Questions tagged [article-writing]
Various aspects of writing mathematics such as style, notation, grammar, frequently used phrases and common mistakes.
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How to properly punctuate "for all" after mathematical expressions?
One thing about mathematical writing that has always puzzled me is how to properly punctuate "for all" after a mathematical expression. Let me give you an example.
A function $f:\mathbb{R}\...
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Which is correct? The sixth kind Chebyshev polynomials or The six$^{\text{th}}$ kind Chebyshev polynomials? [closed]
Which is correct in English grammar?
What is the difference between 6th and 6$^{\text{th}}$?
For example, I know sixth kind Chebyshev polynomials is correct and there is in papers. What about six$^{\...
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1
answer
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Referencing a statement with quantifiers in two separate lines
I want to show that a statement with several quantifiers, e.g., "$f(a, b) <= 0$ for all $a\in [0, 3]$ and all $b\in [-\infty, -1]$", is equivalent to another statement with several ...
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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 ...
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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 ...
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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 ...
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2
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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 ...
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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
$$
e = 2.718\dots
$$
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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 ...
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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 ...
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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 ...
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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{\...
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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 "...
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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 $...
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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 ...
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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 ...
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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 ...
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answer
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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" ...
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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 ...
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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 ...
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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., ...
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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 $\{f(y):\exists x\ (x,y)\in A\}$? ...
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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 ...
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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 ...
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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?
$\forall a \in \mathbb{R} \neq 0,\ldots$
$\forall a \neq 0 \in \mathbb{R},\ldots$
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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{...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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
$K_4$...
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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 ...
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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, ...
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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 ...
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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 $...
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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 ...
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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 ...
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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 ...
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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 ...
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"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 $$ f: D^2\to \mathbb R \quad \mathrm {with} \quad D\subseteq \mathbb R$...
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Which hyphen to use for transformations that are not measure-preserving?
In How to write mathematics, P. R. Halmos has an amusing anecdote:
I once studied certain transformations called "measure-preserving". (Note the hyphen: it plays an important role, by ...
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Notation for multiple elements not equal to each other
I have four elements, $A,B,C$ and $D$. I want to write that none of the elements are equal to each other. Basically, something like this:
$$A \neq B \neq C \neq D$$
However, this is incorrect, since $\...
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