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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4
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3answers
1k views

I have a simple idea that I would like to make into a formula

If I wanted to write one plus one, recurring, equals infinity.... Does this make sense? If so, how would it be written as a formula?
-1
votes
1answer
16 views

Graph: What does $G/xy$ mean?

For example: Let $G=(V,E)$ be a $k-$connected graph an let $xy\in E$. Show that $G/xy$ is $k-$connected if and only if $G\backslash \{x,y\}$ is $(k-1)-$connected. What does $G/xy$ mean ?
1
vote
0answers
46 views

What is $\Bbb E$? Is is $\Bbb R$ with the standard Euclidean topology?

What is $\Bbb E$? I believe this is just alternative notation for $\Bbb R$ where $\Bbb R$ is assumed to have the standard Euclidean topology. Is this correct? Is seems to be used in this way in ...
24
votes
4answers
8k views

What does .9 with a line above the 9 mean?

What does this mean? $$\Large.\overline9 $$ I've never seen this notation before.
2
votes
4answers
725 views

What's the meaning of having ^ over a vector name?

What's the meaning of having ^ over a vector name? (unfortunately, I don't know how to type it here) I cannot understand why some authors use the notation of ...
0
votes
3answers
123 views

what is the symbol generally used for whole numbers?

For subjecting to whole numbers, what symbol should I use? it must be valid for using anywhere from school to college. The symbol should be known and well proper to be understood easily by a school ...
2
votes
1answer
57 views

Period notation in group theory

In the context of finite fields, quotient groups, and characteristics, what does $$n.1=0$$ mean, i.e., what is the period notation?
7
votes
3answers
170 views

Must an irreducible element in $\mathbb{Z}[\sqrt{D}]$ have a prime norm?

Let $D\in \mathbb{Z}$ where $D$ is not a perfect square. Prove that if $\alpha\in \mathbb{Z}[\sqrt{D}]$, and $\alpha= a+b\sqrt{D}$ with: $|a^2-Db^2| = p$, a rational prime, then $...
1
vote
1answer
25 views

Notation of the average of a subset with a constraint

I'm quite new to mathematical notations, so please forgive me for my lack of skills in creating technically correct formulas. I came across a problem, when I have a variable set of numbers. Let the ...
2
votes
0answers
26 views

On permutation notation

I am trying to write up a proof that the parity of permutations on finitely many letters is well-defined. I think I have a proof that involves the number of disjoint cycles that a permutation may be ...
2
votes
1answer
41 views

Notation for integral of a vector function over an ellipsoid

For a short proof, I need to write a point $\pmb y\in\mathbb{R}^p$ as the integral of the surface of the ellipse $\pmb x^{\top}\pmb Q\pmb x=c$ where $\pmb Q$ is a $p$ by $p$ PSD matrix (for now $\...
3
votes
1answer
148 views

Big O Notation and negative “n”

So I'm studying big $O$ notation right now and am working through a problem and got $O(x^{-10})$ and I'm just wondering if it's possible to even have a term with $O(x^{-n})$ because I've never come ...
1
vote
1answer
73 views

Set notation, what is the meaning of <dimension>[]?

I just ran across this notation in a lecture slide and unfortunately it was not explained, This is my first question and because of that I cannot post images, here's a link to an image containing ...
1
vote
2answers
69 views

notation for two random variables with the same distribution

Suppose $X$ and $Y$ have the same distribution, can I write $X \sim Y$ or is there some other notation for this? Using tilde feels a bit strange since usually you have $X \sim N(0, 1)$.
1
vote
1answer
59 views

Difference between $a,b \in S$ and $\forall a,b \in S$

Is there any difference between these two notations, $a,b \in S$ $\forall a,b \in S$ where $S$ is any non-empty set.
1
vote
0answers
81 views

Can you help with Syracuse (3x+1)/2 disjoint tree graph set-builder notation?

These expressions are intended for my first paper, so I need a critique of my notation. Feel free to edit. Here is the Mathematica equivalent. The function $\alpha$ is the $n^{th}$ integer that is $\...
2
votes
0answers
49 views

Who first used the notation $\mathcal{O}_K$ for ring of integers?

I think this is a standard notation since almost every author uses it, but who came up with the notation? After all, what does $\mathcal{O}$ in $\mathcal{O}_K$ stand for? Thanks in advance.
3
votes
4answers
559 views

Math Symbol for “Where”

Pretty much any math text I've read introduces notation through a similar format of equation-notation or notation-equation form e.g ax+b+c where a = ..., b = ..., etc. or Let a = ..., b = ...
1
vote
1answer
78 views

What situations should $\oint$ be used?

Sometimes people put a circle through the integral symbol: $\oint$ What does this mean, and when should we use this integration symbol?
1
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1answer
47 views

What does $\mu^{2}$ mean?

Formula 5 in The Riemann Hypothesis; Borwein, Choi, Rooney, Weirathmueller, page 74, $$\frac{\zeta(s)}{\zeta(2s)} = \sum_{n=1}^{\infty} \frac{\mu^{2}(n)}{n^{s}},$$ $\Re(s)>1,$ where $\mu$ is the ...
0
votes
1answer
47 views

What does $\|u\|_{\mathcal{C}^2(\bar{\Omega})}$ mean?

What might $$\|u\|_{\mathcal{C}^k(\bar{\Omega})}$$ mean? $u$ is a sufficiently often differentiable function $\Omega \rightarrow \mathbb{R}$ and $\Omega \subset \mathbb{R}^n$ a bounded domain. It ...
8
votes
4answers
3k views

How to position negative sign of fraction

For example we have: $$ \frac{-1}{2} $$ Does this mean that only the numerator of the fraction is negative? Can we put it like this? $$ -\frac{1}{2} $$ Does this means that the whole fraction is ...
4
votes
4answers
2k views

What is the use of the double modulus signs?

So far as I can tell, the author uses $\|\cdot\|$ to mean the magnitude of a vector, but I have only seen the notation $|\cdot|$ to mean the magnitude of a vector. Is there any difference? If so, what?...
0
votes
1answer
84 views

What does $\{0, 1\}^*$ mean?

I am reading about Polynomial probabilistic time (PPT) and the input is taken from space $\{0, 1\}^*$ and I am not able to understand how is this working.
2
votes
1answer
113 views

Why Square Brackets for Expectation [duplicate]

I've often seen $\mathbb{E}[X]$ instead of $\mathbb{E}(X)$, but it seems variance is almost always $Var(X)$. E.g., Wikipedia for Expected Value and Variance. Is there a good mathematical reason for ...
2
votes
2answers
49 views

Proper Writing of Functions of Vectors

Let $x \in \mathbb{R}^n$ and $y \in \mathbb{R}^m$. Consider a real-valued function $f = f(x,y)$. Which of the following is the more correct writing of this map, or are they equivalent? $$ f: \mathbb{...
1
vote
2answers
51 views

Clarification of notation $\|fw\|$

this is the question: Show that for each linear map $f:\mathbb R^d → \mathbb R^e$ there exists $a < \infty$ so that $\|fw\|< a\|w\|$ for each $w$ in $\mathbb R^d.$ And my problem is that $f$ ...
1
vote
3answers
83 views

How to denote an average of data satisfying a given condition

I have to write an expression for the following. I have values, one fpr each of the last 5 months: ...
3
votes
0answers
58 views

Is there an established notation for this “replacement” operation?

If $S$ is a set, define $$(x \to y) \cdot S := \begin{cases} (S \setminus \{x\}) \cup \{y\} & \text{ if } x \in S \text{ and } y \not \in S; \\ S & \text{ otherwise.} \end{cases}$$ In other ...
1
vote
3answers
74 views

Is there any symbol for intersects?

Given two polygons $A$ and $B$ the intersection of them is represented by the notation $A \cap B$ that returns a geometry (more precisely the set of intersecting points) resulting from the ...
1
vote
0answers
26 views

Convolution notations and some miscellanous convolution questions

Convolution between distributions over the real number line, as it is mentioned in the optics course in my uni and also in wolfram is defined as: $$f(t) * g(t)=\int_{-\infty}^{\infty}f(\tau)g(t-\tau)...
3
votes
2answers
128 views

Why does unary minus operator sometimes take precedence over exponentiation, and sometimes it doesn't?

How should I evaluate 2*-2^3? Which one of these two is the correct one? 2*((-2)^3) 2*(-(2^3)) I was wondering what was ...
3
votes
3answers
102 views

Is there official notation to represent “perform an operation n times”?

I would like to know if you can represent the idea of say, $$n^n$$ n amount of times without defining a function. For example: $$1$$ $$2^2$$ $$3^{3^3}$$ $$4^{4^{4^4}}$$ $$5^{5^{5^{5^5}}}$$ and so ...
4
votes
1answer
89 views

What is this semi-circular symbol in the middle of a formula?

I have tried every search term I can think of but I can find no way of knowing what this symbol between the (a) and the trP means: Some context here, Point 2 in the third paragraph. Original image ...
2
votes
1answer
39 views

Expressing a differentiable map and curve in a parametrization

This is a question mainly about notation that I just cannot seem to understand. I'm reading Do Carmo's book "Riemannian Geometry" on page 7. Here is some context: (Here, $\alpha : (-\varepsilon, \...
3
votes
0answers
48 views

Interpretation of composite of random variable

Let $~f:[0,1] \to[0,\infty]$ be a measurable function bounded by $c \in \mathbb R$. Let $X_1,X_2,..,X_n \sim i.i.d ~\text{uniform}(0,1)$. How do I interpret the following statement: $$ Var(f \circ ...
1
vote
1answer
115 views

What is the meaning of $:s$ after a mathematical symbol?

I started to read a book about regression analysis, and I faced this latex notation: $e_i$:s, where $e_i$ is a residual. What is the meaning of "$:s$"?
0
votes
1answer
201 views

Why does $\bigcap_{m = 1}^\infty ( \bigcup_{n = m}^\infty A_n)$ mean limsup of sequence of set?

Why does $\bigcap_{m = 1}^\infty ( \bigcup_{n = m}^\infty A_n)$ mean the limit superior of sequence of set? I'm not getting it. ${A_n}$ is a sequence of set in $S$. I do know what limsup means for a ...
2
votes
0answers
55 views

What's the advantage of using bra-ket notation over inner-product notation?

Both notations look pretty similar, and appear similar when undergo algebraic operations. Apart from personal taste (aesthetics) concerning commas ($\langle \phantom{\cdot},\phantom{\cdot} \rangle$) ...
0
votes
0answers
160 views

Math, logic symbol for “instance of”

I saw a discussion of a possible symbol for "example," but I need "example/instance of." There is of course $a \in S$ which is a is a member of/in S, but is there a specific way of stating $a "...
1
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0answers
41 views

asking about the meaning of a notation in a 1942 article

In this article http://projecteuclid.org/euclid.bams/1183505105 what is the meaning of the notation $YX\wedge$, that is what does it mean when you write the notations for two sets together side by ...
0
votes
1answer
86 views

How to insert Gothic letters in Word? [closed]

I do not manage to find in any of the options provided by Word the real Gothic letters used my German mathematicians in their original works. Noe even under the two "gothic" rubrics. just some sparse ...
1
vote
1answer
150 views

How to express outer sum in a matrix form?

So I have the following equation for a matrix $\mathbf{B}$ given $\mathbf{A}$: $$ b_{ij} = \sum_k \sum_l a_{ki} a_{jl} $$ The question is if there is anyway that I can write that one compactly in ...
0
votes
0answers
48 views

How is the second part of a dual number called?

A complex number $a + bi$ has a real part $a$ and an imaginary part $b$. But, what about dual numbers $u + v\epsilon $? I have seen the non-real part $v$ been called the infinitesimal part. Is this a ...
11
votes
6answers
359 views

What is the significance of using “$a$” vs “$x$” in this text?

I'm a web development guy currently learning Calculus and am having some trouble understanding the seemingly unwritten rules of variable naming conventions in mathematics. I've read several other ...
9
votes
2answers
324 views

Does this math formula with $1/PI\begin{cases}^\infty_{-\infty}\end{cases}$ mean anything?

I happened upon an image on the Internet and I wondered whether the math on the chalkboard means anything. Using Google's image search, I found three other related images. Piecing together ...
4
votes
1answer
69 views

Notation for the set of holomorphic differential forms

I used to write $\Omega^p(M)$ for the set of $p$-forms on $M$ and $\Omega^{p,q}(M)$ for the set of $(p,q)$-forms on a complex manifold $M$. Now some authors use $\Omega^p(M)$ to denote the set $\text{...
1
vote
1answer
60 views

Notation for a unit vector

If I have a vector $\vec{v}$, is there a standard concise notation for the unit vector in the same direction of $\vec{v}$ that is $\frac{\vec{v}}{|\vec{v}|}$?
2
votes
0answers
76 views

Is there a name or symbol for the matrix division resulting in a scalar?

I am not talking about the inverse matrix, $A^{-1}$ which gives $A\times A^{-1}=I$, but rather the operation $\frac{1}{n}tr(\space\cdot \times A^{-1})$, which gives 1 when applied to a $n\times n$ ...
0
votes
2answers
1k views

Matrix notation in handwriting

I understand that typically matrices are printed in bold to distinguish them from other mathematical entities with the same symbols. However I find it difficult to actually handwrite in bold. With ...