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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What's a conventional or useful notation for "second-highest"?

What would the conventional or an otherwise useful notation for the second-highest value of $v_i, i=1,\ldots,n$ be? I use $v_{n-1:n}$, which I used in statistics, but that may not be quite intuitively graspable. $v_{(n-1)}$ seems like asking for…
Řídící
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Symbol meaning any constant number?

In mathematics, $\Bbb R$ is used to denote the set of all real numbers, and $\Bbb C$ is used to denote the set of all complex numbers. Is there a symbol used to denote the set of all constant numbers, meaning both real and imaginary? For example,…
user574921
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Correct way to align equations equal to zero

This is a question related to formatting. I have an expression that is equal to zero; I work over this expression to obtain a final relation as shown below: $$\begin{align*} 0 & =\int_{V}\nabla\cdot\mathbf{A}\,\mathrm{d}V\\ &…
nodarkside
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What does the symbol $\lll$ mean?

$A < B$ means $A$ is smaller than $B$. $A \ll B$ means $A$ is some orders of magnitude smaller than $B$ (see also this question for a more in-depth discussion). In modelling, it may mean that $A$ can be neglected ($A + B \approx B$). In the…
gerrit
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Symbol for iterated composition

For numbers $x_1, \ldots, x_n$ one may write $$ \sum_{i = 1}^n x_i $$ for what might otherwise informally be written $x_1 + \cdots + x_n$. For functions $f_1, \ldots, f_n$ is there similar notation for what might otherwise informally be written as…
Mees de Vries
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$f(x) = \Box$ vs $x \mapsto \Box$

In the book I am reading (Abstract Algebra, Dummit & Foote), the author uses 2 ways to define functions: $$f(x) = \Box$$ $$x \mapsto \Box$$ It's not that I don't know what they mean - it's that they use both, which leaves me feeling like I am…
Abel
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What would be the correct notation of antilogarithm if I would also like to specify the base?

In my high school days, my teacher told me that $\mathrm{antilog}( x)$ is the same as $10^x$ and $e^x$ is the same as $\exp x$. While the latter is true, I can't say for sure whether the former is true. After looking it up on Google, I didn't find a…
William
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Meaning of this symbol

What is the mathematical meaning of a horizontal A. I mean that it is like this > but crossed which makes it look like a horizontal A.
mrnobody
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Is there a mathematical notation to express the domain without the range or the range without the domain?

According to the domain's Wikipedia page I can express the domain and range of a function like this $$f:X\rightarrow Y$$ What if I am only interested in the domain of the function? Is it mathematically accepted to write this? $$f:X$$ What if I am…
Cedric Martens
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What does the semi colon in $(x(i),y(i));i=1,\dots,m$ mean?

Question: What does the semicolon mean in "$(x(i), y(i)); i=1,\dots,m$"? My Guess "This is training example $(x_1, y_1)$ and it is in a set where $i$ is in the range $1$ to $m$". Explanation: I'm taking Andrew Ng's Machine Learning course on…
Axle Max
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Generally accepted notation for referencing function without defining it.

Let $F\subseteq (\mathbb R \to\mathbb R)$ be some space of functions, and let $G:F\to \mathbb R$ be a functional. I have a statement of the following form: $$\begin{align}\text{Let } &f^*(x):=x^2. \quad\quad\quad \text{Then }\\ &f^*\in…
user56834
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Difference between $\triangleq$, $:=$, $=$ and $\equiv$ when defining a function

Which of the following notation is a correct definition of the square function? $f(x) \triangleq x^2$ $f(x) := x^2$ $f(x) = x^2$ $f(x) \equiv x^2$ While this question is similar to The meaning of various equality symbols, the aforementioned…
Robbo
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Simple way of denoting a condition on a long equation

I have a few equations that are rather long. They are 0 if the long part would become negative. Let's say they look something like $$ x =\begin{cases} a+b-cd &\quad \text{if}\ \ a+b-cd > 0\\0 &\quad \text{otherwise}.\end{cases} $$ Now I would prefer…
user3460824
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What does $|p\;\square\;q|$ mean?

Given that $p$ and $q$ are both integers, what does $|p\;\square\;q|$ mean? It came up in Theorem 3 of the article “On the Topology of Celtic Knot Designs” from the mathematics department of California Polytechnic State University (Link below). The…
JimG
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What is the difference between $\overset{\Delta}{=}$ and := (delta-equal and :=)?

Both symbols $\overset{\Delta}{=}$ and := are used for definition but I want to know the exact difference of them?
user494522
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