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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Notations for interior product

There are two symbols in the Unicode "Supplementary Mathematical Operators" range whose names intrigue me 2A3C: INTERIOR PRODUCT: ⨼ (like $\lnot$ upside down) 2A3D: RIGHTHAND INTERIOR PRODUCT: ⨽ ...
2
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0answers
73 views

About the differential notation in measure theory

Is there any good reason for which integrating according to a measure includes a $\mathrm d$ as in $\int f\mathrm d\mu$ ? Or is it just a manner to keep formal consistency with the traditional ...
2
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1answer
17 views

In notation for argmin

I saw this notation for $\in$ -- I'm assuming this means "defines", right? $$\hat{\theta} \in \underset{\theta}{\operatorname{argmin}} \dfrac{1}{2} \sum_{j=1}^n (\theta^T x^j - y^j)^2$$ Does anyone ...
2
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2answers
17 views

general sum notation considering also not incremental indexing

I need to write a formula with summation in a general case allowing also the case with not incremental indexing. Example: $ \sum_{i=\underline{i}}^\bar{i}$ where can be ...
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1answer
69 views

Is $\frac{1}{ \frac{1}{x-1}}$ equivalent to $x-1$ when $x=1$?

Is $\frac{1}{ \frac{1}{x-1}}$ equivalent to $x-1$ even when $x=1$?
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0answers
16 views

Help understanding Wiener filtering formula

I would like some help interpreting the following formula, equation 1 from this paper: https://www.math.uni-bielefeld.de/~rehmann/ECM/cdrom/3ecm/pdfs/pant3/strela.pdf $\hat{X} = ...
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3answers
76 views

Can $a|b$ be used to mean $a$ can be divided by $b$? [closed]

Commonly $a|b$ means $a$ divides $b$, and I've seen $a\vdots b$ be written to mean $a$ can be divided by $b$ (meaning $b$ divides $a$). But how often would there be ambiguity if you wrote $a|b$ to ...
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1answer
20 views

Understanding notation of sets

What does it mean if you have a set suppose it is denoted $\theta = R \times (0,\infty)$. I'm a bit confused what the $\times$ represents?
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3answers
88 views

Mid '|' in math?

What does this equation mean? What does the $|$ mean? $446617991732222310 | mn(m^k - n^k)$ Here is the complete question for reference - What is the smallest positive integer $k$, such that for ...
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2answers
41 views

What's the notation for the intersection of stabilizer subgroups on a subset?

Let $G$ acting on the the (finite) set $S$, or the (finite dimensional) space $V$. Let $s \in S$, then the stabilizer $G_s:= \{ g \in G \ \vert \ gs = s \}$. Let $R \subset S$, then there are ...
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1answer
16 views

meaning of $f_{\chi_{E}}$

given $(X,\mathcal{M})$ a measurable space, I Have $E \subset X$ and $\chi_{E}$ is an indicator function. then what is meant by $f_{\chi_{E}}$ ? I am not very clear with this notation and meaning.
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2answers
53 views

Does \dots imply countable?

I am given an arbitrary set $S$. If I say the following: "Suppose that the elements of $S$ are labeled $x_1,x_2,x_3,\dots,$" am I notationally implying that the number of elements in $S$ is ...
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1answer
12 views

Expressing Sub-sequences of a sequence - notation

Given a sequence $b_n = \sin(\frac{n \pi}{2})$, I am trying to show that $(b_n)$ diverges. I have the idea down, I know exactly what to do, but just not HOW to do it. I know that any convergent ...
2
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0answers
24 views

Tensor notation in vectors

I have the following expression $\partial_{x_a}(\partial_{x_b} \rho \partial_{x_b}\rho) - \partial_{x_b}(\partial_{x_a}\rho\partial_{x_b}\rho)$ How do I write this in vector notation? At least the ...
2
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2answers
89 views

Quantifier for “there is at most one”?

As "there is at least one" and "there is exactly one" both have their symbols, I wonder what is the common notation for "there is at most one"? By "common" I mean the desired notation can be used ...
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0answers
20 views

Notation - continuity limit under an integral

I'm currently showing that the following integral is continuous: $$\int_{g_1(x)}^{g_2(x)} f(x,y) dy$$ Where $g_1, g_2, f$ are continuous. I am doing this by taking the following limit: $$\lim ...
6
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1answer
66 views

What does ∗⇒mean?

I am still really new to mathematical notations, and I am still having difficulty understanding most of the languages and notations. A recent notation I am very confused about ...
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0answers
41 views

Can I improve my Chain Rule (derivative) proof?

If $f'(g(x))$ and $g'(x)$ both exist, then $$f'(g(x))=\lim_{\Delta g(x)\to 0}\frac{\Delta f(g(x))}{\Delta g(x)}\stackrel{(1)}\implies \frac{\Delta f(g(x))}{\Delta g(x)}=f'(g(x))+\alpha(\Delta x),$$ ...
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0answers
35 views

What is this symbol ($\Vdash$) called?

This symbol: $$\Vdash$$ What is it called? It is often used in modal logic, like this: $W\Vdash$. I looked for it in wikipedia/modal logic and wikipedia/logic notation, but could not find it.
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1answer
40 views

What does the notation $U(\frak{g})[[\hbar]]$ mean?

I'm reading the following motivation for studying quantum group but I'm unfamiliar with the double bracket notation in $$U(\frak{g})[[\hbar]].$$ Is this a special set of polynomials with coefficient ...
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1answer
44 views

Nested radicals notation

Is there any convenient notation for things like: sqrt(1+sqrt(2+(sqrt(3+... Maybe using limits? I'm asking purely notational-wise.
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1answer
56 views

A few questions about derivative notation

$1)$ How do I denote derivative of $ax^2+b$ in terms of $ax^2$? $(ax^2+b)'(ax^2)$ can easily be confused with $ax^2\cdot(ax^2+b)'$. $2)$ How do I denote the derivative of $ax^2+b$ in terms of ...
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1answer
41 views

Can I denote derivative of $f(g(x))$ in terms of $g(x)$ by $f'(g(x))_{g(x)}$?

How to denote derivative of $f(g(x))$ in terms of $g(x)$ in prime (with $'$ without $\text{d}$) notation? Is it conventional to denote derivative of, say, $\sin(\cos x)$ in terms of $\cos x$ in ...
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3answers
85 views

What is meant by $\frac{d ^2y}{dx^2}$?

I have this homework question: Find $\frac{d^2y}{dx^2}$ for $y = (x^3−5)(2x+3)$. But I do not know why there are squares in $\frac{d^2y}{dx^2}$, so I cannot solve it. What is meant by this?
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43 views

Why is the boundary of a topological space $M$ denoted $\partial M$?

Why is the boundary of a topological space $M$ often denoted $\partial M$? Is there any connection between boundary and partial derivative?
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0answers
13 views

There is a logical or mathematical symbol for compatibility/incompatibility?

Exists a symbol in logic or mathematics to relate two or more compatibility or incompatibility conditions? I dont want to specify a determined area of study (topology, algebra, etc...) I just want to ...
0
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1answer
42 views

Which notation is correct

This one: \begin{align} V &= 100 + 1 \\ &\cong 100 \\ &\cong 50+50 \end{align} or \begin{align} V &= 100 + 1 \\ &\cong 100 \\ &= 50+50 \end{align}
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0answers
10 views

Notation for defining a total ordering with random tiebreaking

Suppose I have a set of 3-tuples $A = \{(3, 4, 5), (3, 4, 6), (2, 5, 7), (1, 1, 1)\}$. I want to define an ordering over elements in this set so that for two elements $x=(x_1, x_2, x_3)$ and $y=(y_1, ...
1
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1answer
39 views

What is the name of the following matrix “product” in which elements are not multiplied?

Assume that I am given the following matrices: $A = \begin{bmatrix} a_{1,1} & \dots & a_{1,n_a} \\ \vdots & \ddots & \vdots \\ a_{m_a,1} & \dots & a_{m_a,n_a} \end{bmatrix}$ ...
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1answer
26 views

Finding powers of prime ideals from its generators and understanding generator notation

I am trying to understand ideal notation with pointed brackets and how to use it. For instance, if I had an ideal $\mathfrak{a}=\left<2,1+\sqrt{-5}\right>$, where $2$ and $1+\sqrt{-5}$ are its ...
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1answer
72 views

What do superscripted numbers inside parentheses on functions mean?

I have a function $G(t) = (tx + (1 - x))^p = \sum\limits_{k=0}^pB_k^p(x)t^k$. I must find two different expressions for $G^{(j)}(1)/j!$. What does the superscript $(j)$ mean in this case?
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1answer
29 views

Is there a quick way to notate 'any intersection of these sets is the empty set'?

Is there a quick way to notate 'any intersection of these sets is the empty set'? I have a number of sets, I want to express that none share any elements with any other. Is there a way to express ...
0
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1answer
40 views

Can someone identify this equations font in ACC paper? [closed]

I am writing a report, and want to use microsoft word 2013 to type the following equation: What type of font it use in microsoft word? (I know it might be written in Latex) (This ia a ...
2
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2answers
23 views

Linear transformation notation question

Well the question is pretty basic, but I am learning math on my own. And I cannot understand the notation of linear transformation. I understand what linear transformation is, its properties and what ...
1
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0answers
23 views

Notation for vector of expectations

I have $n$ 'types' in a population. The frequency of each type is given by a $1 \times n$ row vector $\boldsymbol{x} = (x_{1},...,x_{n})$ (I'm treating this a random vector). I also have an $n \times ...
1
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0answers
35 views

What is this notation $\odot$ for?

(Note that symmetric algebra and symmetric tensor do not coincide when the characteristic is not $0$.) I'm reading this aricle:http://en.m.wikipedia.org/wiki/Symmetric_tensor And here it defines ...
3
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0answers
40 views

Formulating equation for distances between atoms

I'm trying to formulate notation to describe code that calculates the distances between protein atoms (represented as points in 3D space). Fragments consist of residues (amino acids) and each residue ...
2
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1answer
37 views

Notation for the direct sum and Kronecker sum of matrices

The tensor product $w = u \otimes v$ of two vectors $u \in \mathbb{R}^m$ and $v \in \mathbb{R}^n$ is usually defined as \begin{equation} w_{in + j} = u_i v_j \text, \end{equation} and the Kronecker ...
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1answer
22 views

Clarification of absolute Galois group temrinology

In a paper by Mazur, he writes "the profinte group equal to $G_{K,S}$ for some algebraic number field $K$ and finite set of primes $S$ in $K$. I understand $G_K = \text{Aut}(\overline{K}/K)$ but not ...
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0answers
20 views

Product of the LU Factorisation - Correct Formula?

Let's say I have: $$ U = \begin{bmatrix} 1 &2 &3 \\ 0 &1 &1.3 \\ 0& 0 & 1 \end{bmatrix} $$ $$ L = \begin{bmatrix} 10 & 0 & 0 \\ 40 & -30 & 0 \\ 10 & 30 ...
0
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1answer
20 views

Symbol meaning in a paper about elliptic curves

I was reading an introduction on elliptic curves, when the symbol $$\mathbb{F}_p^{\ast}$$ showed up. I understand that $\mathbb{F}_p = \mathbb{Z}/p\mathbb{Z}$ is the Galois field of the integers ...
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1answer
57 views

Where could (do?) we go after exhausting greek letters?

I'm still in high schools but after all my various math and science classes including calculus, statistics, geometry, and physics, I think that we've pretty much run the course of both upper and lower ...
3
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0answers
34 views

Which symbol to use for composition of a sequence of functions [duplicate]

I know how to write the composition of two functions: $f\circ g$ but I don't know whether there's a standard symbol for a sequence (similar to $\sum_i{f_i}$, $\prod_i{f_i}$ or $\bigotimes_i{f_i}$, ...
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5answers
217 views

What does $\prod_{k=-2}^{11}(15-3k)$ mean--and how might I compute it?

$$\prod_{k=-2}^{11}(15-3k)=\;?$$ I'm new to this and have not seen this notation before. Can anyone explain to me what this is called and how to solve or compute it?
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0answers
34 views

How to explain such mathematical notation

I meet such math notation $\mathbb{R}^2_+$ in the paper. However, I wanna whether it means a vector of real number.
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2answers
29 views

Shorthand for elements in a set and elements in a vector/list?

Really basic notation questions ahead. For both cases below, suppose I have an arbitrary set of integers $S$, e.g., $S = \{2, 4, 6, 8\}$. I want to define a list/vector whose elements are ...
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2answers
64 views

The Operator '$d$' Apparently Having two Different Meanings in Differential Geometry.

Given a smooth map $f:M\to N$ between smooth manifolds $M$ and $N$, we denote the global differential of $f$ by $df$. Also, the letter '$d$' is used for denoting exterior derivative of a differential ...
2
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1answer
33 views

Notation of author-defined functions.

I have seen functions defined various ways, and I'm wondering which form I should use for some functions. I am hoping to learn what it might be read as, interpreted, etc. The most common definition ...
3
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0answers
34 views

Can We Write the Differential in Terms of Covectors?

Let $f:\mathbf R^n\to \mathbf R$ be a smooth map. We can write $df:T\mathbf R^n\to \mathbf R$ neatly as $$ df = \sum_{i=1}^n(\partial f/\partial x_i) dx_i $$ For a function $f:M\to \mathbf R$ defined ...
2
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1answer
50 views

Implementing the $\Rightarrow \Leftarrow$ contradiction symbol?

How is the $\Rightarrow \Leftarrow$ symbol actually used in practice? I think my issue here is that I don't know what the symbol is meant to mean. For example, I know that $\implies$ means "which ...