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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Notation of a linear inequality system.

Sorry to bother with this rather trivial question, but nowhere in my lectures or books can I quite find out what the topmost line means. Maybe I'm forgetting something. Anyway: Line 2 and 3 are ...
7
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1answer
65 views

First usage of the symbol ∈

Concerning a book [1] I am reading the symbol $\in$ was first used by Giuseppe Peano and is the first letter $\epsilon$ (epsilon) of the word ἐστί (means "is"). Does anyone know in which work of Peano ...
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21 views

Representing a randomisation function as a formula

I have formula question that I believe will use set theory notation. I'm explaining a randomisation function I developed, but I would rather explain it explicitly with formula notation, rather than ...
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0answers
12 views

Representing trees in Set builder notation?

Is there a way to represent graphs and minimum spanning trees using set builder notation? e.g. I have a weighted graph of n nodes, all connected to each other in a mesh network manner. I am to ...
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1answer
32 views

Set notation of $S^1 \times S^1$

This is a simple question, but should this be written as: $\hspace{120pt}S^1 \times S^1 = \{(z_1,z_2)\in\mathbb{C}\times\mathbb{C}:|z_1|=|z_2|=1\}$
3
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1answer
76 views

What are the differences in mathematical notation around the world?

I just learned that $\text{sen}\,x$ is the Portuguese notation for $\sin x$, and I was inspired to ask: What differences are there in how mathematics is written around the world? Note 1: I am likely ...
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1answer
22 views

Notation question: Group generated by two elements?

Let there be $H$ subgroup of symmetric group $S_4$, so that $H= \langle (12)(34),(234) \rangle$. What does the notation $\langle (12)(34),(234) \rangle$ mean? I know that if there's one elements, then ...
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0answers
25 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
41 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
43 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
56 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?
2
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1answer
43 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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1answer
40 views
+50

$C^\omega$ 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
26 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
41 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
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1answer
70 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
38 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 ...
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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
61 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
32 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 ...
1
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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.
1
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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 ...
0
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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.
0
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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. ...
2
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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 ...
0
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0answers
23 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? ...
0
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0answers
24 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
53 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 ...
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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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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?