# Questions tagged [notation]

Questions on the meaning, history, and usage of mathematical symbols and notation. Please remember to mention where (book, paper, webpage, etc.) you encountered any mathematical notation you are asking about.

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### How do I distinguish between "e" the natural log base and a variable conventionally referred to as "e"?

How does one distinguish between the natural base, usually indicated with "e" and a coefficient that, due to historical reasons, is referred to as "e" (such as in Weibull functions ...
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### Writing/Typing Math in 2024 [closed]

When I was in math grad school three decades ago, everyone took notes, solved problems, and did research with pen and paper. For publication, 99% of work was prepared in LaTeX. (I'm more than a little ...
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### Notation for double integral w.r.t. same variable [closed]

When taking the double integral of a function in terms of the same variable $x$, should I write $\int\int y~\text d^2x$ or $\int\int y~\text dx^2$, and why?
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### Definition of mixture of two distributions

What is the formal definition of a mixture of distributions? Usually one says that we flip a coin, and then choose a distribution out of the two to follow. Is it formally correct, then, to say that a ...
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### Is there a name for non sparse linear operators which are products of convolution-like all-but-oneunities?

Is there a name for non sparse linear operators which are products of convolution-like all-but-one unities? I suppose I will have to apologize for the cryptic question phrasing, but I really could not ...
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### meaning of $IBr(X | Q)$

In the paper 1, there is a notation used without specifying the meaning. It is $IBr(X | Q)$ in Definition $4.1$. What it means? Irreducible Brauer characters of the group X from a block with defect ...
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### Question about notation in Durrett's book

I have been studying Markov Chains through Rick Durrett's book, more precisely I was focusing on the Markov Property (Theorem 5.2.3 on page 276 of the book available at: https://services.math.duke.edu/...
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### If I have a sequence $a_0, a_1, a_2, \cdots$ , then is expressing the limit of this sequence as $a_\omega$ sensible?

If I have a sequence created by some rule which comes to a limit , then I can express it as $a_0, a_1,a_2,\cdots$. If I said $\lim_{n \to \infty} a_n = a_{\omega}$ , is that a sensible thing to do ? ...
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### Further questions about correspondence theorem for rings and quotient ring isomorphism.

Background This is a continuation of a post about correspondence theorem for rings, I will repost what I have written here from the Background section of that post here for ease of reference: The ...
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### Question about notation: arg z

I am reading the "Handbook of Continued Fractions for Special Functions", and it has an odd notation that is not clearly explained. It will have, for example, a series expression with ...
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### What does "the set of all $x$'s" mean?

In the context of set theory, I see on websites that set builder notation like $$\{x \mid P(x)\}$$ is read in natural language as "the set of all $x$'s that satisfy the predicate $P(x)$". ...
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### How to define a set without using itself in its definition?

I am trying to construct a set using set builder notation but I am not succeeding. Let $X$ and $Y$ be arbitrary finite sets, and let $Z\subsetneq Y$ be non-empty. Then, let $F=Y^X$ be the set of all ...
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### How to write an inequality? [duplicate]

I have a very simple doubt regarding the writing of inequalities. Consider any arbitrary finite set $X$ and three functions $f,g,h:X\to\mathbb{R}$. Fix any element $x\in X$ and suppose the following ...
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### Why don't we write complex numbers as $a i^{b}$?

Given that $a i^b$ = $ae^{\frac{\pi}{2}bi}$, why do we not prefer to write complex numbers in the form $a i^{b}$ instead of the usual polar form? Intuitively, fractional powers are a much simpler ...
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### Notation for empirical measure (Dirac measure)

I am writing a paper in an area that I am relatively unfamiliar with, and I am after suggestions concerning notation. Here the notion of empirical measure is introduced in the paper In the notation, ...
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### How to state that a function has a certain trend in a limit

Assuming we have a function $f(r)$ that has the following limit $$\lim_{r\to0} f(r) = \frac{5}{3 r^2} \,.$$ What is the correct symbol to express that the denominator goes like $r^2$? Is the ...
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### e{ } and e( ) Notation

I was reading An Introduction to the Theory of Numbers by Hardy and Wright, and on pages 66 and 67, I encountered the notation, as following What does the $e( )$ and $e\{\}$ notation mean? Any help ...
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### What is the simplest symbolic expression for "for some choice of disjoint pairings of $i$, $j$, $k$, $n$, each variable equals its partner"?

I'm not sure if this is appropriate here since the question is about aesthetics and efficiency more than it's about mathematics, but here it is anyway. It's been surprisingly hard to find a short, ...
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### notation for double limits

I need to consider a double infinite limit for a function $f(v,w)$ where both $v, w$ go to infinity. Is the correct notation? The main point I want to emphasize is that there is no ordering, e.g. I ...
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Background Definition 1: Let $R$ be a commutative ring with identity, $c\in R$ and let $I$ be the set of all multiples of $c$ in $R$, that is, $I=\{rc\mid r\in R\}$. Set $I$ is an ideal and is ...