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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19 views

What does ∈ mean?

I'm reading a textbook on complex analysis and I've come across notation using this (∈) symbol. In the context of "an argument of z = x + iy is a number φ ∈ R such that x = rcosφ and y = rsinφ" what ...
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1answer
421 views

Bar symbol over a matrix

So I am reading a paper (not online) and I come across a definition: $$\mathbb E=R\bar R$$ Where R is a complex matrix. I am thinking that it means complex conjugate, but I honestly have never seen ...
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1answer
17 views

Notation query: matrix projection

I've used the following notation in a report: $G\boldsymbol{w}\in\mathcal{H}_2\,\forall\boldsymbol{w}\in\mathcal{H}_2 $ In other words $G$ projects $\boldsymbol{w}$ back into the same set. But this ...
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6answers
173 views

What is the shortest way to write the number $1234567890$?

Here's a challenge : find the shortest way to write the number $1234567890$ . There is several ways to write the number $1234567890$ : $1.23456789 × 10^9$ $2×3^2×5×3607×3803$ $617283945×2$ But ...
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1answer
21 views

Understanding $Po(np)\{A\}$ probability notation

I am trying to read a textbook on probability and am already stuck on what must be basic notation. It says Thus, for example, if $A$ is any subset of $\mathbb{Z}^+$, it follows that for some ...
16
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6answers
404 views

The formalism behind integration by substitution

When you are doing an integration by substitution you do the following working. $$\begin{align*} u&=f(x)\\ \Rightarrow\frac{du}{dx}&=f^{\prime}(x)\\ \Rightarrow ...
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1answer
25 views

what does this triangle-like notation mean?

$$\triangleright\quad \text{and}\quad \triangleleft$$ I saw these notations in some abstract algebra texts and i don't know what does this mean. What do they mean?
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0answers
35 views

Is there a traditional name for the “eigenspace” function?

Let $A$ denote a field, $X$ denote an $A$-vector spaces, and suppose $\varphi : X \rightarrow X$ is a linear transformation. Is there a traditional name for the corresponding "eigenspace" function? By ...
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0answers
35 views

Precise notation of a sum of a sequence

I need help in rewriting the support of a function $f$ in a more compact or precise way given its upper bound $b$ and lower bound $a$ as \begin{eqnarray} b&=&\max\left( \sum_{n}\alpha_n ...
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3answers
31 views

Question about variable and constant notation in some properties

I am just starting to think about mathematical notation a lot more and some parts of it do not make as much sense to me as I would like. I am operating under the convention that beginning alphabet ...
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2answers
23 views

Limit notation question

lim(d^2 --> infty) d - 1 = infty Is this valid notation, or must it be written using lim(d --> infty) instead? I would like to express that as d^2 tends to infinity, d - 1 tends to infinity as well. ...
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1answer
60 views

When do we use dash instead of equality sign?

I began reading "A Concise Introduction to Mathematical Logic" by Wolfgang Rautenberg and on the 17th page came up with the following notation: The author (as I can understand) uses dash sign ...
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0answers
31 views

Notation for plus-minus sign [on hold]

Is there a well-understood notation for plus-minus ± if you (for some reason) don't have access to character map, or don't know the alt-code on Windows, etc.? In ...
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0answers
24 views

Convert nested for loop to mathematical expression

Does anyone know how I can convert this nested for loop into a mathematical expression? ...
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3answers
54 views

Why the name “umbilic”?

Umbilic points are points on a surface at which the principle curvatures of the surface are equal. "Umbilic(al)" refers to the navel/belly button. But why do we call these points so? What about the ...
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2answers
28 views

What does P(A U B) mean, in terms of real values?

I can't find a proper summary or reference of how to translate formulas in probability notation to arithmetic notation (i.e. when using real values). For example, if $P(A) = .7$ and $P(B)=.35$, what ...
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0answers
12 views

Is there any shorthand notation for linear interpolation?

It is quite common for me to encounter or manipulate expressions of the form $$ x + \alpha(y-x) $$ or equivalently $$ (1 - \alpha) x + \alpha y $$ where any of the expressions ($\alpha, x, y$) ...
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1answer
36 views

How to compute cyclic notation (23)(1)

I seem to become confused whence computing simple cyclic notations as such. From my understanding, the rule goes by starting from the right and to the left. However by doing this I only end up with ...
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2answers
310 views

The double factorial notation

The double factorial is defined as $$n!! = \begin{cases} n \cdot (n-2) \cdot (n-4) \cdots 3 \cdot 1 = \dfrac{(n+1)!}{2^{(n+1)/2}((n+1)/2)!} & \text{ If $n \in \mathbb{Z}^+$, is odd}\\ n \cdot ...
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4answers
2k views

Is there a mathematical symbol for unknown?

I'm searching for two symbols - considering they exist - (1) unknown value; (2) unknown probability. Note: I thought that $x$ was used in a temporary context, whenever I see it, it remains unknown ...
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1answer
8 views

An indexed family of filters and their elements

Let $X$ is an indexed (by some set $n$) family of filters (on some poset $\mathfrak{A}$). Is there any standard notation/terminology for the set $\{ y\in \mathfrak{A}^n \,|\, \forall i\in n:y_i\in ...
4
votes
1answer
211 views

Derivative $\Delta x$ and $dx$ difference

This may seems like a dummy question but I need to ask it. Consider the definition of derivative: $$\frac{d}{dx}F(x) = \lim_{\Delta x->0}\frac{F(x+\Delta x) - F(x)}{\Delta x} = f(x)$$ Also: ...
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1answer
54 views

What does the dot symbol mean?

A = B ⇔ (∀x.x ∈ A ⇔ x ∈ B) What does "∀x.x" mean? This expression means: saying 2 sets are equal, is equivalent to saying they're the same set, right? Thank you.
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2answers
38 views

Why does $d$ mean?

What do the $d$'s mean? I've seen them in other formulas as well.
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0answers
40 views

How can nested for-loops be expressed in mathematical notation?

Apologies if this is an obvious question; I'm not very familiar with mathematical notation for algorithms. I was coding a solution for Project Euler #4, and I came up with an interesting way of ...
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4answers
44 views

Symbol for $\left\{ x \in \mathbb{R} : x > 0 \right\}$ [duplicate]

Is there a symbol for the following set? $$ \left\{ x \in \mathbb{R} : x > 0 \right\} $$
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2answers
71 views

What does $n\gg 0$ mean in abstract algebra?

I am reading this book's page 144. While defining polynomial rings the author uses notation $n\gg 0$. I know that it means very very greater than but in this context it doesn't seem to mean that. ...
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votes
4answers
82 views

What's the meaning of this $(m,n) = 1$

I'm reading this pdf http://rutherglen.science.mq.edu.au/wchen/lndpnfolder/dpn01.pdf I understand some of the expression used in this but I don't understand the part $(m,n) = 1$ Is this a cartesian ...
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1answer
64 views

Simplification of a nested sum

I have a nested sum like so: $$\underbrace{\sum_{k_1=k_0}^{k^*} \ ... \sum_{k_n=k_{n-1}}^{k^*}}_{\text{n times}} 1\quad\ \text{with}\ \ n, k_0, k^* \in \mathbb{N},\ k^*\geq k_0$$ Is there a general, ...
0
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0answers
22 views

Is there a general notation for the Mobius group?

Let $a,b,c,d$ be complex numbers such that $ad-bc\neq 0$. Define $f(z)=\frac{az+b}{cz+d}$. Such function $f:\overline{\mathbb{C}}\rightarrow \overline{\mathbb{C}}$ is called a Mobius transformation. ...
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2answers
27 views

Can this be written in standard “vector calculus notation”?

A formula for the gradient of the magnitude of a vector field $\mathbf{f}(x, y, z)$ is: $$\nabla \|\mathbf{f}\| = \left(\frac{\mathbf{f}}{\|\mathbf{f}\|} \cdot \frac{\partial \mathbf{f}}{\partial x}, ...
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2answers
28 views

How would I read this formula?

$$m=\Bigg[\prod_{i=1}^n x_i\Bigg]^{\frac{1}{n}}$$ I do understand notation similar to this. Like summation formulas using sigma, but this is new to me. Also, how would I read this formula too? ...
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2answers
52 views

What is meant by the double vertical line notation here?

What do the double vertical lines around $\vec i$ and $\vec j$ in this equation actually mean? $$ sim(i,j) = cos(\vec i, \vec j) = \frac{\vec i \cdot \vec j}{\lVert \vec i\rVert^2 * \lVert\vec ...
0
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0answers
23 views

Notation for partial function set.

There is a standard notation for the set of all functions between S and T, namely T^S. Is there a similar notation for the set of all partial functions between S and T?
1
vote
2answers
41 views

How to represent this sequence mathematically?

I need to represent the sequence of pairs $$(N,0), (N-1,1), (N-2,2), \ldots , \left( \frac{N}{2}, \frac{N}{2}\right) $$ in a way I can use in a formula. Is there any way to do this? Thanks!
16
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4answers
2k views

Is there a way to denote the calculation $1+2+3+\dots+n$? [duplicate]

Since $n!$ represents $$1\cdot2\cdot3\cdots n,$$ I am wondering if there is a way to represent $$1+2+3+\dots+n?$$ What are some usual notations for the computation of some common sequences? Any other ...
1
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0answers
15 views

Symbolic cancellation in tensor notation of derivative

Start with this: $\frac{\partial f}{\partial x'^i} = \frac{\partial f}{\partial x^j} \frac{\partial x^j}{\partial x'^i}$ I think(?) the $\partial x^j$s cancel and this simplifies to ...
1
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0answers
13 views

notation “interior to”

I am writing out some notes as review, and a thing I often say is "z is a point interior to C". I was wondering if there is a common shorthand to write this before I make one up for myself. C is a ...
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0answers
35 views

Symbol used to specify that a matrix is symmetric?

A symmetric matrix satisfies $A^T = A$. Is there a specific symbol used to indicate this relationship?
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0answers
21 views

What is the general notation for the principal value of complex exponential?

It is general to distinguish the principal value of complex logarithm set by denoting it $Ln( z)$. Is there any general notation to distinguish the principal value of complex exponential? In complex ...
3
votes
1answer
60 views

Difference between $\mathrm {d} x$ and $\delta x $

Are $\mathrm {d} x $ and $\delta x $ the same mathematical object from the point of view of the nonstandard analysis?
5
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0answers
105 views

What is the Coxeter diagram for?

I understand that Coxeter diagrams are supposed to communicate something about the structure of symmetry groups of polyhedra, but I am baffled about what that something is, or why the Coxeter ...
1
vote
4answers
73 views

Notation for “all integers less than $n$”

Is there a short mathematical notation for all integers less than $n$ where $n$ itself is some integer? The only thing that comes to mind is $$\mathbb{Z} \cap (-\infty, n),$$ But this is pretty ugly ...
3
votes
2answers
104 views

Another notation question: What is $\genfrac{\{}{\}}{0}{}{n}{n-1}$?

Hi I'm sorry to ask another question so soon but I'm unaware of what the following notation means. Again this is taken from a Combinatorics context. It looks like this: $\begin{Bmatrix} n\\ n-1 ...
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2answers
86 views

What does -(-… mean in this equation?

I'm trying to understand what is meant by the -(-w etc. in the equation below. Can someone enlighten me? Source: Section 2.2.3 Case Amplification
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1answer
70 views

Does anyone know what this notation means: $n^{\underline{n}}$?

This is what I don't understand: $n^{\underline{n}}$ This is in a Combinatorics paper I am working my way through, and n is some natural number. I think that it should mean $n!$ The full question is ...
2
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0answers
27 views

What does $s\in \{(u_0,u_1)\in \Bbb R \times\Bbb R^3\}$ mean?

Given the expression $s\in\{(u_0,u_1)\in \Bbb R \times\Bbb R^3\},$ what is s? a single vector in $\Bbb R^4$ consisting a concatenation of the elements of $u_0\in \Bbb R$ and $u_1\in \Bbb R^3$ a ...
0
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0answers
7 views

Is there a convenient general expression to represent multiplication of items with increased dimensions?

First, I am just an engineer so please excuse me if I am describing this problem improperly, or using improper notation. I am trying to figure out if I can generalize some elements of the following ...
0
votes
2answers
32 views

A simple notation question

What does this notation $\mathbb{Z}[x]/(x^{n+1})$ mean? I guess it is a quotient group but I cannot find a precise definition. Here is the context: The cohomology ring of $\mathbb{C}P^n$ is given by ...
4
votes
1answer
5k views

I there some common abbreviation for minimum in equations

I'm searching for some symbol representing minimum that is commonly used in math equations.