0
votes
0answers
12 views

Phrases for uniform boundedness and uniform convergence

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 ...
1
vote
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. ...
0
votes
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 ...
7
votes
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...''. ...
2
votes
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 ...
0
votes
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 ...
6
votes
4answers
448 views

Are there rules in the useage of prepositions in Math?

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 ...
11
votes
4answers
618 views

Short forms like “haven't”, “don't”, “let's” [closed]

Is it true that short forms like "haven't", "don't", "let's" should not be used in serious mathematical texts?