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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52 views

$\mathbb R - \mathbb R$ notation

In multi-variable calculus I find this notation $\mathbb R - \mathbb R$ and $\mathbb R^m - \mathbb R^n$ the course material assumes that I am familiar with this notation. As an example "We usually ...
2
votes
1answer
71 views

Bullet notation

I'm just trying to make acquaintance with homological algebra. I see there the notation $(A_\bullet,b_\bullet)$ as a short notation for $(\dots,A_{-1},A_0,A_1,\dots,\dots,b_{-1},b_0,b_1,\dots)$. ...
0
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0answers
15 views

Is there a common notation for $x \sqcap Yy\neq \bot$

Is there a commonly used shorthand to express the following relation: $x R y \iff X \sqcap Y \neq \bot$? That is, the greatest lower bound of the two elements is not bottom. In terms of sets, the ...
30
votes
5answers
2k views

Notation of the second derivative - Where does the d go?

In school I was taught that we use $\frac{du}{dx}$ as a notation for the first derivative of a function $u(x)$. I was also told that we could use the $d$ just like any variable. After some time we ...
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2answers
26 views

Notation for equal via isomorphism

I am working with tensor products and there are a lot of identities, etc. that are true after appropriate identifications (between tensor products) are made. For example, if $V$ is a vector space, ...
1
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0answers
74 views

Why are $\pi$ and $e$ simply referred to as “pi” and “e”?

I'm aware of the names "Archimedes' constant" and "Euler's number" for $\pi$ and $e$ respectively, but these don't seem to be used very commonly. Even in school I remember $\pi$ and $e$ being almost ...
1
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2answers
40 views

Can a complex quantity have both a finite and an infinite part?

Of course, infinity is not a number but sometimes it is convenient to use it in place of a number, and this is very common in calculus, for example when expressing a limit. So I was wondering if it ...
1
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1answer
23 views

Questions about notation

Over the years, I have had many questions I left unanswered regarding notation. Forgive the fact that the points in this list are somewhat unrelated, but I thought it best to group them all in one ...
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2answers
49 views

Unknown matrix notation.

I have found this notation of a diagonal matrix in a demonstration: $$D=[\lambda_i \delta_{ij}]$$ Also, in the same demonstration, this other diagonal matrix is used: $$A=[a_i \delta_{ij}]$$ And then ...
2
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1answer
46 views

colon operator between matrices

While reading a paper, I have seen in several equations a colon operator used between matrices. Here are some examples, using matrices $F$, $P$ and $C$: $\delta F : \delta P > 0$ $\delta F : ...
3
votes
1answer
57 views

Would the order of Taylor Polynomial change after substitution?

I found the order of Taylor Polynomial is kind of confusing. For example, we know: $$T_4e^x = 1 + x + \frac {x^2} {2!} + \frac {x^3} {3!} + \frac {x^4} {4!}$$ After substitute $x$ as $t^2$, we ...
3
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1answer
47 views

Meaning of $\vee$ notation after an integral

I have an equation with the $\vee$ notation that I've not come across before. $$ \tilde f(\omega, t) = e^{-2\pi i\omega t}\int_{-\infty}^{\infty} e^{2\pi i v t} \, \bar{g}(v - \omega) \, \hat f(v) ...
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1answer
25 views

Notation for writing multinomial coefficient as sum of smaller multinomial coefficients

This question is an attempt to extend the Pascal triangle's hockey stick identity to multinomial coefficients as asked in question Hockey-Stick Theorem for Multinomial Coefficients. Consider the ...
4
votes
3answers
666 views

Confusion regarding $\log(x)$ and $\ln(x)$

I was solving an integral and I encountered in some question $$\displaystyle \int_{2}^{4}\frac{1}{x} \, \mathrm dx$$ I know its integration is $\log(x)$. But my answer comes correct when I use ...
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4answers
116 views

writing ''for all' with $\forall$

Suppose I want to write, in the context of a proof, say, that $x>0$ for all $x$ in some set $A$. There are several options how to do this: 1) $x>0$ for all $x\in A$ 2) $x>0$ for all $x$ in ...
1
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1answer
49 views

Unknown symbol about divisibility in paper re FLT

What does $\bigslopedwedge$ symbol mean? I saw it in Nigel Boston's paper about FLT. It is an upside down V (a wedge) but not symmetric. The right leg is vertical and the left is not. First arg is a ...
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2answers
37 views

What does this notation mean: $f(x)\in\mathbb{Z}[x]$

I have come across this excercise: Find all $f(x)\in\mathbb{Z}[x]$ such that $x^6+x^3f''(x)=f(x^3)+x^3$. What is the meaning of this notation: $f(x)\in\mathbb{Z}[x]$?
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2answers
629 views

Notation: Is $(\Delta x)^2 = \Delta x^2$?

I read this in a book and was wondering whether it's valid or not: I thought $\Delta x^2$ would mean 'change in $x^2$', which would be quantitatively different to $(\Delta x)^2$; no?
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0answers
44 views

What is the difference between $o(x)$ and $o(x^{2})$?

I think both $f(x) = o(x)$ and $g(x) = o(x^{2})$ tell $\lim_ {x\rightarrow \infty} f(x) = 0 $ and $\lim_ {x\rightarrow \infty} g(x) = 0 $ So, how does the degree of inner x in the little o notation ...
0
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1answer
33 views

Constrained optimization with alternates in special conditions

I have the following optimization problem. $$\max_{a b} acx+bdy+z \ \ \ \ \ \ $$ subjected to $$ c = \begin{cases} 1, & \text{if } 2xa-yb-z\geq 4\\ 0, & \text{if} \ 2ax<yb+z\\ ...
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0answers
9 views

How should I denote subelement of some object.

For example I have set of graphs $S = \{G : G = (V, E)$} and I want to say in "math notation" that none of S's graph V is not empty. In other words I want to address the subelemnt of G like I do it in ...
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2answers
36 views

LIM without x->a

I was working through the first few pages of Problem-Solving Strategies by Arthur Engel (Which may or may not be a little above my level), and I came upon an interesting form of notation I haven't ...
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1answer
30 views

Notation: meaning of {∗} ( bracket with star )

What is the meaning of the mathematical symbol $\{∗\}$? The Context is the wikipedia article on the Fock Space: Often the one particle space H is given as $L_2(X, \mu)$, the space of ...
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0answers
13 views

Right enunciation/notation in utility maximisation model

I am working on a model that can be defined as a utility optimisation problem but I'm struggling with the enunciation and notation. The model should describe how the utilities of a set of agents ...
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4answers
112 views

What does $\textstyle y \in \Re^{100}$ mean?

Just reading online and came across this: $\textstyle y \in \Re^{100}$ I am guessing it's something like "y is an element of [something about real numbers]". Can anyone help me out?
2
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1answer
71 views

A short guide explaining “How mathematicians talk” and common mathematical notations

Is there an introductary text/note, say like 5-15 pages that specifially focuses on explaining "How mathematicians talk", e.g. formulations like "Let A be a set. $\forall x \in A, \exists y \in B$" ...
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1answer
50 views

Name of this type of exponential notation?

If I have the number $45682$ and I write it as $$4\times 10^4+ 5\times 10^3+ 6\times 10^2+8\times 10^1 +2\times 10^0,$$ what is the latter notation called?
13
votes
4answers
3k views

Is there a symbol for plus and minus as opposed to plus or minus?

I know that you can use $\pm$ for when the answer could be either positive or negative, e.g., $x^2=16$, $x=\pm 4$. But is there a symbol that implies that you use both the positive and the negative ...
0
votes
0answers
28 views

What does notation $C^{\beta}[0,1]$ mean?

What does the notation $C^{\beta}[0,1]$ for $\beta \in (0,1]$ mean? I know $C[0,1]$ is the space of all continuous functions on the interval $[0,1]$, but what about $C^{\beta}[0,1]$? Usually ...
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2answers
67 views

why double Sigma summation?

The lecture slides is about covariance. One page it is on the other page, it is Why there are double Sigma summation on the first one?Is it just a typo?
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0answers
32 views

Are maximize/minimize operators in optimization problem?

Note: I'm not sure if Math.SX is the best community to ask (TeX.SX might be also good), but I decided to post here because my question is about mathematical rule rather than about (La)TeX technique. ...
0
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1answer
24 views

In a context-free grammar production rule, how to formally write a production rule $x \rightarrow \text{foo}$ where I don't know what $\text{foo}$ is?

I'm trying to formally describe a production rule $$x \rightarrow \text{foo}$$ in a context-free grammar, but I don't know the value of the right-hand side (only that there is a production rule of the ...
2
votes
1answer
38 views

Confusion regarding notation of a dual transformation

I'm reading Spivak's Calculus on Manifolds and in Chapter 4 he defines the dual transformation (although he doesn't call it that) as follows: If $f:V \rightarrow W$ is a linear transformation, a ...
0
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1answer
33 views

Is this a correct identity for the Kronecker delta and the Alternating Tensor?

If $\varepsilon_{ijk}$ is the alternating tensor and $\delta_{in}$ is the Kronecker delta, am I correct in thinking that $$ \delta_{in}\varepsilon_{ijk} = \varepsilon_{ink} $$ If not, what is the ...
0
votes
2answers
17 views

Notation for a Probability Distribution

I came across this in a paper: $$w_i\tilde{} \mathcal{CN}(0,2\sigma_{w_i}^2)$$ I am wondering what it refers to.
5
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0answers
47 views

Notation for inhabited sets

A set $X$ is called inhabited if it has some element. In classical mathematics, this means that it is not the empty set, so that one usually writes $X \neq \emptyset$. However, in intuitionistic ...
2
votes
2answers
80 views

Semi-colon in set notation

In a math text, what does something like $$ \{ (1,2,3,\dots, n); n\in \mathbb{N}\} $$ mean? More specifically, would it be $\{(1,2,3,\dots, n)\}$ for a specific $n \in \mathbb{N}$, or would it be $\{ ...
1
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2answers
105 views

Symbol for “the greater of the two values”

I'm looking for an operator that returns the greater of two values. Here's an example. If $a=5$, $b=6$ and $???$ is the operator, I'd like to have $x$ equal $b$ when I do $x=a???b$, since $b$ is the ...
0
votes
0answers
12 views

What's mean $\int_{\omega\in S^2} (\omega_i)^2 \ d\omega$?

I know that: $$\iint_S \vec F\ dS := \iint_T \vec F(\vec x(u,v))\Big(\frac{\partial \vec x}{\partial u}\times \frac{\partial \vec x}{\partial v}\Big)\ dudv$$ with $\vec x:T\to V$ parametrization of ...
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1answer
45 views

What is $\mathbb D$ [closed]

What exactly is $\mathbb D$? Is it the unit ball? I think it is a subset of the reals...
3
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1answer
47 views

How can there be no largest number in an interval set?

The question I have is: Given the interval $[1,3)$, explain why there is no largest number in this set. I don't understand how that interval set does not have a largest number. I know what this ...
0
votes
1answer
18 views

Why is the expression $u_{j}\frac{\partial u_{j}}{\partial x_{i}}$ equivalent to $\frac{1}{2}\frac{\partial}{\partial x_{i}}(u_{j}u_{j})$?

It says in my lecture notes that the index notation $u_{j}\frac{\partial u_{j}}{\partial x_{i}}$ is equivalent to $\frac{1}{2}\frac{\partial}{\partial x_{i}}(u_{j}u_{j})$, but does not explain why. ...
0
votes
0answers
15 views

Set notation for flatting sets

I have a graph $G = (V, E)$ where $V$ is a vertex set and $E$ is an edge set ($e = (a,b) \in E, a,b \in V)$ Now I have a subset of edges $E_I \subseteq E$ and I would like to obtain a set of all ...
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1answer
20 views

Notation question: characteristic subgroup?

The definition included that $f(H)=H$. This does not mean $\forall x\in H | f(x)=x$ right? Or not?!
0
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2answers
46 views

What does Im(AB) mean?

A and B are matrices. I see this notation used in a lot of online forums, but my textbook doesn't make use of it.
3
votes
2answers
67 views

Origin of the notation for statistical divergence

The unusual notation $D(P||Q)$ seems to be universally used for statistical divergences (e.g. KL divergence). What is the origin of this notation, and do the double bars (pipe symbols) have any ...
4
votes
1answer
58 views

difference between the dual space of $H^1(\Omega)$ and the dual of $H^1_0(\Omega)$

In the Partial Differential Equations by Evans (2nd edition p299), $H^{-1}(\Omega)$ denotes the dual space to $H^1_0(\Omega)$ where $\Omega$ is an open subset of $\mathbb{R}^n$ and ...
2
votes
1answer
29 views

Identifying a sequence as subset of subspace

If I have some sequence $\mathcal A = (a_i)$ of objects $a_i$ (maybe finite, maybe countably infinite) how can I say that those objects all exist in some subspace $S$? Is it correct to say $\mathcal ...
2
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0answers
29 views

Problem with a notation of symbolic derivatives.

Let's say we have got a function $F(G(B)\cdot C)$, i.e function $F$, which is a function of a function $G$ and variable $C$; also function $G$ is a function of variable $B$. Now I want to obtain the ...
0
votes
1answer
28 views

What is summation notation for functions of decreasing integers?

Wondering how may write following expression in sigma notation for summation? \begin{eqnarray} S &=& f(x_1,x_2,\cdots,x_n-1)+f(x_1,x_2,\cdots,x_n-2)+\cdots+f(x_1,x_2,\cdots,0)\\ ...