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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24 views

Abstract algebra notation

I am new to learning abstract algebra and using multiple books but the notation varies enough to throw me off. Could someone explain to me the differences between: $\mathbb{Z}\left\{ p\right\}$ ...
4
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1answer
37 views

Uncomfortable using Leibniz notation for the chain rule.

I am working through the following solved problem which uses separation of variables to get two ODEs. The problem is to show that $$\frac{1}{\sin\theta ...
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1answer
37 views

Notation question A $\subset \subset B$

I am a bit confused about the notation A $\subset \subset B$ used in functional analysis. The definition I have says: $A \subset \subset B$ iff $A \subseteq B$ and $\bar{A}$ compact in $B$. Wikipedia ...
4
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1answer
50 views

Is there a difference between writing $f: X\rightarrow Y$ and writing $f:X\mapsto Y$?

I think I've heard about a year ago that "$\mapsto$" is only used for a bijection, or do they mean the same thing?
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1answer
33 views

Lie derivatives and covariant derivatives (notation)

I am having troubling interpreting a particular expression in differential geometry. It arose in computing the Lie derivative along a unit normal, $n$, of the extrinsic curvature of a sub-manifold ...
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0answers
21 views

$C^\omega$ notation for real analytic functions

I've seen the notation $C^\omega$ used for the set of real analytic functions (e.g. on an interval). Where does it come from? What exactly does it mean? What is the reason behind it? Who first used ...
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2answers
22 views

Looking for notation of set of all entries of some matrix?

I'm busy writing my thesis, and I'm looking for some concise notation to denote the supremum of the matrix entries of, say $A \in M_n(\mathbb{R})$. How should I do this? Looking for something like ...
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1answer
22 views

Notation Question about Rings

If $S = \langle2\rangle$ is the ideal generated by $2$ in $\mathbb{Z}$, what does $S[x]$ represent?
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1answer
40 views

How does the presenter in this video derive this formula?

I am watching this coursera video on entropy (in the information theory sense of the word). Right around the two minute mark the presenter shows two forms for H(p). The first (after the equals sign) ...
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2answers
35 views

How would I express the statement “Let H be a subspace of V” in mathematical notation?

How would I express the statement "Let H be a subspace of V" in mathematical notation? Does something like this work? $$ ( \ \ H(\mathbb{R})\subset V(\mathbb{R}) \ ) $$
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0answers
21 views

Groups - Compositions

If the f is written to the right of its argument does that mean the composition of $f g$ is actually $g(f(x))$ instead of being $f(g(x))$ which is the notation I'm used to. I ask this because I read ...
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1answer
30 views

Groups/Sets Notation Question

Simple question: But what does the sigma small Y mean, does it just represent a group? Also have seen this with numbers, and not quite sure what it means. Thanks
2
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1answer
68 views

What does $\in$ mean?

I'm reading a textbook on complex analysis and I've come across notation using this ($\in$) symbol. In the context of "an argument of $z = x + iy$ is a number $\phi \in \mathbb R$ such that $x = ...
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2answers
23 views

Notation - Transpose of Block Matrices [Lay P121 Q2.4.12]

Definition of Transpose is $(A^T)_{ij} = A_{ji}$ $1.$ Why $\begin{bmatrix} M & N \end{bmatrix}^T = \begin{bmatrix} M^T \\ N^T \end{bmatrix}$, and NOT $\begin{bmatrix} M \\ N\end{bmatrix}$? ...
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1answer
23 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 ...
0
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1answer
26 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
36 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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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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0answers
31 views

Notation for plus-minus sign [closed]

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
25 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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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
55 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
30 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
13 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
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 ...
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6answers
179 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
57 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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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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0answers
42 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
39 views

Why does $d$ mean?

What do the $d$'s mean? I've seen them in other formulas as well.
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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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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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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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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?
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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!
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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 ...
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 ...
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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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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 ...
17
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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 ...
3
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1answer
61 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?
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0answers
29 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 ...
3
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2answers
105 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 ...
16
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6answers
409 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 ...
0
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0answers
8 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 ...