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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How to write $\frac{k}{k}$ using $\sum$ notation?

I want to use $\sum$ notation for this:$$\underbrace{\frac{1}{k}+\frac{1}{k}+\ldots +\frac{1}{k}+\frac{1}{k}}_{k\text{ times}}$$ I guessed$$\sum_1^k\frac{1}{k} ,$$but it equals $$1+\frac{1}{2}+\dots+\frac{1}{k-1}+\frac{1}{k}.$$
Silent
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When to use congruent vs approximately?

What is the appropriate usage of the congruent ($\cong$) vs. the approximately ($\approx$) symbols?
mrsoltys
  • 181
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Math typesetting conventions: two-letter subscripts in an equation

Are there any conventions for using two-letter subscripts in equations? I need to use fr for friction, and the normal math italic in TeX ($\omega_{fr}$) doesn't look very good, it appears like f and r are two unrelated concepts hanging out together…
Jason S
  • 3,109
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$n^{th}$ minimum/maximum notation

Given a set $S$ of comparable items, such that $|S|=m$, can I say that the $n^{th}$ minimum (maximun), say $a$, is: $$a=\min_m \{S\}$$ where $n \leqslant m$. If not, which is the correct notation?
mat_boy
  • 145
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What is the double bracket notation used here?

Its kind of a bracket but I'm not sure what it means. I have two ideas about it: It means the number of times the expression in satisfied or it changes for $1$ or $0$ depending on the result every time the $i$ value changes.
Marx Guimarães
  • 73
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Why is the set of all function from $X$ to $Y$ denoted $Y^X$?

Let $X$ and $Y$ be finite sets, and let $P$ be some property. I am defining the set $Z$ to be the set of all functions with domain $X$ and codomain $Y$ that satisfy property $P$ as follows: \begin{gather} Z=\{z\in Y^X\mid z\text{ satisfies property…
EoDmnFOr3q
  • 1,050
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What do the Periods and Commas mean in this Mathematical Definition of the Modulo function?

I have come across the following notation on a cryptography lecture slide that supposedly defines the modulo function: $\forall a, n. \exists q, r. a = q \times n + r \text{ where } 0 \leq r < n$ Whilst I have a general idea of what it's doing, I…
Connor
  • 647
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Why is the standard notation that functions act on the left?

In most texts I have seen applying function $f$ to an element $x$ is denoted by $f(x)$, as opposed to $xf$ or $(x)f$ or $x(f)$. This makes function composition inconvenient. Given a diagram $A \xrightarrow{f} B \xrightarrow{g} C$ I need to write $f$…
Vasily Ilin
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Can the dot of the dot product be omitted?

In arithmetic, the symbol for multiplication, "$\cdot$" or "$\times$", is usually omitted for letters, right? (e.g., $y = a + bx$ rather than $y = a + b \cdot x$ or $y = a + b \times x$). Can we do the same for the dot product of two vectors in a…
Patrick
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Mathematical Notation after braces

I was searching for an equation to calculate the arc length of the archimedean spiral and found the following notation: $$ \frac{b}{2}[\theta\sqrt{1+\theta^2}+ln(\theta+\sqrt{1+\theta^2})]^{\theta_2}_{\theta_1} $$ which, by the context, I know it…
Carlos Barcellos
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What does the notation $1_\Omega(x)$ mean?

An author in a paper suggests that a binary function f(x) can be expressed as $f(x) = 1_\Omega(x)$ where $f(x) \in \{0,1\}$ for all $ x \in R^2$ $\Omega$ is an arbitrary bounded measurable subset of $R^2$ What does he mean when he expresses…
AnkurVijay
  • 647
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Which notation is better (more common) in math?

Which one is better? $$\arccos^2x^2\quad\quad \text{or}\quad\quad(\arccos x^2)^2$$ Are both notations acceptable?
Etemon
  • 6,437
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What does $\mathcal{C}^{\infty}_{\mathcal{C}}(Z)$ mean?

In my course material I have the following notation $$ \varphi \in \mathcal{C}^{\infty}_{\mathcal{C}}(Z) $$ where $Z⊂R^{n}$ is a bounded open set. I was wondering what does this notation mean? What is the set $\varphi$ belongs into? Please, help me…
machniik
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What does $\doteqdot$ mean?

I am reading the following document of Solitary waves page $14$. And I found the following symbol $\doteqdot$. What does $\doteqdot$ mean? For example: $$y_t \doteqdot -c_0y_x $$
Alex Pozo
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Notation for there exists and let

I sometimes encounter proofs as the following: $\exists n\in\mathbb N$ such that …. Then $n$… But the fact in that $n$ is not defined in the second sentence. A correct proof would contain instead: $\exists n\in\mathbb N$ such that …. Let such a…
user835055
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