# Tagged Questions

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

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### Soft Question: Good strategies for writing a technical book or textbook

Most people would agree that doing technical work, whether it be pure or applied, and learning the background knowledge necessary to do this work comprises most of the literature and curriculum in ...
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### How to write a set with an index

I'd like to write a set $\{x_1, x_2, ..., x_n\}$ in a simple way. What is a popular way? In my high school, I wrote it as $\{x_i\}_{i=1}^{n}$. Is it a correct way?
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### How to represent “not an empty set”?

I'm writing a academic paper and need to represent "A is not the empty set". What is usual way for professional mathematicians? My idea is: $|A| > 0$ However, using the emptyset $\emptyset$ ...
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### Is there an alternative way to represent the $\operatorname{diag}$ function?

In optimization, it is common to see the so called $\operatorname{diag}$ function Given a vector $x \in \mathbb{R}^n$, $\operatorname{diag}(x)$ = $n \times n$ diagonal matrix with components of $x$ ...
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### 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? ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 $\forall x, y\in A.\ [x]_R=[y]_R.$ ...
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### 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 ...
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### 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 \leftrightarrow....
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### 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 ''left-tail ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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 ...
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 := span\,...