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.

learn more… | top users | synonyms

1
vote
0answers
735 views

What is meant by an integral with $\Omega$ as its range: $\int_{\Omega}$

What does it mean when $\Omega$ is range of integral? $$\iint G \frac{\partial U}{\partial n} - U(J k G) ds =\int_{\Omega}{G\left(\frac{\partial U}{\partial n} -j k U\right)R^2 dw} $$ I do not ...
1
vote
2answers
43 views

Limiting the scope of an operator

With the product rule, one has to limit the scope of operators (without using $f'$ or $\partial f/\partial x$): $$ \frac\partial{\partial x} u(x) v(x) = \left(\frac\partial{\partial x} u(x)\right) v(x)...
1
vote
2answers
60 views

Tensor field notation

Let $L$ be a finite dimensional vector space. A tensor of type $(p,q)$ on $L$ is an element of the tensor product $L^{\otimes q}\otimes (L^{*})^{\otimes p}$. How to interpret the following formulation ...
0
votes
2answers
81 views

Shorthand Notation for Bicubic Graphs

I remember that I once read/heard that graphs may be given a shorthand notation when you take the upper diagonal of the adjacence matrix, put the resulting lines next to each other and convert ...
6
votes
2answers
224 views

The notations change as we grow up

In school life we were taught that $<$ and $>$ are strict inequalities while $\ge$ and $\le$ aren't. We were also taught that $\subset$ was strict containment but. $\subseteq$ wasn't. My ...
1
vote
1answer
98 views

backwards membership notation set theory

This is more of a notational/historical question. I had a course last quarter where the professor would write things like $A \in x$ for $A$ a subset of some bigger space $X$ and $x$ an element of $X$. ...
0
votes
3answers
238 views

Notation of “defined for all complex numbers except the negative integers and zero”

The Euler and Weierstrass forms of the gamma function are : $$\mathop{\mathrm{\Gamma}}\left(z\right)=\frac{1}{z}\prod^{\infty}_{n=1}\frac{\left(1+\frac{1}{n}\right)^{z}}{\left(1+\frac{z}{n}\right)}=\...
3
votes
1answer
108 views

Is the notation $[x,\to[$ common?

I recently started reading Topology and Groupoids by Ronald Brown and this notation came up. The notations is $$[x,\to[ \; =\{z \mid x \leq z\}$$ and a similar notation for other type of intervals. I ...
0
votes
1answer
96 views

What is the semantic of square brackets after the set denoting coefficients of polynomial?

I have the following excerpt: Unless stated otherwise, we assume all polynomials take integer coefficients, i.e. a polynomial $f \in \mathbb{Z}[{\bf y}, x]$ is of the form $$f(y, x) = a_m · x^{d_m} +...
3
votes
1answer
95 views

Simplifing formulas using tensor notation

Im trying to symplify formulas like: $$\operatorname{div}(\operatorname{rot}\vec{F}),\qquad \operatorname{rot}(\operatorname{rot}\vec{F}) $$ or something more strange like: $$\operatorname{rot}(\...
11
votes
3answers
464 views

Meaning of $\int\mathop{}\!\mathrm{d}^4x$

What the following formula mean? $$\int\mathop{}\!\mathrm{d}^4x$$ I know that this $\int f(x)\mathop{}\!\mathrm{d}x$ is the integral of the function $f$ over the $x$ variable, but the following $\...
0
votes
1answer
159 views

Concise notation for the successor of a cyclic index

Very frequently we index "cyclic objects" using the integers. For instance, we might say that the vertices of a polygon are $x_1, x_2, \dotsc, x_n$, where the "next vertex" after $x_n$ is $x_1$. This ...
1
vote
0answers
34 views

Equivalence of Notation for Momentum Continuum

This wikipedia page for Magnetohydrodynamics lists the conservation of momentum in a continuum as: \begin{equation} \rho \left( \frac{\partial}{\partial t} + \vec v \cdot \nabla \right) \vec v = \vec ...
0
votes
1answer
58 views

Help identify this operator

Except the whole operator is more compact. It is used between two fractions like.... x / y mystery operator x /y . I don't know how to write it on my computer. ...
-1
votes
1answer
107 views

Quick question: local-to-global spectral sequence [closed]

What does "$\implies$" mean in the following: $E_2^{p,q} = H^p(\mathcal Ext^q(F,G)) \implies Ext^{p+q}(F,G)$ Could you explain the meaning of the whole thing? (Let's say $F$ and $G$ are sheaves on ...
1
vote
0answers
83 views

Canonical way of denoting the set of all (totally) ordered subsets

Given a finite set $S$, we usually denote the set of all subsets of $S$ by $\mathcal{P}(S)$, i.e. the power set of $S$. I need to denote the set of all totally ordered subsets of $S$, let us call it $...
3
votes
4answers
4k views

Learning to read complex math formulas

could anybody point me to a book or article where I could learn how to read formulas like this one: I have no idea what that means.
0
votes
2answers
128 views

Meaning of $\bar{i}:=i+n\mathbb{Z}$ in Modular Arithmetic

I am starting to learn graph theory and ran into the following definition: The set $\mathbb{Z}/n\mathbb{Z}$ of integers modulo $n$ is denoted by $\mathbb{Z}_n$; its elements are written as $\color{...
2
votes
1answer
55 views

Notation for function being differentiable at a certain point

This question describes a notation for a function $f(x)$ being (continuously) differentiable on some domain $A$. Often, I see the requirement that some function $f(x)$ be differentiable only (or ...
1
vote
1answer
40 views

In a normal space, $E\subset U\subset \overline{U}\subset V$, or $E\subseteq U\subseteq \overline{U}\subseteq V$?

I'm trying to understand the proof of Urysohn's lemma (just to get some pespective). This article says that "A topological space $X$ is normal iff for each closed subset $E$ of $X$ and each open set ...
3
votes
1answer
2k views

What does the notation min max mean?

Min clearly means minimum and max maximum, but I am confused about a question that says "With $x, y, z$ being positive numbers, let $xyz=1$, use the AM-GM inequality to show that min max $[x+y,$ $x+z,$...
2
votes
1answer
63 views

What does an expression $[x^n](1-x)^{-1}(1-x^2)^{-1}(1-x^3)^{-1}(1-x^4)^{-1}…$ mean?

I came across the function that describes number of partitions of $n$ (I mean partitions like $5=4+1=3+2=3+1+1$ and so on. There was defined a Cartesian product: $$\{0,1,1+1,1+1+1,...\}\times\{0,2,2+...
2
votes
1answer
1k views

How to write two for loops in math notation?

I have a vector of numbers that looks like this: [1, 2, 3, 4, 5] For every number the vector, I would like to multiply each number by every other number and find ...
0
votes
1answer
176 views

Joining finite sequences [duplicate]

How do I describe the joining of two finite sequences in mathematical notation? For example, suppose the following: $$ A=(a_i)_{i=1,2}=(4,2)\\ B=(b_i)_{i=1,2}=(9,5)\\ C=(c_i)_{i=1,...,4}=(4,2,9,5) $$ ...
2
votes
1answer
95 views

prime notation clarification

When I first learned calculus, I was taught that $'$ for derivatives was only a valid notation when used with function notation: $f'(x)$ or $g'(x)$, or when used with the coordinate variable $y$, as ...
0
votes
2answers
165 views

I don't understand this notation… - Series with ln

I found this notation in my book $$ \sum\limits_{i=1}^n \ln^n3 $$ and I don't know how to interpret it. Is it $$ \sum\limits_{i=1}^n \ln((1^n)\cdot3)\;? $$ And btw, how to check if this series ...
0
votes
1answer
102 views

question about epsilon, delta limit definition

Sometimes, when describing the closeness of $x$ to $a$ as being less than $\delta$, it's stated as $|x-a|<\delta$ and sometimes it's stated as $0<|x-a|<\delta$. What is the " $0<$ " part ...
4
votes
1answer
174 views

$\delta$ Notation in linear algebra

In this equation below, what is $\delta_{l,q}$ denoting? Is $\delta$ a standard notation, or anything to do with all one's or the basis matrix etc? $$A_{ij}=\delta_{l,q}\left(\sum_{h=1}^n B_{l,h} + ...
2
votes
2answers
98 views

Default metrics for $c_0$ and $l^{\infty}$

In my book there is a question like Let $\{a^{(k)}\}$ be a convergent sequence of points in $l^1$. Prove that $\{a^{(k)}\}$ converges in $l^{\infty}$. Now I don't see it mentioned anywhere what ...
1
vote
1answer
68 views

What does $\|$ mean in this definition of the total derivative of a function?

What does $\|$ mean in this definition of total derivative? picture:
2
votes
0answers
54 views

Notation for n-array function with domains of different types.

I'm wondering what notation I should use to express a function R that maps elements from different sets to either 0 or 1. Is the following a reasonable usage? $$ R: S_1 \times S_2 \times ... \times ...
2
votes
2answers
199 views

useful notation for pullback

Let $f:A\to C\leftarrow B:g$ be morphisms in a category. There exists in literature a useful notation for the morphisms $\bar f:A\times_C B\to B$ and $\bar g:A\times_C B\to A$ in terms of $f$ and $g$?
1
vote
0answers
445 views

Time series notation

I'm developing formal software requirements specifications for processing time series data and thus need to mathematically describe time series and operations on time series. Is there establish ...
3
votes
2answers
93 views

Conventions on definitional if(f)

When defining a term it seems common to use 'if' when the stronger 'iff' is also true. For instance: Definition 1: A set $A$ is open in $(X,d)$ if $\forall x \in A$, $\exists \epsilon \gt 0$ such ...
1
vote
1answer
774 views

Notation for Multiple summation

Is there an alternate way to represent the multiple summation given below? $\sum_{i_k=k}^{n} \sum_{i_{k-1}=k-1}^{i_k} \dots \sum_{i_2=2}^{i_3} \sum_{i_1=1}^{i_2}$ It guess it is wrong to write it as a ...
0
votes
1answer
221 views

correct expansion of a sum using multiple indexes

I have looked for a similar posting but haven't found anything... but then I am also a bit unsure of how to search because I've never posted a math question before. In my introductory finite element ...
3
votes
3answers
2k views

What 's the differece between $\cot(x)$ and $\arctan(x)$? [duplicate]

I know that $\displaystyle \cot(x)=\frac{1}{\tan(x)}$ and $\space \displaystyle \arctan(x)=\tan(x)^{-1}=\frac{1}{\tan(x)}$ What is the difference between these two function? Is $\cot(x)$ the ...
4
votes
2answers
1k views

Mathematical symbol for “has”

Just out of curiosity, I was wondering if there was a symbol for "has" so intead of saying $x \in A$, we could say something like "$A$ has $x$", they both mean the same thing but I was just wondering ...
5
votes
1answer
310 views

Why do we write second derivatives like $\frac{d^2x}{dt^2}$ [duplicate]

Why do we write the second derivative of $x$ with respect to $t$ as $\frac{d^2x}{dt^2}$? It's never been explained to me, and I've never found a particularly good explanation. What's up with this ...
2
votes
1answer
144 views

Getting rid of the set builder notation in the expression $\{ f(x) \mid P(x) \} = \{ g(x)\mid Q(x) \}$

The set-builer notation is used to have $$\{ x \mid P(x) \} = \{ x \mid Q(x) \}$$ denote $$\forall x\ \big(P(x) \Leftrightarrow Q(x) \big).$$ And some people write $$\{ x \in U \mid P(x) ...
4
votes
1answer
171 views

Nomenclature and notation for some aspects of weighted directed graph.

I'm having some problem with nomenclature some structures and quantities related to weighted directed graph. Suppose that $A \in \mathbb{R}_+^{N \times N}$ is the weighted adjacency matrix of a ...
2
votes
1answer
56 views

A question about the validity of a notation

I am writing a paper and using such a notation. Do you think that it is mathematically a reasonable notation? $$ \hat{{\cal{P}}}_{i}=\{\hat{Q}: \hat{Q}_i|G_i[q_1/q_0<t]\stackrel{i=1}{\underset{i=0}...
6
votes
4answers
763 views

Confusion about the usage of points vs. vectors

As far as definitions go, understand the difference between a vector and a point. A vector can be translated and still be the same vector, whereas a point is fixed. But I would like some clarification ...
3
votes
1answer
295 views

Notation for set of all closed sets

Is there a common notation for the set of all closed sets of a topological space? I have been using $(X,\tau)$ to denote a topological space with $\tau$ being the topology, set of all open sets. I ...
2
votes
1answer
125 views

What does the notation $[V]^2$ mean (in graph theory)?

In graph theory, a graph is a pair $G=(E,V)$ of sets satisfying $E\subseteq[V]^2$. But what is $[V]^2$? I suppose that it is the same as $V\times V=V^2$, but I do not know where the square brackets ...
1
vote
1answer
82 views

Is this notation for Stokes' theorem?

I'm trying to figure out what $\iint_R \nabla\times\vec{F}\cdot d\textbf{S}$ means. I have a feeling that it has something to do with the classical Stokes' theorem. The Stokes' theorem that I have ...
4
votes
1answer
2k views

Is there a symbol for matrix multiplication operator?

Title says it all. Is there any specific operator symbol for matrix multiplication? Not just write down side by side but symbols like cross ($\times$).
0
votes
2answers
257 views

Horizontal bar notation for isomorphisms or bijections

I have seen in many books, particularly on category theory, the use of an horizontal bar to indicate some sort of equivalence, but I have not seen a proper definition in any context. For example: $X ...
4
votes
4answers
2k views

What is the notation for the set of all $m\times n$ matrices?

Given that $\mathbb{R}^n$ is the notation used for n-dimensional vectors, is there an accepted equivalent notation for matrices?
0
votes
1answer
90 views

Postfix notation in MAPLE

I usually use MATHEMATICA as a computer algebra system and there I heavily employ the postfix notation (achieved by "//" at the end of some command), e.g. ...