding.