Various aspects of writing mathematics such as style, notation, grammar, frequently used phrases and common mistakes.

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2
votes
1answer
42 views

How do you say in a correct way using some technique?

Sorry, I know it's not really related to Math itself, but I still need a native English Mathematician to help me through that and don't know where else to ask... So please don't close it because it ...
0
votes
0answers
32 views

Translation of a book

I am an undergrad studend, my professor told me that a good work I can do is to translate a book on universal algebra (subject which I like a lot) in my language. I'm asking if this kind of work is ...
2
votes
2answers
47 views

Mathematical usage of “$\dots$” during enumeration, is it ok to be imprecise?

I am guilty of writing things like the following in proofs: so by lemma 1.2 we have that for $k<n$ all of the integers $k,k+1,k+2,k+3,\dots ,n$ are pompous. I really like how this looks, the ...
1
vote
1answer
26 views

“The following are equivalent” for only two statements

I often see "The following are equivalent" in theorems that proceed to only have two statements, (a) and (b) be equivalent to each other. When is this appropriate to do rather than say "if and only ...
2
votes
0answers
16 views

Additive and Multiplicative Effects: Terminology

I am trying to explain the relationship between several variables. The outcome of interest is $Y \in \mathbb{R}$, and the predictors of interest are $A \in \mathbb{R}$ and $B \in \mathbb{R}_{>0}$. ...
3
votes
0answers
84 views

When should we use `\frak{…}` in LaTeX

I saw in a note that when writing a paper some notations must be written by \frak{ }, in LaTeX, I want to know what the meaning of some notations is, and where I ...
11
votes
3answers
543 views

Is it acceptable style to mix equalities and inequalities in one line

Is this considered bad style $$2 = \sqrt{4} < \sqrt{16} = 4?$$ It seems as though this is not strictly correct, since $2 = \sqrt{4}$ is a logical proposition which represents boolean value (true ...
0
votes
0answers
21 views

In mathematical writing, what does the phase “Class of nonlinear system” mean?

In many engineering and applied mathematics resources, author specify his work or theory for "a class of Y , Y={Nonlinear systems, Hybrid systems, discontinuous systems .. etc}" what does this mean? ...
1
vote
1answer
24 views

Difference between “Let x be a …” and “Let x … be arbitrary”

What is the difference between "Let x be a ..." and "Let x ... be arbitrary"? Consider the following example: Let $R$ be an equivalence Relation on $A$. Then $\forall x, y\in A.\ [x]_R=[y]_R.$ ...
0
votes
1answer
38 views

Is it ok to make an operation over some definition at very the first time you are defining it?

Suppose we have an expression and want refer to it with some symbol. Usually one can write something like "$X:= \text{Expression}$" to mean the symbol $X$ is defined to be the expression after the ...
1
vote
1answer
32 views

When is it appropriate to use \rightarrow or \leftrightarrow

When writing papers on maths, when is it appropriate to use \rightarrow or \leftrightarrow, and when should one refrain from using them. For example, would this be appropriate use of ...
0
votes
1answer
50 views

Tail driven inequality [closed]

In this empirical model, Lj is a measure of left-tail driven inequality and Rj a measure of right-tail driven inequality. It represents what in this article? What exactly is the meaning of ...
4
votes
3answers
59 views

Good way to state, in english, the negation of “$f$ equals zero almost everywhere”.

Let $X = (X, \mathcal{E}, \mu)$ be a measure space and let $f$ be a measurable function on $X$. Consider the statement: $f$ equals zero almost everywhere Is there an concise, unambiguous way of ...
1
vote
1answer
20 views

Best practice for naming variables to distinguish chosen upper bound from computed maximum.

Say I have a vector of a matrix's singular values $[s_1, s_2, \cdots, s_N]$, and would like to define two variables, one which holds the maximum value in the vector, and another which holds an ...
0
votes
0answers
6 views

Tree decomposition (Citation needed)

Recently, I read the statement "Fix $k\geq 1$, Any tree with at least $k$ edges may be decomposed as a union of edge-disjoint subtrees, each having between $k$ and $3k$ edges" Now I was wondering ...
1
vote
2answers
51 views

How widely known are Iverson brackets?

Here on the Mathematics Stack Exchange I recently learned about the Iverson bracket notation: $[P] = \begin{cases} 1 & \text{if } P \text{ is true;} \\ 0 & \text{otherwise} \end{cases}$ It ...
1
vote
1answer
40 views

End of step symbol

This is more of a style question. We all know to end a proof with the good old QED (I use LaTeX's $\qed$ $\square$). I have a proof that is kind of long, and I was ...
2
votes
0answers
17 views

Changing Notation in Direct Quote

Tried asking this on Academia.SE but the mathjax doesn't render. Direct quote: "...the estimator for the expected logarithmic return, $\hat{\mu} \equiv [\sum_1^n X_k]/h$, will have the properties ...
8
votes
1answer
76 views

English possessive in Mathematics

As a non-native English speaker, I wonder what is the correct way to use the English possessive, also known as Saxon genitive, when dealing with mathematical objects. It seems to me that there is not ...
0
votes
1answer
58 views

The use of English language in mathematics

My question is about the use of English language in mathematics. Should I write "Given a basis $b_n$ of the linear space $B_n := span\,b_n$..." or "Given a basis $b_n$ of a linear space $B_n := ...
0
votes
1answer
54 views

On the mathematical convention used to talk about biconditional proofs

Given $P \Longleftrightarrow Q$, the following does apply: $P \Rightarrow Q$ is equivalent to: $P$ is a sufficient condition for $Q$, $Q$ is a necessary condition for $P$. $Q \Rightarrow P$ is ...
0
votes
0answers
15 views

writing rolling formulas -e.g. average-

Question about writing a formula. Can someone verify if they are correct? Assume Rt = one-period simple return on asset in month t. The average return, Mu, is calculated over the sample from t = 1, ...
0
votes
1answer
22 views

Definition of a function whose codomain is set of probability measure over cartesian product with dependency between sets in the product

I am thinking about the following function: $$ p : A \to \Delta \big( F(x, y(t) ) \times T \big) ,$$ where $t \in T$ denotes continuous time, and $\Delta (X)$ denotes the set of all probability ...
0
votes
0answers
26 views

$\mapsto$ functional notation and probability distributions

I have a question concerning mathematical writing. If we have a function $f: X \to Y$, we can write it \begin{align} f: \ & X \to Y \\ & x \mapsto f(x), \end{align} where $f(x)$ can ...
1
vote
1answer
58 views

How to simplify the equation of combination?

If there are three random variables and three related thresholds, how to simplify the following expression by summation or multiply or other operators? Thank you. ...
2
votes
2answers
95 views

Concise description of why rotation quaternions use half the angle

I'm currently writing the report on my master thesis project, where I use Android sensors to perform inertial navigation in a heavy industrial environment. In my application, I make use of quaternions ...
0
votes
0answers
19 views

Proper way of adding a glossary to an article

I am thinking of adding a glossary to an article of mine, I was wondering if there is an etiquette regarding adding a glossary of symbols and notations? To be frank I have not seen one in any recent ...
0
votes
0answers
43 views

Formulation: Smooth vs. finitely often differentiable

I treat the cases $f\in C^\infty$ and $f\in C^k$ in different sections of my thesis. While I am happy with the title smooth functions for the first section, I am not so sure if finitely often ...
0
votes
0answers
47 views

Article writing: How to represent a matrix by its elements?

Intuitively I guess that parantheses with subscript and superscripts is a way of representing a matrix or an array by its elements, e.g., $$ A = (a_{i,j})_{i,j=1}^n $$ (This is taken from here) ...
9
votes
3answers
434 views

Should I cite the original source or a book?

In the introduction to my thesis, I cite a lot of classical results from the 19th and early 20th century. Should I try and cite the original source for these results, or does that look like I am ...
2
votes
1answer
67 views

Two questions regarding mathematical writing

I am a German mathematics student. I have two questions: First question: When writing several equivalent equations, we usually write this as: $x^2 = 4$ $\Leftrightarrow x = \pm 2$ I have never ...
1
vote
0answers
41 views

How to formally express a negative statement (in the wording or formulation of a theorem, for instance)

This is a doubt about English mathematical formal language. I would like to know the best way to express a negative hypothesis, in the formulation or statement of a theorem, proposition, etc., using ...
2
votes
2answers
57 views

Huge case analysis in an article

I am writing this article on a graph related problem. In an important lemma dealing with classification of a type of graphs, I am undergoing this huge and tedious case analysis involving ...
13
votes
4answers
738 views

How to learn/speak “mathematical english”?

Good day! I was wondering if there is a good way to learn "maths in english". I am studying mathematics in Germany (I am from Germany, so english is not my native language) and have recently started ...
20
votes
4answers
838 views

Why do single-author math papers use “we” instead of “I”? [duplicate]

Even when math papers are authored by one person, you will see stuff like "We now prove so and so" or "In the following section, we show that...". How come papers with one author use "we" instead of ...
0
votes
1answer
29 views

Placement of quantifiers in a symbolic statement

I have the statement: Let $A_n$ be an indexed set of numbers defined by $A_n = n\mathbb{Z}_{\geq m}$ for $n,m \in \mathbb{Z}$. Consider the claim C: For all $n$, if $x,y$ is in $A_n$, then ...
8
votes
6answers
1k views

What is an adjective for “weaker than weak”?

I defined a notion (say, some kind of equivalence) in three forms, the first implies the second, which in turn implies the third. I would like to use "strong", (nothing), and "weak" to describe them. ...
0
votes
2answers
54 views

Proper use of indicator function

Given a set $X$ and a subset $A \subseteq X$ the indicator function $\boldsymbol{1}_{A} : X \rightarrow \{0,1\}$ of $A$ is defined as $$\boldsymbol{1}_{A}(x) = \begin{cases} 1 & \text{if } x \in A ...
9
votes
1answer
109 views

Is there a standard name for this “continuous induction” principle?

I am working on a paper, and I want to prove that some statement $P(x)$ holds for every value of a parameter $x \in [0,\infty)$. I plan to proceed as follows: Show that $P(0)$; Show that if $P(x)$ ...
7
votes
3answers
127 views

Formal writing in math: equations

What is the formally correct way to solve a bunch of equations in math? Is it \begin{align} 42x = 4324 \\ x = 4324/42 \end{align} or \begin{align} 42x = 4324 \\ \Rightarrow x = 4324/42 \end{align} or ...
3
votes
1answer
70 views

Is there a name for this curve? Or, how should I describe the behavior of this graph (in words)?

I simulated some results that look like this: but I don't want to include the plot (my advisor is keeping me to a strict limit on figures and these are minor intermediate results). Is there a name ...
1
vote
1answer
26 views

How should I describe this limiting operation in an equation

In the code I've written, I receive a delta between two position vectors, I then limit this delta by a maximum delta and return the value. To be clear: the direction of the vector remains the same, ...
3
votes
1answer
165 views

Referencing a Theorem in a Paper?

I'm making the final edits for a paper and I have a question more about the etiquette. I want to use a theorem from another paper and its obvious I have to cite it, but do I need to prove it too? I ...
0
votes
0answers
33 views

Writing finite field notation

I am trying to write about finite fields in a word document, and although usually writing in latex form works, it's not in this case. It works fine here: $\mathbb{F}$: I used \mathbb{F} But it ...
6
votes
0answers
338 views

In a math paper, what is a remark?

I sometimes see paragraphs labeled 'Remark.' However, papers that include remarks also include unlabeled explanatory paragraphs (i.e. all the other writing in the article) that seem to be remarks. ...
2
votes
0answers
36 views

Is there a published standard for the sectioning of math papers?

Most papers seem to use sections (e.g. 3) and sub-sections (e.g. 3.1). Is there a published standard that says what sort of thing warrants its own section and what sort of thing warrants its own ...
3
votes
0answers
51 views

Formulating equation for distances between atoms

I'm trying to formulate notation to describe code that calculates the distances between protein atoms (represented as points in 3D space). Fragments consist of residues (amino acids) and each residue ...
0
votes
1answer
32 views

The use of “consistent with”.

This is a simple question about writing but I'm a little bit confused now about the logic in using "consistent with". The context is as follows: We first derive a formula for a special case, say, for ...
2
votes
0answers
112 views

a.s. for all $t$ or for all $t$ a.s.?

Assume that we have some equality, $$ X (t) = Y(t). \quad \quad \quad \quad \quad \quad \quad (1) $$ I imagine that if I say "(1) holds a.s. for all $t>0$" it means that $$ P\{X (t) = Y(t) ...
-1
votes
1answer
442 views

Is the phrase “recall that…” an abuse? [closed]

I love how in some proofs delivered formally or informally, you would always encounter the phrase "recall that". The irony here is that you precisely do not recall this notion or formula e.g. the ...