Questions tagged [article-writing]

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

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Book or article on Bernoulli numbers and polynomials

I am looking for a book or article that deals in detail with the Bernoulli numbers and polynomials.
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35 views

In which cases can the article "the" in sentences be eliminated? [closed]

In the sentence "Geometric interpretation of the non-commutativity of unit quaternion multiplication", can we just write "... of non-commutativity of ..." ?
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1 answer
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Measurement or measure of a complex number?

In math, do we write "measure of an angle of two vectors" or "measurement of an angle of two vectors"?
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1 vote
1 answer
65 views

How to write maths

In the sentence below, which expression is better to choose: "their multiplications" or "their multiplication" : "This identification allows us, first, to present a new polar ...
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63 views

Why do we say a non-negative real number

In some articles, we write "non-negative real number". Why we don't simply say "positive real number" ?
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1 vote
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Cross-references in a LaTeX document [migrated]

When I click on the link of a reference (equation, image, section...) it sends me to the beginning of the page where the reference is and not to its exact location.
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How do I express that something is distributed over an interval?

I have a set of states between $t=0$ and $t\to\infty$. I'd like to write the following: The states are distributed over $t=\left(0,\infty\right)$, so the intervals in $t$ between them are ...
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47 views

Mathematical English in PDE's type paper

I am trying to write some materials in PDE content. However, my English is not very good. Do we have some PDE's type papers or books that is well-written? I am reading the book by Trinduger, but I can ...
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25 views

Is there a name to refer to point $A$ / point $B$ when discussing vector $\overrightarrow{AB}$?

In a code, I am writing a concise documentation of a function that needs 2 vectors defining a triangle $ABC$. The function performs an operation which is invariant up to a translation, so two vectors ...
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Rephrasing statement: Let $S$ be a set of eigenvalues of an operator $T$. Then $S=[1..n]$

How can I write the following statement in a concise English sentence, using the expressions commonly used in math context (e.g., unique, if and only if)? My question is about the exposition of the ...
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3 votes
1 answer
79 views

How can I say "$T \to \infty$ implies ..."?

I would like to know a better way to say "$T \rightarrow \infty$ implies ..." when writing / speaking. I tend to write this as "Limiting $T$ to $\infty$ implies ...", but others ...
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18 views

Correct description/numbering of formulas across multiple pages

I don't want to discuss a mathematical problem here, I want to ask how to meaningfully present formulas that extend over several pages. Attached is my suggestion where on the first page the equation ...
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3 votes
1 answer
105 views

Can I change a Lemma to a Proposition?

I am getting confused about one thing: I am reading a paper say X. Paper X has a Lemma in it. I am also writing a paper for my dissertation. I want to use the Lemma from Paper X in proving a theorem ...
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14 views

Writing mathematical expression for limit on allowed repetitions

I have to write the expression explaining, in $0\leq C_1 \leq C_2\leq \cdots \leq C_r$ "There are no more than $l$ numbers (i.e. $C_i$'s) that can have the same value." How do I write the ...
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0 answers
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When to use "in" versus "into" when talking about embeddings?

Let $A$ and $B$ be mathematical structures of some kind. Consider the following statements: $A$ embeds in/into $B$. $A$ does not embed in/into $B$. There is an embedding of $A$ in/into $B$. We say $...
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4 votes
1 answer
96 views

How to write an equation and its simplification next to it (math etiquette wise)?

I always have this problem where I want to write an equation then immediately its simplification after it. I used to use the imply or equivalent symbol such as: Therefore we end up with $$ \frac{a^2}{...
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Denoting Repeated Value from First Column of Table

In a manuscript I am preparing, I have a large table with entries that are repeated along some rows. For example, including all numbers would look like Main Column Column 2 Column 2 1.03 1.03 1.03 ...
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1 vote
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42 views

What is the equation for the standard deviation of the set of all odd integers?

I have a set containing all of the odd integers in the integer set. It is denoted by $O=\{2n+1\mid n\in \mathbb{Z}\}$. I want to write an equation that equals the standard deviation of the set. If I ...
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42 views

Would you demand a proof that this is a cyclic subgroup of $(Z/NZ, *)$?

I'm mostly looking for advice on how to say, how to write this, how to prove it. I think it probably dispenses a proof. I'm writing this to a small number-theory audience, so I don't think they need ...
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7 votes
1 answer
116 views

"Theorems 1 and 2 imply" vs. "Theorem 1 and Theorem 2 imply"

To convey that $$\text{Theorem 1} \wedge \text{Theorem 2} \implies A$$ which style is better? Theorems 1 and 2 imply $A$. Theorem 1 and Theorem 2 imply $A$. Which style manuals prefer which form? (...
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2 votes
0 answers
89 views

How do I write mathematics?

Currently, I’m teaching myself mathematics as a part of my self-study. I’m working on Calculus, and I plan to do so for the next few months or years (I’m in first year of high school, so I have time). ...
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0 votes
1 answer
92 views

Set definition problem

I want to write in a Proposition: "There exists $x_1$ and $x_2\geq x_1$ so that (a) If $x\in [0,x_1)$, then $A>B$. (b) If $x\in [x_1,x_2)$, then $A\leq B$. (c) If $x\in [x_2,\infty)$, then $A&...
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1 vote
2 answers
81 views

Feedback on Proof of Squeeze Theorem

I wrote out a proof of the Squeeze Theorem for my personal notes as I study AP Calculus. This is my first time really writing out a proof using a combination of natural language and logic. I would ...
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45 views

Meaning of "a particular case of" and "special case"

When people says that function $f$ is a particular case of function $g$, does this mean that $f$ is a special case of $g$? Are "special case" and "particular case" the same thing? ...
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1 vote
1 answer
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What do you call the set definition part of a formula?

Suppose I have a formula with two parts: First is a description of the element and set on which an equation will depend, and the second is the equation itself. Example: First, the formula quantifies ...
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26 views

How to simpilfy a function $ f(x_1^1,x^1_2,...,x^1_q,x^2_1,...,x^N_q)=0 $ in a correctly way?

I have a function $f(.)=0$, with respect to $x^{I}_i$, where $I=1,2,...,N$ and $i=1,2,...,q$. We can write the function in the way: $f(x_1^1,x^1_2,...,x^1_q,x^2_1,...,x^N_q)$=0. It looks very ugly. I ...
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30 views

How to express orthogonal basis of space spanned by some vector in a correct way?

I have a series of vectors, suppose ${a,b,c,d,e}$. These vector span a space. $span \{a,b,c,d,e\}$. I have the orthogonal base of the space, supposed called $u,v,x,y,z$. How can I express the ...
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1 vote
1 answer
26 views

Does the choice of variable matters in area function using definite integrals?

Consider the following context and definition from the sub-section 7.8.1 Area function of the chapter Integrals from the NCERT textbook We have defined $\int_{a}^{b} f(x) dx$ as the area of the ...
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1 vote
2 answers
87 views

A+B is sufficient and necessary for C. C is unnecessary for D. Is it flawless to formally write that "A and B are unnecessary condition for D"?

Condition A+B is sufficient and necessary for condition C. Condition C is sufficient but not necessary for D. Is it flawless to write that: "A and B are unnecessary condition for D "? I am ...
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9 votes
1 answer
289 views

Mixing fraction notation with slash notation

I am writing a theorem, and in it, I mix $\frac ab$ and $a/b $. The reason for this is that I find $$\lceil a/b \rceil \tag{1}$$ better-looking than: $\displaystyle \biggr \lceil \frac ab \biggr \...
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0 votes
1 answer
56 views

Representing the total derivative

This is a quick question about syntax. I have the function: $$\hat{x_i} = \frac{x_i - \mu_\beta}{\sqrt{\sigma^2_\beta+\epsilon}}$$ where $\sigma^2_\beta$ is an intermediate function: $$\sigma^2_\beta =...
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1 vote
2 answers
51 views

Can you say "The inequality B encompasses A"?

I know this is a silly question for English speakers, but as a non-native speaker, please help me communicate in math. I am about to report in a formal academic paper on inequality B, which is a ...
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0 votes
0 answers
21 views

What is the most common and appropriate way to express sub-matrix

Suppose I have this matrix A, I am wondering if this is the correct and formal way to express the red rectangle submatrix, S=A1,2;2,4 Also looking forward if there is a better solution. Thanks in ...
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2 votes
0 answers
47 views

Remark inside a proof

It is a good practice to define a remark inside the proof of a theorem to highlight a necessary observation to go on the proof? Edit (the scheme that I imagine is the following): $\textit{Proof }$ ... ...
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9 votes
2 answers
270 views

The best way to use notation in the proof

I have two simple questions regarding the writing styles. Assume that I make a remark~$1.1$ and I define two sets say $A:=\text{something}$ and $B:=\text{something}$. My question is that I will use ...
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0 votes
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84 views

The use of definite and indefinite articles in math (the vs. a/an)

This question has been on my mind for a while now. Not being a native speaker and coming from a country, where grammatical cases are used to modify nouns and nominal parts of speech, the use of ...
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2 votes
2 answers
60 views

Is writing $m=\text{undefined}$ formally correct?

I often find some of my students write $m=\text{undefined}$ in their answer sheets. Is it formally correct? Should I suggest them to write $m$ is undefined instead? For example the question is ...
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1 vote
1 answer
28 views

Conventional notation for congruence to multiple numbers

Is there a more concise notation for the following sentence? "Thus $ f(n) \equiv 0 \pmod{12} $ for all $ n \equiv x \pmod{12} $ where $ x \in \{ 0, 1, 3, 6, 7, 11\} $." Is this an acceptable ...
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0 votes
1 answer
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Logic symbols in a math paper? Is this correct?

I am writing a mathematics paper with the intent to publish it in a peer-review journal. I have written something along the lines of Theorem 2. (1) something (2) something else. (end of Theorem 2). ...
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1 vote
1 answer
115 views

Multiset/Set/List initiation and use in pseudocode

I'm writing a paper and I've come across interesting problem. In my algorithm, I create a list of 0's (example [0,0,0,0]), where the number of 0's is given by parameter "x". Later I want to ...
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0 votes
1 answer
65 views

the equation (A) vs Equation (A)

Quick question about grammar in English. Consider the equation $$x^2=c \tag{A}$$ Do we say that: For every $c<0$, the equation (A) has no real solution. For every $c<0$, Equation (A) has no ...
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0 votes
1 answer
52 views

Using existential statements in informal mathematical reasoning

In symbolic logic, existence statements are normally written as $\exists x P$ where $P$ is some smaller statement. The $x$ is bound by the existential quantifier and the scope of $x$ is $P$. When ...
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0 votes
1 answer
22 views

Summing Term over only edges involving a particular node

I've got a quick notation question. Currently I'm trying to do a sum over all edges of a graph as so: $$ \sum_{i, j\ \in {E}}^{m}\frac{J_{i j}}{4}Z_{i} $$ What notation would indicate I only wanted to ...
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0 votes
1 answer
127 views

How do I write equations for this Fibonacci sequence

The Fibonacci sequence can be defined using the recurrence relations: $F_0 = 0, F_1=1, F_{n} = F_{n-1} + F_{n-2}~~$ for $n \in \mathbb{N} \colon n \geq 2~~~$ (1) $ F_0 = 0, F_1=1, F_{m+2} = F_m + F_{...
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0 votes
0 answers
88 views

Summarising a Research Paper

I thought to put this out to the community. I am an Undergraduate student summarising maths papers, firstly to get to grips with reading mathematical research and collecting a body of interesting ...
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1 vote
1 answer
42 views

Compact notation for limit at two different points of interest

Is it acceptable to replace $$ \lim_{x\to a}f(x)=\lim_{x\to b}f(x)=c $$ with $$ \lim_{x\to \{a,b\}}f(x)=c? $$ If not, is there another way I could state such a fact in a compact manner without having ...
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1 vote
1 answer
47 views

Interpretation of "[Numbers] are taken modulo" in scientific writing and best practice suggestions

This is a question specific to scientific writing and not about the modulo operation. The final question will be: Is this expression well-formed, or should it come with clarification? On several ...
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1 vote
1 answer
20 views

Grammatical standard for ordinals of complex expressions

In English, ordinals are usually created by appending a “-th” or “-eth” sound to the end. In mathematics, this extends to variables, hence the word “$n$th”. But the numbers 1, 2, 3, and 5 are ...
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-1 votes
4 answers
58 views

Which does "themselves" qualify, "proofs" or "three theorems" in this sentence? (Michael Spivak "Calculus 3rd Edition") [closed]

I am reading "Calculus 3rd Edition" by Michael Spivak. There is the following sentence in this book: The proofs of the three theorems themselves will not be given until the next chapter, ...
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0 votes
1 answer
48 views

How to write a mathematical expression defining a set with double "such that"?

I have a sentence I am trying to translate as a mathematical expression but I am not sure if the expression matches what I mean. The mathematical expression I came up with: What I actually mean: F is ...
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