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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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 $L[f(t)](p)$
1
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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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0answers
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
18 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 ...
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0answers
22 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
96 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 ...
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2answers
71 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 ...
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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
11 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 ...
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5answers
139 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 ...
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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 ...
2
votes
1answer
48 views

Powers of powers. Is there a single interpretation of this notation

Prompted by another question on this site is this notation clear and unambiguous $$x^{y^z}$$ One answer there seems to imply the meaning is $$x^{(y^z)}$$ Mathcad seams to agree with this making ...
2
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0answers
36 views

Tensor transpose notation

I have a rank 3 tensor $\mathbf{Q}$. What notation should I use to denote the transposition of two of the dimensions? For instance, if I want to transpose the first and second dimensions, one way I ...
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8answers
688 views

How to denote “powers” of a function?

I'm working with functions themselves, and I have learned that functional powers mean composition so: $f^3 = f \circ f \circ f$ But I'm looking for something that means $fff$. So $(fff)(x) = ...
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0answers
17 views

What does the notation $S(U(N)\times U(M))$ mean?

I've encountered the following equation in my physics book: $$ S(U(N)\times U(M)) \simeq SU(N) \times SU(M) \times U(1) $$ where $U(N)$ is the unitary group, etc. I'm not familiar with what ...
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0answers
15 views

Including/Excluding Function Arguments

My questions are regarding choices of including/excluding function arguments, and the statement authors are intending to make when making these choices. In a paper I'm reading the author states the ...
3
votes
2answers
36 views

Meaning of the following, partial derivatives..

What is the meaning of $${\partial^kG \over \partial t^k} \in C$$ how is this function explained $G(t,s)$, does it mean that the k-th derivative of $G$ is continuous. I've done some studying on this ...
0
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2answers
32 views

What is the “component projection” of vector a onto vector b, with the notation (a, b)?

I stumbled across this notation while reading the article "A handwritten character recognition system using directional element feature and asymmetric Mahalanobis distance" ...
0
votes
2answers
50 views

What are $\mathbb{R}^2$ and $\mathbb{R}^3$?

What are $\mathbb{R}^2$ and $\mathbb{R}^3$? I've seen them referred to, I'm guessing they refer to a plane an a space that can be defined in Cartesian coordinates in 2 and 3 dimensions respectively, ...
4
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1answer
136 views

Why we do those mathematicals terms $“dx”,dy“,dz” \cdots $ at the end of any integral? [closed]

I have a question in my mind and let me confused however I convince my self by a trivials answers , I would be interest to know what it does mean the mathematicals symboles $"dx" , "dy" , dz" $ ...
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0answers
17 views

Čech cohomology and fundamental class

I have a notational question. Simplified, I have a Cech cohomology on a simplical complex $\Sigma$ generated from the nerve of a covering of a set $X$. I also have a map $f: \Delta^n \to \Sigma$. In ...
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1answer
34 views

Indices at the left of a tensor in mathematical physics/differential geometry?

I am a mathematician and I am reading a paper in mathematical physics and I found the following notation: Let $Y$ be a two–form on $M$ such that $$\nabla({}_iY_j)_k = 0.$$ Here, $\nabla$ is ...
1
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5answers
74 views

Why the set of irrational numbers is represented as $\mathbb{R}\setminus\mathbb{Q}$ instead of $\mathbb{R}-\mathbb{Q}$?

What does the "\" symbol means in this context? I have seen it used for quotient sets like $X /{\sim}$ where $X$ is a set and $\sim$ is an equivalence relation but I don't know what it means applied ...
0
votes
1answer
75 views

What does an apostrophe mean in a function?

In a workbook, I saw the function $f(x)=x^2$. Then, there was the same function with an apostrophe $f'(x)$. It was stated that $f'(x)=2x$. What is the apostrophe, and why does it change the function? ...
0
votes
1answer
11 views

What is the meaning of the deltas in this score function?

I am learning stats. I just read a definition for a score function and hit some unfamiliar notation. I am familiar with the Leibniz notation for the derivative: $\frac{dy}{dx}$ The score function ...
0
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0answers
24 views

Interpretation of function notation

Consider the following statements, seen in this order in a paper ("An equilibrium characterization of the term structure" by Vasicek (1977)): (1) "Let $P(t,s)$ denote the price." (2) (after some ...
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3answers
1k views

I have a simple idea that I would like to make into a formula

If I wanted to write one plus one, recurring, equals infinity.... Does this make sense? If so, how would it be written as a formula?
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votes
1answer
13 views

Graph: What does $G/xy$ mean?

For example: Let $G=(V,E)$ be a $k-$connected graph an let $xy\in E$. Show that $G/xy$ is $k-$connected if and only if $G\backslash \{x,y\}$ is $(k-1)-$connected. What does $G/xy$ mean ?
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0answers
38 views

What is $\Bbb E$? Is is $\Bbb R$ with the standard Euclidean topology?

What is $\Bbb E$? I believe this is just alternative notation for $\Bbb R$ where $\Bbb R$ is assumed to have the standard Euclidean topology. Is this correct? Is seems to be used in this way in ...
24
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4answers
4k views

What does .9 with a line above the 9 mean?

What does this mean? $$\Large.\overline9 $$ I've never seen this notation before.
2
votes
4answers
482 views

What's the meaning of having ^ over a vector name?

What's the meaning of having ^ over a vector name? (unfortunately, I don't know how to type it here) I cannot understand why some authors use the notation of ...
0
votes
3answers
64 views

what is the symbol generally used for whole numbers?

For subjecting to whole numbers, what symbol should I use? it must be valid for using anywhere from school to college. The symbol should be known and well proper to be understood easily by a school ...
2
votes
1answer
44 views

Period notation in group theory

In the context of finite fields, quotient groups, and characteristics, what does $$n.1=0$$ mean, i.e., what is the period notation?
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3answers
69 views

Must an irreducible element in $\mathbb{Z}[\sqrt{D}]$ have a prime norm?

Let $D\in \mathbb{Z}$ where $D$ is not a perfect square. Prove that if $\alpha\in \mathbb{Z}[\sqrt{D}]$, and $\alpha= a+b\sqrt{D}$ with: $|a^2-Db^2| = p$, a rational prime, ...
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1answer
11 views

Notation of the average of a subset with a constraint

I'm quite new to mathematical notations, so please forgive me for my lack of skills in creating technically correct formulas. I came across a problem, when I have a variable set of numbers. Let the ...
2
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0answers
20 views

On permutation notation

I am trying to write up a proof that the parity of permutations on finitely many letters is well-defined. I think I have a proof that involves the number of disjoint cycles that a permutation may be ...
2
votes
1answer
27 views

Notation for integral of a vector function over an ellipsoid

For a short proof, I need to write a point $\pmb y\in\mathbb{R}^p$ as the integral of the surface of the ellipse $\pmb x^{\top}\pmb Q\pmb x=c$ where $\pmb Q$ is a $p$ by $p$ PSD matrix (for now ...
3
votes
1answer
32 views

Big O Notation and negative “n”

So I'm studying big $O$ notation right now and am working through a problem and got $O(x^{-10})$ and I'm just wondering if it's possible to even have a term with $O(x^{-n})$ because I've never come ...
1
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1answer
56 views

Set notation, what is the meaning of <dimension>[]?

I just ran across this notation in a lecture slide and unfortunately it was not explained, This is my first question and because of that I cannot post images, here's a link to an image containing ...