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I have some doubts about using prepositions. I. Let $f_a : \mathbb{R} \to \mathbb{R}$, $f : \mathbb{R} \to \mathbb{R}$. Assume that $f_a (x)$ converges uniformly to $f (x)$, $x \in [0;1]$, as $a ... 3answers 211 views ### Is there an adjective appropriate for describing mathematical terminology that you feel needs to be phased out? [closed] Let me firstly apologize; this is more of an English language question, so posting it here is perhaps slightly inappropriate. But I couldn't think of a non-mathematical example, so here we are. ... 1answer 51 views ### Writing a chain of implications in English How to write a theorem of the form$A\Rightarrow B\Rightarrow C\Rightarrow D$where every$A$,$B$,$C$,$D$are formulated with words (English) rather than with formulas? One idea: The next item of ... 1answer 236 views ### What is “observation”? Often in mathematical writing one encounters texts like ''..we observe that this-and-that..''. Also one may find a review report basically saying ''..the paper is just a chain of observations...''. ... 3answers 69 views ### Notation for definition and equivalence I would like some clarification about the usage/meaning of$:=$and$\equiv$. I have been using$A := B$to denote "Let$A$be defined as$B$." This is akin to assignment ... 1answer 32 views ### How could I define this$\mathrm{nw}(X)$by using only one sentence? A family$\mathcal N$of subsets of a topological space$X$is a network for$X$if for every point$x\in X$and any neighbourhood$U$of$x$there exists an$M \in \mathcal N$such that$x\in M ...
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 ...