# Tagged Questions

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

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### Notation and Quantifiers

I was wondering what is a natural way to write certain formal expressions, without make them look too cumbersome. In particular, what I learned from various books is that, when we deal with the ...
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### representing a periodic circular shift for a vector formally

I'm writing an algorithm in which the operation of circular shift to a given vector $x=[1 \ 0 \ 0\ ... 0]$ is needed on periodic basis i.e. every $\Delta t$ a circular shift will occur. How this ...
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### Let $f\colon A\to B$ be a function

The following sentence is often used in mathematical articles and writings: Let $f\colon A\to B$ be a function. I wonder, why this senctence is used often, since it is redundant. It is like I ...
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### Papers with unorthodox writing style

I'm not sure if this is the right forum for this question, in any case probably CW is appropriate? I've been looking around the mathblogosphere for the past few weeks and ran into mathgen. It's ...
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### Simple visualisation tool for small graphs

I am looking for a way to add illustrations to a paper I am currently writing. I want to display very basic graphs (not more than 8 vertices, a few edges). The focus is on the edge crossings - I need ...
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### Proper way to write a mathematical theorem

Consider the Bernoulli Inequality, for instance. Basically it says the following: For all $x\in\mathbb{R}$ such that $x\geq -1$ and all $n\in\mathbb{Z}^+$, we have that $(1+x)^n \geq 1+nx$. I'm ...
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### Is it acceptable to use “But” in a proof that doesn't use contradiction?

I have recently read a lot of proofs that like to say "But..." right before the punchline. I feel that the word "But..." should be used if what follows is contradictory in some way, as in proofs by ...
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### 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, ...
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### LaTeX/TeX Vs. Mathematica for Typesetting [closed]

I know Mathematica like the back of my hand, but I do not know a speck of $\LaTeX$ or $\TeX$. With regard to mathematical typesetting, is there something significant I can do in $\LaTeX$/$\TeX$ that I ...
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### Checking that a $3$-D diagram is commutative

When proving certain results I need to use commutative diagrams, some of which quite complicated. My question is: Do we need to check every small square all the time to make sure that they are all ...
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### 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 ...
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### $\mapsto$ 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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 ...
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) ...