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.

learn more… | top users | synonyms

0
votes
0answers
17 views

Including/Excluding Function Arguments

My questions are regarding choices of including/excluding function arguments, and the statement authors are intending to make when making these choices. In a paper I'm reading the author states the ...
3
votes
2answers
36 views

Meaning of the following, partial derivatives..

What is the meaning of $${\partial^kG \over \partial t^k} \in C$$ how is this function explained $G(t,s)$, does it mean that the k-th derivative of $G$ is continuous. I've done some studying on this ...
0
votes
2answers
36 views

What is the “component projection” of vector a onto vector b, with the notation (a, b)?

I stumbled across this notation while reading the article "A handwritten character recognition system using directional element feature and asymmetric Mahalanobis distance" ...
0
votes
2answers
50 views

What are $\mathbb{R}^2$ and $\mathbb{R}^3$?

What are $\mathbb{R}^2$ and $\mathbb{R}^3$? I've seen them referred to, I'm guessing they refer to a plane an a space that can be defined in Cartesian coordinates in 2 and 3 dimensions respectively, ...
4
votes
1answer
139 views

Why we do those mathematicals terms $“dx”,dy“,dz” \cdots $ at the end of any integral? [closed]

I have a question in my mind and let me confused however I convince my self by a trivials answers , I would be interest to know what it does mean the mathematicals symboles $"dx" , "dy" , dz" $ ...
0
votes
0answers
18 views

Čech cohomology and fundamental class

I have a notational question. Simplified, I have a Cech cohomology on a simplical complex $\Sigma$ generated from the nerve of a covering of a set $X$. I also have a map $f: \Delta^n \to \Sigma$. In ...
2
votes
1answer
34 views

Indices at the left of a tensor in mathematical physics/differential geometry?

I am a mathematician and I am reading a paper in mathematical physics and I found the following notation: Let $Y$ be a two–form on $M$ such that $$\nabla({}_iY_j)_k = 0.$$ Here, $\nabla$ is ...
1
vote
5answers
76 views

Why the set of irrational numbers is represented as $\mathbb{R}\setminus\mathbb{Q}$ instead of $\mathbb{R}-\mathbb{Q}$?

What does the "\" symbol means in this context? I have seen it used for quotient sets like $X /{\sim}$ where $X$ is a set and $\sim$ is an equivalence relation but I don't know what it means applied ...
0
votes
1answer
117 views

What does an apostrophe mean in a function?

In a workbook, I saw the function $f(x)=x^2$. Then, there was the same function with an apostrophe $f'(x)$. It was stated that $f'(x)=2x$. What is the apostrophe, and why does it change the function? ...
0
votes
1answer
13 views

What is the meaning of the deltas in this score function?

I am learning stats. I just read a definition for a score function and hit some unfamiliar notation. I am familiar with the Leibniz notation for the derivative: $\frac{dy}{dx}$ The score function ...
0
votes
0answers
25 views

Interpretation of function notation

Consider the following statements, seen in this order in a paper ("An equilibrium characterization of the term structure" by Vasicek (1977)): (1) "Let $P(t,s)$ denote the price." (2) (after some ...
4
votes
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
13 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
38 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
4k 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
497 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
68 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
45 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?
9
votes
3answers
71 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, ...
1
vote
1answer
13 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
23 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
29 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
36 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
60 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
32 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
56 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.
0
votes
0answers
8 views

notation for contragredient matrix

Is there a standard notation for denoting the contragredient of an invertible matrix $A$. (The contragredient matrix of an invertible matrix is the inverse of its transpose).
1
vote
0answers
73 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
4answers
114 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
75 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
vote
1answer
43 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
26 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
160 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
757 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, ...
0
votes
1answer
65 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
40 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
38 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: ...
1
vote
2answers
50 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
36 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
46 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 ...
0
votes
3answers
63 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
15 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) * ...
2
votes
2answers
62 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 ...
2
votes
3answers
88 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 ...
3
votes
1answer
75 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
29 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
29 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 ...
2
votes
1answer
81 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
93 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 ...
2
votes
0answers
34 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 ($\langle \phantom{\cdot},\phantom{\cdot} \rangle$) ...