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.

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What does the notation n* mean?

Are there any conventions about the use of $n^*$ as notation of a variable? I have seen it for the first time here.
Eli Frey
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What does "$\times_i$" mean in function notation? As in "$\phi:\times_iM_i^\phi\to A$"

What does the $\times_i$ mean? For reference, $M_i$ is a set.
mitmath514
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Notation for the set of all $x_i$

Maybe a silly question, but what is the most compact way of clearly expressing the set of all $x_i$ if it is obvious that $i$ runs from 1 to $n$? $\{x_i\}$? $\{x_i\}_i$? $\{x_i\}_{i=1}^n$? $\{x_1, x_2, \dotsc, x_n\}$?
Neil G
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Are all notation equal by derivatives?

Here I read that Suppose you have a general function: y = f(x). All of the following notations can be read as "the derivative of y with respect to x" or less formally, "the derivative of the function": f'(x), f', y', df/dx, dy/dx,…
inf3rno
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Notation for "function from a subset of $X$ into $Y$"?

The notation $f: X \to Y$ implies that $X$ is the domain of $f$. It is very regularly convenient to say something like: Let $U \subset X$ and $f: U \to Y$. but in situations where the actual set $U$ isn't that important, just that it's a subset…
preferred_anon
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Mathematical symbol to express monotonic relation between variables

I wonder if there exists a symbol with which we could express that a variable $y=y(x)$ is monotonic with respect to $x$. In a similar way that the $\propto$ symbol expresses proportionality but in a wider sense, without requiring a linear…
Quaerendo
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What is the formal way to express the meaning of a variable?

I would like to know what is the formal way (if any) of defining the meaning of variables. When I start writing a proof, or if I simply want to establish a formal definition, I usually follow the notation below, but I recently understood that this…
cinico
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How do I break down the math symbols in this equation

$$\frac{n}{\phi(n)}=\frac{n}{n\prod_{p|n}\left(1-\frac{1}{p}\right)}=\frac{1}{\prod_{p|n}\left(1-\frac{1}{p}\right)}$$ How do I learn to understand these equations by myself as I can't seem to find the mathematical notation descriptions online?
Po Chen Liu
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How do I tell the difference between the Legendre symbol and a fraction?

This question is probably dumb but I can't find anyone else on the internet who seems to be troubled by this. The Legendre symbol is denoted as $\left(\dfrac37\right)$, which is very useful for number theory and quadratic residues. On the other…
greenturtle3141
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What is this symbol?

I am reading "Sets, Numbers and Topology" by Masahiko Saito. And the following symbol is used to denote the set of equivalence classes in the book. What is this symbol? $J$? $T$?
tchappy ha
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What does this symbol signify ('\Game' in mathcha.io editor)?

While playing around in an online LaTex-like editor (mathcha.io) I came across the following symbol, entered with '\Game': Can anyone tell me what it signifies? All my online searches came up short on this one.
g_uint
  • 133
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Notation of $\max$

What is the meaning of: \begin{equation} \max_{x_0\le x\le x_2}f^{\prime \prime}(x) \end{equation} Is it the max of the second derivative at any $x$ between $x_0$ and $x_2$
Meistro
  • 133
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Is there a shorthand for signifying that the numerator/denominator hasn't changed?

Sometimes, when I'm solving problems in school, the numerator or the denominator will stay the same throughout multiple steps as I solve the other. This gets very tedious, and I was wondering if there was a shorthand or symbol I can use to show that…
Moeez Muhammad
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Incredibly basic notation question: Is $-1^2$ 1 or -1? How about $-x^2$ where $x$ is $1$?

Notation question: Is $-1^2$ equal to $1$ (because it's $(-1)^2$, as seems obvious) or $-1$ (because it's $-(1^2)$). E.g., is the $-1$ a single thing (token or whatever) in the equation? Similarly, let $x$ be $1$. Is $-x^2$ $1$ or $-1$? I believe…
T.J. Crowder
  • 133
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What does an integral with only one integration limit mean?

I am supervising an end of degree project related to Sturm-Liouville problems. In the paper Singular Sturm comparison theorems I saw the next strange integrals in Theorem 1: Let $P(x)$, $p(x)$ be continuous functions on the open, finite or…
Math wind
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