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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How to use correct notation to include only one element from $\arg\max$

I have a summation which should go over a set, excluding one of the elements which returns the maximum value. What I first wrote was: $$ \sum_{\substack {j \in M \\ j \neq \arg\max_{j} \{f_j\}}} f_j $$ but since $\arg \max$ may return more than one…
Mostafa
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notation for sum subelements from a list of elements

For example, we have a list $\mathcal{L}$ of elements. $\mathcal{L} = [\mathcal{E}_1,\mathcal{E}_2,...,\mathcal{E}_n]$ Each element $\mathcal{E}$ contain two values $x$ and $y$: Example: $x = 3$, $y = 10$ I need to sum up the $y$ values from…
Ximi
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Syntax to represent a permutation?

If I have a set Zn = { 0, 1, …, n-1 }, and I want to indicate that P is a permutation of Zn, is there any mathematical shorthand/symbol that I can use to express this relationship?
Ryan Pierce Williams
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What is mathematical notation to sort a set

Let $$ X= \{10,5,48,9,1\} $$ We sort it, $$ Y= sort(X) $$ and Y becomes $$ Y= \{48,10,9,5,1\} $$ What should be a mathematical notation for Y= sort(X)
Adnan Ali
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looking for symbol to denote - opposite of ~, or something equal to K(A)<<1>>K(A) for K(A)

My teacher wrote K(A) ~ 1, (called it almost equal to 1) i need the opposite, such as K(A) is far from 1. I wrote K(A) << 1 >> K(A), but it definitely looks redundant. Alternatively I could write 1<>1 (is this better math…
user53617
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Should I use larger parentheses when writing logical statements that contain a sum?

Let $N$ and $X$ be finite sets, and let $f:X\to\mathbb{R}^N$ be a function. I want to say that there exists some number $a>0$ such that for all $x\in X$, the sum of all elements of the $n$-tuple $f(x)$ adds up to $a$. I am currently writing this as…
EoDmnFOr3q
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The usage of $\wedge$ in mathematical statements

Consider the following statement (from a convex optimization context): "There exists an unique $\mathbf{x}^{\star}$ in the $n$-dimensonal real space such that $f(\mathbf{x}^{\star})$ is equal to or lower than $f(\mathbf{y})$ for all $\mathbf{y}$ in…
Rubem Pacelli
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Explain the notation $x^\alpha = x_1^{\alpha_1} \dots x_n^{\alpha_n}$ .

I am confused by the notation introduced in a physics paper. Let $d\in\mathbb N$, $x \in \mathbb R ^d$, and $\alpha = (\alpha_1, \dots, \alpha_d) \in \mathbb N^d$. Define $$x^\alpha = x_1^{\alpha_1} \dots x_n^{\alpha_n}$$ Let $\beta \in \mathbb…
Talmsmen
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What is the meaning when the value of a function is a set

I am reading a paper where the sign function is defined as the following $$\text{sign}(u)=\begin{cases}1, & u>0 \\ [-1,1], & u=0 \\ -1, & u<0 \end{cases}.$$ And the equations with equal sign is replaced by the belong sign $\in$, for example, $p$ and…
user1104082
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What does $\{0,1\}^n$ mean?

Could you explain what the below text means? What does $\{0,1\}^n$ mean? the keys are chosen uniformly from the set of words of length of the alphabet $\{0,1\}$ denoted by $\{0,1\}^n$.
FARHAN ALSHAMMARI
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What is the meaning of $\mathbb{R}^n$?

I know that $\mathbb{R}$ represents the set of all real numbers. But what does $\mathbb{R}^2$, $\mathbb{R}^3$, ..., $\mathbb{R}^n$ mean?
ArijitKD
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How to concisely express"min of the intersections of two functions"?

I have two functions: $f(x)$ and $g(x)$. I wonder if there is a way to mathematically express "the min of $f(x)$ and $g(x)$ intersections"? $\min(f(x)=g(x))$ is what I could think of, but it doesn't seems right.
zj_tw
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Which is the correct postfix expression for $a\;+\;b\;*\;(\;c\;+\;d\;)\;+\;e\;*\;f$

Most computer algorithms turn $a+b*(c+d)+e*f$ into $a\, b\, c\, d + * + e f * + $. But this performs an addition before a multiplication. If you follow order of operations, shouldn't the expression actually be: $$a\; b\; c\; d\; +\; *\; e\; f\; *\;…
Ben Alan
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Notation usage for the function called inside another function

I want to define a function that is called by another function. When we define the called function, which notations could it use? Hence, can it use the same notations as the function is called. In programming we can use the same parameter names for…
alper
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Is it fine to use `[]` notation in formulas?

[] is used in most programming languages to define a variable as an array. In a mathematical formula, is it fine to indicate the symbol I am using is an array, if yes how can I achieve it? For that reason, could I use [] next to a symbol definition…
alper
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