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 do we write a function that outputs the solution to an equation?

I want to define a function abstractly, rather than directly. So I want to define a function $f(r)$ as the value of $x$ for which the equation $g(x,r)=0$, for example. I'd like to do this without words. Is there a generally accepted notation to…
user56834
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What branch of mathematics does sigma notation fall into?

My high school curriculum here in New Zealand seemed to just skip out on this aspect of maths. I'm trying to get a better foundation in this area, and I've been looking through the libraries at university and on the internet. However, I'm not sure…
yoonsi
  • 279
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Using parenthesis for decimals with exponents

Should we add parenthesis to decimal numbers when raised to an exponent as the following: $$(0.26)^2$$ or we don't need to, so it should be displayed as: $$0.26^2$$ I always used the parenthesis in such cases for the following situations…
Neweshy
  • 111
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Sign as a qualifier: Difference between +Number and Number+

People often use the + sign to qualify numbers. It's common to see this in resumes, e.g.: Managed a +$1M portfolio Lead interviews with 50+ people What is the exact meaning of the + sign in each of these cases? Does it mean exactly the same…
Josh
  • 467
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What does $f(\cdot)$ mean in math

Let $f:\mathbb{R} \to \mathbb{R}$ be a function, what does $f(\cdot)$ mean usually? Is it another way of writing this function, or is it a real number?
Shamisen Expert
  • 8,092
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Is the "$\mapsto$" notation considered "proper" mathematics?

A few years ago in an analysis class, I had a teacher tell me that the notation "$\mapsto$" (e.g. $f \mapsto f'$) wasn't "proper" mathematics. Since then, I have ardently avoided it, even to the point that if I saw it in a book, I found the book…
TheLaughingAlgebrist
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Accepted syntax for writing multiline equation with approximation steps

I want to write the statement $A \approx B = C$ in a multi-line format. Is it appropriate to write it as \begin{equation} \begin{split} A &\approx B \\ &= C \end{split} \end{equation} or does this imply that $A = C$? In other words, do…
user2913171
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Is there a commonly used notation for flipped composition?

We have $ (f \circ g) = x \mapsto f(g(x)) $ however since I read left to write it always seems backwards to me. Is there a symbol like $ ( g \ggg f) = x \mapsto f(g(x)) $. It is especially grating in situations like. $$ \require{AMScd} \begin{CD}…
Q the Platypus
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Need help with notation. Slightly off topic.

I am designing a coffee cup and I want to check the notation, (L-R order, and operator). What is the best to express these quotes? $$\text{Coffee}_{\text{Strong}} \iff \text{Theorem}{}^{\left[\text{Alfred…
Fred Daniel Kline
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Diacritic (Modifier) Symbol for Variance

Using a bar over a variable seems to be standard shorthand notation for the mean value: $\bar x = \frac{1}{N}\sum_i x_i$ Now, what is suitable shortand notation for the variance? I can only find $\sigma^2$ or $\mathrm{Var}$, but no diacritic…
Edgar
  • 131
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How to denote vector of mean values of a matrix columns?

I have matrix $\textbf{X}$. And I need to denote the vector of mean values of the matrix columns. Is it correct to use $\bar{\textbf{x}}$? Or Should I use different notation? Or is this notation correct if I use explanation what it means? What is…
matousc
  • 147
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Notation for discrete intervals

The well-known notation for continuous intervals is $[a,b]$. But what's the case for discrete intervals? Actually they are sets of finite elements $\left\{a, a+1, ..., b-1, b\right\}$ or infinite elements $\left\{0, 1, 2, ...\right\}$. Is there any…
plasmacel
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How does $\left\{f\mid f\colon\mathbb{N}\to\mathbb{R}\right\}$ mean 'the set of all real-valued functions of one natural number variable'?

On pg. 83 of Hefferon's Linear Algebra, it says this: The set $\left \{ f\mid f\colon\mathbb{N}\rightarrow \mathbb{R} \right \}$ of all real-valued functions of one natural number variable is a vector space under the operations. How do I read the…
DragonautX
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Interval Notation - What is the purpose?

I understand that you can write an inequality: $$ x \leq 3 $$ as $$ x \in (-\infty, 3 ] $$ in interval notation, but, I don't understand the practicality of doing this. When is this used? How does it help?
user38392
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When should I make a colon in a statement?

As an example, take a look at the Cauchy's convergence test: $\forall_{\varepsilon>0} \exists_{n_0\in\mathbb{N}} \forall_{m,n \geq n_0} \colon \left|a_m-a_n \right|<\varepsilon $ or $\forall_{\varepsilon>0} \colon \exists_{n_0\in\mathbb{N}} \colon…
Martin Thoma
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