Mathematics Stack Exchange
Mathematics Stack Exchange

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.

Before asking a question on the site, please check if you can find your answer in Earliest Uses of Various Mathematical Symbols or the book A History of Mathematical Notations.

Alternatively, a textbook or paper usually takes the time to explain the notation they're using; please remember to mention where you've seen the notation you are asking about.

12848 questions
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Meaning of dot symbol "·" in this context?

In this context, what does the dot symbol "·" mean? Multiplication? I looked it up on Wikipedia but couldn't find it.
user2979713
  • 27
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Correct notation for variable substitution?

Is this notation conventional to indicate that $M$ should be replaced with 2? $$ \left. \frac{(D + M - 1)!}{(D - 1)!M!} \right|_{M = 2} $$
Raj
  • 964
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3 answers

Symbol for $\left\{ x \in \mathbb{R} : x > 0 \right\}$

Is there a symbol for the following set? $$ \left\{ x \in \mathbb{R} : x > 0 \right\} $$
Jordan Kelk
  • 29
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What does $s\in \{(u_0,u_1)\in \Bbb R \times\Bbb R^3\}$ mean?

Given the expression $s\in\{(u_0,u_1)\in \Bbb R \times\Bbb R^3\},$ what is s? a single vector in $\Bbb R^4$ consisting a concatenation of the elements of $u_0\in \Bbb R$ and $u_1\in \Bbb R^3$ a set of two vectors in $\{u_0, u_1\in\Bbb R^4\}$ a…
mel
  • 31
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Notation in derivation theorem

Can you explain what does $ \frac{\partial}{\partial x^i}$ means?
Nazar Serdyuk
  • 289
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0 answers

Notation of List other than Set, and related operations?

we all know that a single capital letter (e.g., $S$) usually represent a set (containing non-duplicate objects) and we can write a number of operations on set such as $|S|$, $|S|$ union $|S'|$ etc. However in my case I need to define a list, that is…
Ziqi
  • 121
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2 answers

Typesetting of per-degree

What is the best (most accepted) way to typeset something like $5$ per (angular, not temperature) degree (in $\LaTeX$)? I came up with the following options (using ^\circ for the $^\circ$ symbol): $5 \frac{1}{^\circ}$ $5/^\circ$ (eventually with a…
Ragnar
  • 6,233
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3 answers

Why is the notation for differentiation like this?

Consider the notation for denoting the differentiation of a function $f(x)$. $$\frac{d[f(x)]}{dx}$$ I mean, this notation doesn't make any sense. $dx$ means a vanishingly small $x$, which can be understood, if we take $x$ to mean $\Delta x$ in a…
Gerard
  • 4,264
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1 answer

Distinguishing definitions from equivalences.

I'm used to people using the symbol $\equiv$ when defining quantities. I might see expressions like $$\frac{df}{dx} \equiv \lim_{\delta\to 0} \frac{f(x+\delta) - f(x)}{\delta} = 2x \,.$$ where the first part is what is meant by the symbol $df/dx$,…
gj255
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  • 32
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What's the difference between ]a,b[ and (a,b)?

Is there any difference between $]a,b[$ and $(a,b)$? If there is no difference, what would be the motivation of using $]a,b[$ over $(a,b)$?
Chang
  • 243
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Explain the symbol $\bigvee$ in "Adventures in Stochastic Processes"

What does the symbol $\bigvee$ mean in statement 1.5.1.2? Thank you.
hans-t
  • 437
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2 answers

Use set notation to define vector or matrix?

I'm looking for a concise way to define the following (horizontal) vector: $$\mathbf{x} = [x_{-k}, \dots ,x_{k}]$$ where $x_k = \mathrm{i}$ if $k$ is odd and zero otherwise, and $|k| \le K $. So far I though I thought something like $$\mathbf{x} =…
geometrikal
  • 425
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1 answer

notation for equations solving

I have some notation questions on the following equation solving: 2+x=5$\iff$x=5-2$\iff$x=3 Would you read the above as "two plus x equals five if and only if x equals five minus two if and only if x equals three" ? Somehow it doesn't sound natural…
Marcus Junius Brutus
  • 913
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2 answers

Double left-right arrow meaning

While reading Hilbert's Tenth Problem (English version of a talk by Y. Matiyasevich) at page 3 I found: ...On the other hand let $$D(x_1,...,x_m) = 0 \quad (3)$$ be an arbitrary Diophantine equation; suppose that we are looking for its solutions in…
Vor
  • 690
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votes
2 answers

Notation for vector composed of subset of elements of another vector

Suppose I have a vector $\boldsymbol{x} = (x_1,x_2,\ldots,x_N)$ in $\mathbb{R}^N$. I need to express a function $\boldsymbol{y} : \mathbb{R}^N \mapsto \mathbb{R}^{M(\boldsymbol{x})}$ where $M(\boldsymbol{x}) \le N$ such that the vector…
synaptik
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