Mathematics Stack Exchange
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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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notation meaning - braces in the variable's subscript

I am trying to understand the meaning of the braces in the subscript of a variable. I've encountered it in a paper Distributional Reinforcement Learning with Quantile Regression, page 5 Does it mean "as long as the condition is met"? But what is…
Kari
  • 229
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Notation using "such that"

Is it correct to say "$a_t=\alpha:\alpha\in A_{\sigma}$" with the following meaning: $a_t$ is equal to $\alpha$ and $\alpha$ belongs to set $A_\sigma$.
Paulo Fracasso
  • 91
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Short notation for a column vector where each element is the mean of each row of a given matrix

I have a matrix $A$ defined as: $$ A = \begin{bmatrix} a_{1,1} & a_{1,2} & \ldots & a_{1,m} \\ a_{2,1} & a_{2,2} & \ldots & a_{1,m} \\ \vdots & \vdots & \ddots & a_{1,m} \\ a_{n,1} & a_{n,2} & \ldots & a_{n,m} \end{bmatrix} $$ I have also a column…
gvgramazio
  • 143
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What Notations Describe a Mapping

How are these notations related (if at all), or are they the same? Since I'm not sure if it's what people usually write, I'll clarify $\langle,\rangle$ is a mapping. $\langle a,b\rangle=c$ $a:b\to c$ $a(b)=c$ (a as a function of…
Pineapple Fish
  • 1,512
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the symbol for translation, transformation, or conversion

What is the symbol for demonstrating syntactic conversion (transformation or translation)? For example, I want to show a calculation sequence, from $ \neg ( A \wedge B ) $ to $ \neg A \vee \neg B $. Now I just use $ \vdash $: $ \neg ( A \wedge B )…
WIZARDELF
  • 187
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Is there a prevalent notation for the set $\{-n+1, …, n-1\}$?

Quite often, the set $\{0, …, n-1\}$ is denoted by $[n]$. Is there similarly a notion for the set $\{-n+1,…,n-1\}$ (other and shorter than $[n] ∪ -[n]$)?
k.stm
  • 18,539
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Proper notation for enumeration

Between these two options, is there a best practice notation for enumeration or are they both equivalently acceptable: \begin{equation} \forall i = 0,1,\dots,n-1 \qquad (1) \end{equation} \begin{equation} \forall i \in \{0,1,\dots,n-1\} \qquad…
N. Short
  • 59
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(Very pedantic) notation of an indexed set?

Consider the following very often-used notation: $$(I, \{x_i\}_{i\in I})$$ My question is: is this notation strictly speaking correct, if we require that we can retrieve which $x_i$ belongs to which $i$? The reason I doubt so is the following: A…
user56834
  • 12,925
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Is that a correct notation?

$$\dfrac{1}{n}\sum_{i=1}^{n}1_{[y_{i}f(x_{i})<0]}$$ this gives me the number of how many times the expression in brackets is less then zero. But is it correct? I see it for the first time, so where(textbook) I can encounter it in an elucidating…
Hrisip
  • 227
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What does the notation (0,v] mean?

I am reading the paper Linear Work Suffix Array Construction by Juha Karkkainen, Peter Sanders, Stefan Burkhardt, and in a number of places they use the notation $$(0,v].$$ I assumed it was a mistake, but they use it a number of times. What does it…
superbriggs
  • 175
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What is the Versus symbol?

I've never really studied math, but was wondering, is there a designated symbol used for implying "versus", or would you just write "Vs."? For example, I'm working on a calculation like this: Cost expense A "versus" cost expense B + cost expense C +…
larry909
  • 131
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What is the equivalent of "eval" function in math notations?

Given two sets $X$ and $Y$, and a function $f : X \to Y$, would it be correct to write: \begin{equation} \forall y \in \{a,b,c\} : \textit{Fy} \triangleq \{ x \in X \mid f(x) = y \}. \end{equation} as an equivalent of: \begin{equation} \textit{Fa}…
N. Short
  • 59
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What does the notation $(\frac12)^3_n$ mean??

Equation 97 in http://mathworld.wolfram.com/PiFormulas.html introduces this notation I have never seen before: $\left(\displaystyle\frac12\right)^3_n$ Everyone knows that 3 is an exponent, but what the heck is the $n$ doing down there??? I've tried…
greenturtle3141
  • 906
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notation for sequences and families of sets

Maybe this is more about language and convention than actual math. Literally, the notation $\{x_i:i\in I\}$ or $\{x_i\}_{i\in I}$ means the range of the function $x$ with domain $I$. But then many people seem to use this symbol to stand for the…
isthisreallife
  • 649
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What does the notation $E^{(k)}$ mean in this proof of Bool’s inequality?

I'm reading through some notes which give a proof by induction for Bool's inequality, and I wondered if someone could explain what the notation. I'm confused by the $E^{(k)}$, what does this mean? $$ \begin{align*} \Pr\left[\bigcup_{i=1}^{k+1}…
superbriggs
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