Questions tagged [article-writing]

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

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Writing style of mathematical paper.

I want to write a mathematical paper that is tailored for applied mathematics. To be more specific, it is using extensively differential equations and integrals. I observed that there are two ...
Aschoolar's user avatar
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What is the proper notation for cartesian coordinates with decimals in your native language? [closed]

For simple integers, (1, 2) is what most people are taught in elementary school. This appears to be true regardless or whether their language's decimal separator is ...
octosquidopus's user avatar
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In English grammar, is a mathematical expression considered a clause or a noun phrase?

In English grammar, is a mathematical expression considered a clause or a noun phrase? When I read the mathematical proof, I find that it is not uniform for authors to treat the mathematical ...
magpie's user avatar
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2 answers
85 views

Notation for a fraction of $n!$

Suppose I want to write $n!/2$, can I just write $\tfrac{1}{2}n!$ or is that easily confused with $(\tfrac{1}{2}n)!$ and I have to write $\tfrac{1}{2}(n!)$? Are there precedence rules for these ...
Jeroen Boschma's user avatar
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2 answers
58 views

Is it incorrect to use ellipses when writing an irrational number's approximate value with a $\approx$?

For example, is it incorrect to write that Euler's number is $$ e \approx 2.718\dots $$ or is it more proper to write $$ e \approx 2.718 $$ or, maybe I should just write $$ e = 2.718\dots $$
Kalcifer's user avatar
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7 votes
2 answers
235 views

A better way of presenting mathematical content

Traditionally, mathematical work is presented in a linear fashion. Books, papers and articles are single streams of text meant to be read sequentially, from beginning to end. However, mathematical ...
Alex's user avatar
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-3 votes
4 answers
3k views

Which definition of "power" is true: Britannica's or Wikipedia's? [closed]

Britannica says $a^k$ is the power; Wikipedia says that the power is $k$. Which one is it? Did someone make a mistake? Exponents Just as a repeated sum $a + a + \cdots + a$ of $k$ summands is written ...
bp2017's user avatar
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1 answer
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A one word name for "taking a root" operation?

We have addition and subtraction, multiplication and division, But what about raising to a power and taking roots? I hear about "exponentiation" recently, a term that I don't recall being ...
bp2017's user avatar
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New Formula for the Payback Period (PBP) of an investment

$\bf1$. Context: Payback Period (or PBP): Time required to recover initial investment in a project. Payback Period = $\bf3.25$ years (to recover the $50,000$) $\bf2$. Unliked Formula: PBP = $\frac{\...
InanimateBeing's user avatar
3 votes
1 answer
456 views

Does 'hence' (thus, therefore) need a comma after it?

In mathematical papers, when "hence" is placed at the beginning of a sentence, I have observed that some authors use a comma while others do not. The same issue can arise with "...
licheng's user avatar
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9 votes
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Is "William only eats icecream when the sun is shining" a biimplication?

William only eats icecream when the sun is shining Let $P(t)$ be the sun is shining at time $t.$ Let $Q(t)$ be William is eating an icecream at time $t.$ Which implication is there between $P(t)$ and $...
Marcus K. Johnson's user avatar
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Concise yet Rigorous Proof: How to Modify It?

The following proposition is standard. Proposition 1. Let $G$ be a graph with a planar drawing $D$ and at least three vertices. Then, $D$ can be extended to a multi planar drawing $D^*$ by adding ...
licheng's user avatar
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-2 votes
1 answer
137 views

How to avoid using the same phrases repetitively? [closed]

In my paper, I have used the expression "It is well known that" twice in a row. Using the same expression repeatedly may appear monotonous. Are there any other commonly used alternatives for ...
licheng's user avatar
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1 vote
1 answer
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Is the term "n-order graph" commonly used?

Order of a graph is the number of vertices in the graph. I don't know if "n-order graph" is common or standard. For example, We obtain a 25-order graph with minimum degree 5. I'm aware ...
licheng's user avatar
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2 votes
1 answer
45 views

How can we improve the following sentence?

How can we improve the following sentence? Let $G$ be a planar graph with $n$ vertices with minimum degree $5$ with diameter two where $n$ is odd. Firstly, I realized that I used "with" ...
licheng's user avatar
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2 votes
3 answers
331 views

How do we translate between Logic and Mathematical English?

Take the statement "Let $a \in \mathbb{R}$ and let $z=ai.$" $(1)$ In English, this means "Let's choose any real $a$ then define $z$ such that $z=ai$ for that particular $a$ we have just ...
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Is it not suitable to use Arabic numerals here? [duplicate]

In the reviewer's comments on my paper, he/she suggests replacing the following Arabic numerals with English letters (in the following examples). I believe his/her suggestions are correct. But I'm ...
licheng's user avatar
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1 vote
1 answer
50 views

What is the right punctuation when introducing mathematical terms in a sentence? [duplicate]

This is not a mathematical question as such, but more about the correct grammatical way to describe the mathematical terms that are being introduced in a sentence. I am used to writing sentences in ...
jbx's user avatar
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What is the right numbering scheme in a paper with several theorems, lemmata, claim, proposition etc.?

There could be two ways: The creatures 'theorem', 'lemma', ... remain separate. So, Theorem 2 can come after Lemma 5, because they are separately numbered. OR A consolidated numbering scheme, e.g., ...
Pagol's user avatar
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Is the $\exists x$ in $\{f(y):\exists x\ (x,y)\in A\}$ necessary?

Suppose $A$ is a subset of the Cartesian product $X\times Y$, and $f$ is a function from $Y$ to some set. Is it acceptable to write $\{f(y):(x,y)\in A\}$ instead of $\{f(y):\exists x\ (x,y)\in A\}$? ...
new account's user avatar
1 vote
1 answer
122 views

Should I use plural nouns when the number of objects may be one or more?

I have the impression that it's a tacit convention that when there may be one or more objects in concern, we can just use a plural noun, but now I'm dithering. I wrote the statement "every ...
Long Horn's user avatar
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13 votes
5 answers
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"a Euler graph" or "an Euler graph"?

I recently referenced the following article in my manuscript. S. Toida, Properties of a Euler graph, J. Franklin Inst. 295 (1973) 343–34. However, my grammar checker flagged “a Euler graph” as a ...
licheng's user avatar
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3 votes
3 answers
137 views

What is the correct notation for "for all nonzero $a$ in the real numbers"?

For all nonzero $a$ in the real numbers,... Which, or neither, is the correct notation for the above quantification? $\forall a \in \mathbb{R} \neq 0,\ldots$ $\forall a \neq 0 \in \mathbb{R},\ldots$
Antonio De Angelis's user avatar
3 votes
1 answer
71 views

What does the word 'with' mean in this theorem?

If $a, b$ and $c$ are positive integers with $a, b ≥ 2$, then equation (1.1) has at most one solution in positive integers $x$ and $y$ with $b^y ≥ 6000 c^{1/δ∗(a,b)}.$ I'm unclear about the above ...
Nimish's user avatar
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2 votes
0 answers
88 views

Enunciation in mathematical text (style)

I'm writing longer mathematical texts (lecture notes) regularly, and I don't know where else to ask this question. I regularly find myself enunciating (in the typographical sense) every statement I ...
Gargantuar's user avatar
2 votes
1 answer
300 views

In which cases the subscript is a "0" (zero) and an "o" (letter o)?

As stated in the title, the question is simple, about formatting. Reading through physics papers, I have seen $\varepsilon_o$, $\rho_o$, $\mu_o$, to denote some physical constants. Note that all of ...
Ismael Valero's user avatar
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0 answers
41 views

Differences between $\mathrm{End}(V)$, $L(V)$ and $B(V)$

I was wondering what are the differences for, e.g. some vector space $V$ (over a field $\mathbb{k}$), between $\mathrm{End}(V)$, $L(V)$ and $B(V)$. I know this is a naive question but I would like to ...
bdt's user avatar
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'if' and 'if and only if' equivalence in mathematical definition

I am always puzzled by the difference between 'if' and 'if and only if'. I know that an 'if' statement is one-way while an 'if and only if' is two-way. However, I also know that it is a convention to ...
Sam's user avatar
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2 votes
1 answer
136 views

How can the notation $\operatorname{atan2}(y, x)$ be used in scientific papers?

During a presentation for a PhD engineering topic I had shown the $\operatorname{atan2}(y, x)$ function within a slide as part of an equation. I received a remark by a professor that $\operatorname{...
Phill Donn's user avatar
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2 answers
192 views

Which of these translates the universal and existential quantifiers better?

Consider this proposition (which I know is false): $$(\exists y{\in}\mathbb Z)\,(\forall x{\in}\mathbb Z)\,(y > x).$$ I am wondering whether the analogy of picking a variable value according to the ...
Princess Mia's user avatar
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2 votes
1 answer
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Interpretation of: *(Statement 1 holds), if (Statement 2)*

I have come across a question in a Real Analysis assignment (contents of the question are not important), where I need to prove that: (Statement 1 holds), if (Statement 2). I'm confused about the ...
Pourush Sood's user avatar
2 votes
2 answers
121 views

What is good english grammar and punctuation with mathematics statements? [duplicate]

Consider the following alternative paragraphs containing a line of mathematics. The mathematics is in its own line (thus not in line with the text), e.g., for the sake of emphasis. This paragraph ...
pele's user avatar
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0 votes
1 answer
73 views

Should I use by construction or by assumption?

I'm solving a differential equation with some boundary condition. When I use the boundary condition in my solution, should I say ... is true by construction or by assumption? Or should I use some ...
orangecat's user avatar
  • 303
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0 answers
61 views

Is it necessary to add brackets behind $\arg\max$?

If an expression consists of more than one term, e.g., $x^2 + x$, is it necessary to add brackets to it when it is following an $\arg\max$ notation like $\arg\max(x^2 + x)$? I found that, in some ...
Haozheng Wang's user avatar
1 vote
2 answers
116 views

Is it correct to write "$100 \leq x,y \leq 380$"?

I am solving a problem in which I am looking for integers $x$ and $y$ in between $100$ and $380$ (including $100$ and $380$). Is it mathematically correct to write $$100 \leq x,y \leq 380,$$ or am I ...
x3la.F's user avatar
  • 119
2 votes
1 answer
59 views

How can we express this sentence more concisely?

Let $w_1,w_2,w_3,w_4$ be vertices of $K_4$. The sentence I intend to express is the following: Based on how the four vertices $w_i$'s are placed in the sphere, there are possibly two drawings of $K_4$...
licheng's user avatar
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0 votes
0 answers
70 views

How to express " without loss of generality" appropriately?

In my article, I would like to write the following sentence: There exisits a vertex in $H$, without loss of generality, let it be $v$, such that $H-v$ is connected. I think the sentence above is ...
licheng's user avatar
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0 votes
0 answers
54 views

Word/phrase for proving something stronger

I remember encountering a (probably Latin) word/phrase which is used when you prove something stronger than what was desired, and therefore our desired claim follows. I like to collect mots justes, ...
Aditya's user avatar
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37 views

Objects that can be 'pulled apart' without touching each other

Is the following definition of objects (defined by compact sets) which may be 'pulled apart' without physically touching each other acceptable? Two compact sets $A, B \subset \mathbb{R}^3$ are said to ...
FabrizzioMuzz's user avatar
2 votes
0 answers
63 views

Terminology problem: what if the historical term is not convenient for me while writing paper?

I am a graduate student and I am writing a paper. For an irreducible Markov chain $P$ with spectral radius $\rho$, the historial literature says that it is $\rho$-transient iff its Green function at $...
Chennes's user avatar
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1 vote
0 answers
187 views

Software/tool to grammar-check mathematical document

Several softwares/tools are available to grammar-check a document (research paper, report, book, etc.). But, all of them have trouble performing when there are inline mathematical equations in the ...
Cyriac Antony's user avatar
2 votes
1 answer
81 views

An English expression problem about making symmetric differences over multiple sets

I give the definition of symmetric difference of two sets in my article. The symmetric difference of two sets is the set of elements that are in either of the sets but not in their intersection. A ...
licheng's user avatar
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0 votes
0 answers
37 views

How to cite when using an idea from another author?

Firstly: Please help me find a proper tag for this question. I explicitly didn't post it on academia stack exchange because it has no latex support and to get answers from more people that might write ...
manuel459's user avatar
  • 257
0 votes
1 answer
41 views

Is there a conventional order to write commutative parts of an expression?

This stemmed from an office discussion. Often when writing expressions, it feels like there is a more natural way to write parts of an expression that are commutative. For instance, it seems as though ...
scs-erin's user avatar
1 vote
0 answers
64 views

"with", "where" or "and"? A question about good writing style.

If I am writing down this function $$ f: D^2\to \mathbb R $$ and want to communicate that $D\subseteq \mathbb R$, should I write $$ f: D^2\to \mathbb R \quad \mathrm {with} \quad D\subseteq \mathbb R$...
Florian's user avatar
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1 vote
0 answers
28 views

Which hyphen to use for transformations that are not measure-preserving?

In How to write mathematics, P. R. Halmos has an amusing anecdote: I once studied certain transformations called "measure-preserving". (Note the hyphen: it plays an important role, by ...
red_trumpet's user avatar
  • 8,302
5 votes
2 answers
460 views

Notation for multiple elements not equal to each other

I have four elements, $A,B,C$ and $D$. I want to write that none of the elements are equal to each other. Basically, something like this: $$A \neq B \neq C \neq D$$ However, this is incorrect, since $\...
user3053216's user avatar
7 votes
1 answer
120 views

Is it "a" or "an" in front of Greek letters beginning with a vowel?

Good evening! I know that it is a basic rule in English that before most vowels, the indefinite particle a becomes an. My question now is: Does this also apply in front of (non-latenized) Greek ...
Nuke_Gunray's user avatar
  • 2,616
0 votes
0 answers
175 views

Can “equality” be used in the plural form?

An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. The "inequality" has a plural form by "inequalities". I would ...
licheng's user avatar
  • 2,226
0 votes
1 answer
44 views

How could I rewrite a formula looking to me too much summarized/simplified?

On a book, to present me a transformation required during a Principal Component Analysis (PCA), with: $\mathbf{I}$ : the set of individuals $\mathbf{i}$ : an index going over one individual $\mathbf{l}...
Marc Le Bihan's user avatar

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