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Questions tagged [notation]

Question 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.

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what is $W^{-1,2}$?

I have been reading about the weak Poincare lemma in the book "Linear and Nonlinear Functional Analysis with Applications" by P.G. Ciarlet. Let $\Omega$ be a simply connected domain in $\mathbb R^n$...
2
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0answers
25 views

Clarification of notation used in differential games

I'm working through Rufus Isaacs's work on differential games and I need clarification on the notation used. Some context: The Value of the game is to be the minmax of the payoff which symbolically is ...
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1answer
11 views

Upper and Lower shapes in Perlin Noise Generated Terrain

I am trying to learn about Perlin Noise and procedural generation. I am reading through an online tutorial about generating landscapes with noise, but I don't understand part of the author's ...
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1answer
81 views

What does this physics paper mean by having a matrix in a denominator?

I am not familiar with any notation used in physics. The paper "Non-hermitian random matrix theory: Method of hermitian reduction" by Joshua Feinberg and A. Zee (Nuclear Physics B, 1997) states: A ...
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1answer
31 views

Notation of Probability space

Assume we have red and a black cube (normal cubes with 6 sides). We roll these two dice. Is it true that the sample space is $$\Omega = \left\{ (r,s) \mid r \in \{ 1, \dots, 6\}, s \in \{ 1, \dots, 6\...
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1answer
35 views

Notation for “congruent to a member of”

Is it acceptable to write $x\in S\pmod m$ to denote "$x$ is congruent to a member of $S$ modulo $m$"? Are there any established alternatives to this notation? An example of use: "When $m\ge 5$ is ...
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1answer
22 views

Index (x_i) with two rows in latex [on hold]

I have following problem in latex formatting: I want to write for a matrix : $ (a_{ij})_{\underset{j=1,\ldots , n}{i=1,\ldots ,m}} $ but I want the $i=\ldots$ and $j=\ldots$ to be the same size... ...
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1answer
34 views

Is there a symbol to mean “$x$ fits completely $v$ times in $y$”?

Is there a simpler way to write "$x$ fits completely $v$ times in $y$," i.e. is there a mathematical symbol or way to write for example: "32 fits 0 times completely in 4" or for example "32 fits 1 ...
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2answers
40 views

Editor asks me to define arg lim min

I have recently submitted a paper to IEEE Trans. on Information Theory. I got the reviewer comments and one reviewer seemed to me like he/she was obsessive with the notations. For example he was ...
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1answer
24 views

Regarding notation, for $f(x,y)$ are $f_x(x,g(x))$ and $\frac{\partial}{\partial x}f(x,g(x))$ interpreted differently?

More specifically, I see $\frac{\partial}{\partial x}f(x,g(x))$ as meaning take the derivative of $f(x,g(x))$ w.r.t $x$. On the other hand, I see $f_x(x,g(x))$ as meaning the partial derivative of $f(...
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Notation: limit with no variable under it next to infimum with variable under it

My statistics text has the following definition for a uniform asymptotic confidence interval: $$\lim \inf_{n \to \infty} \inf_{\theta \in \Theta} \mathbb{P}(\theta \in C_n) \geq (1-\alpha)$$ How do ...
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29 views

Solving equations over multiple lines: notational convention

Consider, for example, the following equation: \begin{align} x^2 - 2x = 1. \end{align} I'd like to solve the equation for $x$ in detail and am wondering how to write it down. Let me offer two ...
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1answer
58 views

What does $5\mathbb{Z}_{25}$ mean? (Notation help)

Does $5 \mathbb{Z}_{25}$ refer to the numbers in $\mathbb{Z}_{25}$ multiplied by $5 $ -- i.e., there are 25 elements -- or does it refer to multiples of $5$ in $\mathbb{Z}_{25}$ -- i.e., there are $5$ ...
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1answer
22 views

What does this Markov Chain notation mean?

So, I don't know the meaning of much of the notation present in the following slide. I know basically what a Discrete Markov Chain and a Transitional Probability Matrix are, but I'd like to what ...
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2answers
38 views

How to correctly write the set of all vectors of the form $(a,b,c)$, where $a+2b-c=0$

I'm not 100% sure if this is where this should go, but my LA prof wants us to practice writing more mathematically using correct notation. this is one of our homework problems and I wrote down the ...
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1answer
17 views

Matrix notation for double sum of row and column with the same index

a biologist/ecologist here, I never took any courses in algebra (definitely missing in my education) but I am working with matrices all day. For one paper, I have to write the matrix formulation but ...
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1answer
70 views

What does this notation mean? $\Phi(x) \downarrow, \Phi(x) \uparrow$

I'm not sure how I am supposed to know this, I have never used notation like this in my previous school. Is this notation logic or is it something I should have learned in math class? What I am ...
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21 views

Decipephering Notation and plugging in values for ellipse formula

Premise I had asked a question on stats exchange about calculating error ellipses for a given scatter plot. I got an answer that seems acceptable, but I'm having trouble implementing it because my ...
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1answer
39 views

How to put an arrow above a letter? [closed]

Can anyone help me put $\rightharpoonup$ above $C_3$ in latex? Need to do so to indicate line integral for Green's Theorem. Any help would be appreciated.
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1answer
59 views

Looking for a proper math notation to deal with intervals

Say we have two sets like this: $A = \{a_1,a_2,a_3,a_4,a_5,a_6,a_7,a_8,a_9,a_{10}\}$ and $B = \{b_1,b_2,b_3,b_4,b_5,b_6,b_7,b_8,b_9,b_{10}\}$ I want to be able to build something like this: $[(a_{1},...
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Notational way to say that something is a set

When you want to say, for example, that $a$ is an integer, you write it as $a \in \mathbb{Z}$, which is read as "$a$ is an element of the set of all integers". But, because of the notorious ...
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3answers
43 views

Composite versus square notation in functions

What is meaning of $f^2(x)$ ? There seems to be confusion in its interpretation. Is $f^2(x)$ same as $(f(x))^2$ or $f\circ f$?
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2answers
27 views

About indexed family of sets and their products

An indexed family of sets is a function $A=(i\mapsto A_i)_{i\in I}:I\to E$ for some $I\ne \emptyset$ and some $E$, where each $A_i$ is a set. I suppose $E$ is a set that contains all $A_i$ and ...
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Notation of density functions

Assume two jointly normally distributed variables X,Y. Then what I often see is that densities are written as follows: $f_X(x)$ as the density of X, $f_Y(y)$ as the density of Y, $f_{X,Y}(x,y)$ as ...
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24 views

Are there time where, instead of writing a function as $f(w,x,y,z)$ we would instead write it with more complicated arguments like $f(w,x,y-z,z)$?

By "complicated arguments " I mean where the arguments are themselves functions (like $f(x,x^2,y,z)$ or something) As a rough example, would we ever write $f(x,y)= (x-y)^2+x$ as $f(x-y,x)$ instead (...
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1answer
28 views

Notation for “or” in inclusion-exclusion formula

Suppose that I have a set $A$ and I want to compute the probability that this set contains at least one of the elements $x_1,\dots, x_n$. In other words, $p(x_1 \in A \text{ or } \dots \text{ or } ...
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1answer
33 views

What is the standard asymptotic notation when $x\rightarrow 0$

I understand big "$\mathcal{O}$” and little "o" notation but every definition I have seen is for $n\rightarrow\infty$. But what about something like $f(x)\in o(g(x))$ for $x\rightarrow 0$? Is there a ...
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0answers
29 views

Doubt of geometric notation about vertices and polygons

If ABCD is a quadrilateral, does this notation imply that vertex B is connected with vertex A and with vertex C?
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2answers
65 views

The hookrightarrow and its meaning

Very weirdly I found a $\hookrightarrow $ in my Algebra book just like that. Could someone please just tell me what it means? Sorry for this maybe stupid question in advance but very much appreciate ...
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1answer
52 views

Summing over set of sets

I am having trouble trying to understand an expression based on the multivariate Taylor series which is used to generate a system of residual equations. The expression is from Chauhan (2017) ...
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1answer
26 views

Having trouble notating an equation determining how much XP is to be given to players while referencing variables found in our database.

In the game being developed, players will be playing best-of-three matches against one another. XP will be given out depending on their score vs the average score and will receive a bonus for whether ...
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37 views

Notation for random point on an area

Given that $S $ is a surface area. What is a good notation to indicate that a variable (position) $x_0$ is set to a random point on $S$. For now my solution is to simply write $x_0 \gets rnd(S)$, ...
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1answer
23 views

How to distinguish argument parentheses and grouping parentheses?

$$s(a+b)$$ Does it mean s times a+b, or is s a funtion and take a+b as arguments? $$(s(a+b))(c+d)$$ Does it mean s(a+b) times (c+d), or is s a high order function and s(a+b) return a function which ...
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62 views
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Confusion regarding the notation of associated operator of a PDE.

I'm given the following PDE: $$u_{tt}-u_{xx}+u^3=0$$ My source says that the associated operator is $$L:=\frac{\partial^2}{\partial t^2}-\frac{\partial^2}{\partial x^2}+u^2$$ which is arrived at ...
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17 views

Difference between notation in the derivation of Maxwell's equations

This question is more about the mathematical notation and little about physics. I have two books, Tipler and Halliday, when studying the derivation of Maxwell's equations they use the same example ...
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5answers
64 views

Why write $\exp(x)$, instead of $e^x$?

Why write $\exp(x)$, instead of $e^x$? I would have thought that if $x$ is a long expression, $\exp(x)$ would be preferred, so that it is clear? But I have seen that this is not the case.
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1answer
42 views

How to understand such a complex event $\left((a\cap\grave{b})\cup(b\cap\grave{a})\right)$ in probability?

What is the meaning of the event $\left((a\cap\grave{b})\cup(b\cap\grave{a})\right)$ in probability?
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30 views

Meaning of symbol $\looparrowright$ in math

Is there a conventional meaning for the symbol $\looparrowright$ when used in math. I came across this symbol in here (see slide 2 for e.g.).
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3answers
2k views

What is the dot in “$1.2.4$”.

I am not a mathematician. I did additional maths O’level back in the stone age but did not pursue maths further (much to my regret). I am reading David Acheson’s fascinating book ‘The Story of ...
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0answers
51 views

Why we care only about $\Pi_1$ parameters in axiom schemes?

There is exist tradition to formulate axiom schemes such as induction, comprehension or replacment in a way like "for each formula $\phi(y,\overline{x})$ with free variables $y$ and $\overline{x}=x_1,....
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1answer
17 views

Correct notation for broadcasting operation

In Python numpy a row vector $u \in \mathbb{R}^n$ and its transposed $u^T$ can be added, multiplied or subtracted, yielding a $\mathbb{R}^{n\times n}$ matrix, where each element $(i,j)$ is the ...
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0answers
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Is the codomain part of the function?

If functions are defined as sets of ordered pairs, then how does it make sense to talk about the codomain of a function, or talk about a function being surjective (rather than saying something like “...
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14 views

How do I evaluate this limit: $\max \{\lim_{x,k \to \infty} G_k(x)\}$

Let $$G_k(x)=A(x)B_k(x)=\pi(x)^{\frac{1}{\log(x)}}\pi(k-x)^{\frac{1}{\log(k-x)}},$$ where $\pi(x)$ is the prime counting function. What is $$\max \{\lim_{x,k \to \infty} G_k(x)\}?$$ This is what I ...
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2answers
14 views

Infinitesimal squared in metrics

Metrics are often formulated by appealing to the square of an infinitesimal quantities. Examples of such are: $$ (ds)^2=(dx)^2+(dy)^2 $$ or $$ ds^2=dx^2+dy^2 $$ or $$ d(s^2)=d(x^2)+d(y^2) $$ ...
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1answer
44 views

Representing Iterations in Math

I'm coming from a software engineering background and not a mathematical one. You may have to explain the exact notation to me but I would really appreciate it. I want to represent one of my processes ...
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0answers
9 views

Correct formulation of all unordered subindeces

Suppose we have an index set $\{1, \dots, n\}$. Now I want to take all the subindices. For example, if the set $\{1, 2, 3\}$, I want to a collection of $\{1\}, \{2\}, \{3\}, \{1, 2\}, \{2, 3\}, \{1, 3\...
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1answer
23 views

Notation for number sets

Variables a and b assume values of two number sets as part of a grid search. a assumes the first 21 multiples of 1440, b assumes values from 0 to 1 in steps of $\dfrac{1}{100}$. To clarify ... $$a = [...
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38 views

Is there any math notation for `be denoted by`?

https://mathoverflow.net/questions/325185/is-there-any-math-notation-for-be-denoted-by The sentence s "In many supervised learning problems one has an output variable $y$ and a vector of input ...
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3answers
65 views

What does the notation $A^{-2}$ mean if $A$ is a matrix?

$A^2$ means to multiple the matrix by itself, and $A^{-1}$ refers to the matrix's inverse. Would $A^{-2}$ be the square of the inverse or the inverse of the square?
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2answers
35 views

How to read/interpret $\hat{f}(y)(x)$

I'm currently in a point-set topology class and was presented with the following definition on a homework assignment. If $f: X\times Y\to Z$ is a continuous function, we can define $\hat{f}: Y\to \...