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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18 views

Proper formulation of one-to-one and onto proofs for group isomorphism

I have to construct an isomorphism for the two groups. I have the isomorphism itself but I'm not sure if my formulation is correct in regard to proving the mapping being 1-1 and onto and I don't want ...
1
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1answer
40 views

How to express double orthogonal complement?

Let $V$ be a Hilbert space and $U \subseteq V$. Then $U^\perp = \{\mathbf{v} \in V|\forall \mathbf{u} \in U, \langle \mathbf{u}, \mathbf{v} \rangle = 0 \}$. My question is, how do you express ...
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0answers
31 views

What does this matrix notation mean?

What does $|\textbf{M}|$ mean, where $\textbf{M}$ is a matrix? I am under the impression that you can element-wise divide $\textbf{M}$ by $|\textbf{M}|$ to normalize it in some way, kind of like how ...
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0answers
46 views

Connection between harmonic functions, Bochner Laplacian and Ricci curvature

I stumbled upon the following claim in a paper: "We write the (Bochner) Laplacian in suffix notation: $\Delta_B = \nabla ^k \nabla_k$". after this statement, the following is written: ($M$ is a ...
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1answer
35 views

What is the proper use of Leibniz notation for one-sided derivatives?

The only notation I've seen has been restricted to either Lagrange's prime notation or Euler's $D$. Here are some of the variants: $$f'(a^+):=\lim_{x\to a^+}\frac{f(x)-f(a)}{x-a}$$ ...
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1answer
58 views

What does $\Bbb R/2\pi$ for a set mean?

I simply cannot figure out what this means. I read this on an article about the scalar product of $2\pi$ periodic functions. it says that < f,g > goes from $\Bbb R/2\pi \to \Bbb C$ (complex) Do ...
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1answer
46 views

Can ∂x and ∂y in a derivate be seen as ∂ times x or ∂ times y?

I'm watching some tutorials on machine learning and know just enough calculus to have an intuition on what a derivative is, but that's it. But this question is bugging me so much that now I'm pretty ...
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0answers
53 views

Set Theory Notation: What does it mean to “\” one set with another? [duplicate]

What does the "\" operator mean in the above context?
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7answers
143 views

The meaning of the symbol $\infty$ in Spivak's calculus book

Spivak in "Calculus" writes ... symbols of $\infty$ and $- \infty$ are purely suggestive: there is no number $``\infty"$ which satisfies $\infty \geq a$ for all numbers $a$. What is the meaning ...
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1answer
54 views

In the expression $p^2=4q_1$, what does the small $1$ mean?

In the image below there is $p^2 = 4q$ and then a small $1$. What is the name/meaning of this notation? I have never seen it before and can't find what the meaning of it is. Help is appreciated! See ...
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1answer
27 views

Notation question $|X^2|$

I am studying a little bit of set theory, and one of the questions in the book (in Efe A. Ok's real analysis book) asked to show that $\dim(X,\succeq)\leq |X^2|$, where $X$ is a finite set and ...
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1answer
51 views

Is there a short symbol that denotes integration?

I want to illustrate partial integration, see below. With derivatives we can just write $(term)'$. Is there something similar for integration? The best I could come up with is $\int(term)\mathrm{d}x$. ...
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0answers
29 views

What does a * mean after a letter signaling a result?

I have this equation from a biology publication. It's about an ecosystem model. $$\frac{df}{dt}=w(f)f(1-f)-vf$$ $w(f)$ is a function and $vf$ is a multiplication. Then what does $f^*=0$ or ...
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1answer
26 views

Meaning of “$\triangledown$u*ñ=0 on the boundary”

I'm doing homework for my PDE class, I'm coming across this notation and I don't what the ñ means: $\triangledown$u* ñ=0. I have tried to google it, but unfortunately questions like this don't really ...
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1answer
21 views

Symbol representing a vector composing of two vectors

I have a vector including two vector's elements. How do I simply represent a vector with elemental vectors. Formally, I have three vectors $x, a=(a_i), b =(b_i)$ and $x=(a_1, a_2, ...
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1answer
21 views

Question concerning big-Oh and small-Oh notation

What would the notation $a_n = (1+ o(1))b_n$ stand for? (And similarly for $a_n = (1 + O(1))b_n$).
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2answers
45 views

Equal sign or approximation sign?

I want to solve the equation $2\enspace \sin^2\enspace \theta+2\enspace \sin\enspace \theta-1=0$, $0\leq\theta<2\pi$. Using the quadratic formula, I found one of the solution to be ...
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4answers
199 views

How to write $\aleph$ by hand

So far, I've only seen the symbol $\aleph$ in its printed form and am wondering how this symbol could be written by hand on paper or on a board (in mathematical contexts, of course). Whenever I try to ...
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1answer
15 views

About the exact form of a gaussian kernel

Traditionally we define a gaussian function at a point x (assuming mean to be 0) as follows $$g_{\sigma}(x) = \frac{1}{\sqrt{2\pi \sigma^{2}}} \exp\left(\frac{x^{2}}{2\sigma^{2}}\right)$$ In ...
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2answers
60 views

Correct notational use of $:=$

Suppose I use the notation $:=$ to define some symbol the first time it is introduced, e.g. $A:=\Im(f+f^2)$. If later on I make use/remind the reader of the symbol definition, e.g. ...
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3answers
247 views

Arnold Trivium Problem 39

We find in Arnold's Trivium the following problem, numbered 39. (The double integral should have a circle through it, but the command /oiint does not work here.) Calculate the Gauss integral ...
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1answer
33 views

Fourier analysis notation - Sh and Ch

I reading something dealing with Fourier analysis and don't know what "Sh" and "Ch" indicate. Thanks!
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2answers
65 views

Symbol in Linear Algebra

I'm newbie in linear algebra and I do not understand the symbol that is selected with blue color. What does this symbol means? What is the purpose to use this symbol? What context is this symbol ...
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0answers
34 views

Given bifunctor $F$, what is the name of the functor with switched arguments?

Sorry for the unspecific title. Here the actual question: Given categories $\mathcal{A},\mathcal{B}$, let $S$ be the canonical functor $\mathcal{B} \times \mathcal{A} \to \mathcal{A} \times ...
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0answers
16 views

What does the notation $\mathcal{O}_{\mathbb{P}^n}(1)$ mean?

I have tried looking at my sheaves notes but couldn't find anything.
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2answers
270 views

Where can I find the official rule for multi-line expressions?

Consider this simple exercise: $$1+1+11+1+1 = 15\tag{A}$$ But what if it were a very long expression? Let's assume that it is, then $$\begin{equation*} \begin{split} 1+1+\; & \\ ...
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0answers
37 views

“Projective tangent space” to a projective variety

Is there an established notation for the linear subvariety tangent to a projective variety $V$ at a point $x$? I've seen this called the "projective tangent space" in some places. The closest thing ...
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1answer
31 views

What is the remainder of an n-th root called?

I feel like there should be a better word than remainder, but I don't know it. What do you call the thing that's left over when performing an $n$-th root? For example, $\sqrt[3]{29}$ is $3$ with 2 ...
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1answer
10 views

$F^{(n)} (p)$ do you first differentiate and afterward apply the Laplace?

If you have a Laplace transform: $F^{(n)} (p)$, do you first differentiate and afterwards apply the Laplace? $F(p)$ meaning $L[f(t)](p)$
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2answers
13 views

Notation for a function with multiple return values

I want to define a function $f$ whose domain is given by the set $V$ whose return value is a subset of $C$. Please correct me if I am wrong, I assume that $f : V \rightarrow C$ would mean that the ...
1
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0answers
15 views

Notation for binary permutation

Given a number $x \in \mathbb{N}$ , I want to write down following algorithm in a notation which can be written without the need for providing an example. Step (1): Find all unique prime factors ...
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0answers
30 views

What is meaning of big U in sets? [duplicate]

What does big U below signify? And what is number written above and below it?
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28 views

Clarification on notation in Siegfried Bosch's Commutative Algebra book about primary decomposition of ideals.

I'm reading through Siegfried Bosch's Commutative Algebra book, and I'm confused on his notation in one his proofs. He uses this notation a lot, so I think I should I understand it. The notation first ...
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0answers
17 views

Notation: how can I say variable drawn from a distribution D lies in space X

Suppose I have a random distribution $D$ for which, if $x\sim D$, then $x\in X$. Is there a standard notation involving only $D$ and $X$? For example, let $N$ be the multinormal distribution with ...
0
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0answers
21 views

Name for measure of non-injectivity of a covering map

Suppose that $p:C\to X$ is a covering map. For $x\in X$, is there a name for the number $Card(p^{-1}(x))$? So that for $p(z)=z^5:\mathbb{C}\setminus\{0\}\to\mathbb{C}\setminus\{0\}$, one might say ...
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1answer
87 views

Why ∫ dn is = N?

Maybe a simple question here but I was wondering how $\int \, dn=N$? I understand if you intergrate say 1 in terms of $X$ you get $X$ but if you intergrate $0$ how does that equal $X$ or $N$ in this ...
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0answers
22 views

Meaning of “p-adic fields” in Jacques Tits' article on classification of semisimple groups

In Jacques Tits' article "Classification of Algebraic Semisimple Groups", which appears in "Algebraic Groups and Discontinuous Subgroups: Proceedings of Symposia in Pure Mathematics, Volume IX", when ...
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2answers
23 views

A question on summation notation and pi notation for multiplication.

As I am in high school, I know the basics to summation and pi notation. However when people put things other than numbers on the top and bottom of the summation, I do not understand what they mean. ...
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0answers
10 views

Selfdecomposability and Lévy processes

I am trying to understand Levy processes and I have some issues with this. A random variable x is selfdecomposable then x has a representation of the form \begin{equation} x=\int ...
1
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2answers
70 views

A misleading commutative diagram

Let $U$ be a set, let $\phi$ be an involutive bijection of $U$ with itself. Let $A$, $B$ be subsets of $U$. Consider the commutative diagram $A \overset{\phi}{\leftrightarrow} B$ describing a ...
1
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1answer
25 views

Notation for the limit to the boundary of the support of a function

So let $f(z)$ by a density function for $z\in\operatorname{supp}f$. In some cases (for example when $f$ is the pdf of the normal distribution), $\operatorname{supp}f$ will be $\mathbb{R}$ and one ...
2
votes
2answers
36 views

What does the vertical bar mean in $ \left.\frac{\partial f}{\partial x}\right\rvert $

I want to know what the symbol '|' besides a function means. For example: $$ \left.\frac{\partial f}{\partial x}\right\rvert $$
4
votes
1answer
89 views

Why do mathematicians use $\Delta$ instead of $\nabla^2$?

I often hear that, when writing PDEs, $\nabla^2$ is the convention among physicists and engineers, while mathematicians write $\Delta$ instead. To me, the physicists' notation seems like it is ...
1
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2answers
50 views

What does this notation mean $\{a_k\}_{k=i}^n$?

What does this notation mean $\{a_k\}_{k=i}^n$? I saw it in sites talking about sequences but there was no explanation of what it meant. E: I reviewed the other post, this is not a duplicate, and ...
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0answers
10 views

Notation: $u_x(s,t)$ or $u_s(s,t)$

Let $\Omega \subset \mathbb{R}$ and $u \in C^{1,1}(\Omega \times [0,\infty))$. I generally use the notation $u(x,t)$ for $x \in \Omega$ and $t \ge 0$. When I want to refer to ...
3
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1answer
38 views

What does $\overset \times =$ mean?

I came across this symbol on page xix of the book Universal Artificial Intelligence by Hutter: (link to full text of book) It is used for the Solomonoff-Levin universal semi-measure. I've ...
0
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0answers
12 views

common symbolic notations for multi-valued and bag-valued functions

What are the commonly used notations for a multi-valued $f_m: A\rightarrow B$, and bag-valued $f_b:A \rightarrow B$ functions from A to B? To be more precise: $f: A \rightarrow B$ is usually used to ...
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0answers
36 views

Find mathmatical notation for a relation

I need help to express an computational solution as mathematical notation. Its all aboz the relation of tasks $A$ and resources in terms of videos $V$ and sections $S$ of videos. I started with the ...
6
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5answers
136 views

Do $\Bbb Q (\sqrt 2)$ and $\Bbb Q [\sqrt 2]$ mean the same?

Do $\Bbb Q (\sqrt 2)$ and $\Bbb Q [\sqrt 2]$ mean the same? I'm trying to refer to the field of the real numbers of the form $a + b \sqrt 2$ where $a$ and $b$ are rationals. E: I'm sorry, my ...
0
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2answers
19 views

Question about notation, subsets of a graph and intersection of vertices

I have the following description of a graph: Let $G$ be a graph such that all of its vertices are subsets with two elements of $\{1,2,...,n\} (n\ge 2)$ where two sets $A,B$ are adjacent iff ...