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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31 views

Notation for intersection of functions

Suppose $f,g : [0,1] \mapsto [0,1]$ are continuous, $f$ is non-decreasing, $g$ is non-increasing, and $f(0)<g(0)$, $f(1)>g(1)$. Is there a standard notation for the intersection point $x_0$ of ...
-1
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1answer
36 views

What is the meaning of |⋯| notation for an index subset?

I am currently working on a research project. In the attached image what does the capital $|I|$ and $|J|$ mean ?
3
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1answer
53 views

Notation of logarithms

Here's the problem: Me and my teacher are having a discussion about the notation of a logarithm. My teacher says that the only way of notating a logarithm is like this: $$^2\log\bigg(\frac 15\bigg)$$ ...
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2answers
33 views

What does a mini circle between f and h(x) mean?

I am currently doing a math problem and have come across an unfamiliar notation. A mini circle between $f$ and $h(x)$ The question ask me to find for 'the functions $f(x)=2x-1$ and $h(x)=3x+2$' $$f ...
3
votes
1answer
32 views

How to learn ideals and quotient rings?

I have difficulties to learn ideals of ring and how to operate with them. Is there somewhere a good tutorial on those? Like I saw from an algebra book the Artin–Rees lemma and it looked a bit scary as ...
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2answers
19 views

Divide elements of a matrix by row

Suppose I have a matrix that looks like this: $$A=\begin{bmatrix} 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 1 \end{bmatrix}$$ I want to divide each term by the sum of terms in that row, ...
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0answers
29 views

Notation confusion about sum of $\Lambda (n)$

This is hopefully a small point of notation I am missing. I am used to the first two equalities below. $$\sum_{n \geq 1} \Lambda(n) n^{-s} = \sum_{p \mbox{ prime}} \sum_{m \geq 1} \Lambda(p^m) ...
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1answer
38 views

Set theory - Can someone explain sequence operator?

I'm reading up on set theory and relation and I need help understanding this: Two sequences of the same element type can be composed to form a single sequence in such a way that the order of each ...
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2answers
35 views

Notation for the vector space of functions with $k$ continuous derivatives

I saw the following definition given at the mathworld web site: A function with $k$ continuous derivatives is called a $C^k$ function. In order to specify a $C^k$ function on a domain $X$, the ...
2
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1answer
43 views

Naming a function in a paper

I'm writing a paper (in physics), and I want use the same name for two related functions that have different domains. Please allow me to elaborate. I have function $f: R\longmapsto R$. I want to ...
0
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1answer
50 views

What does it mean to write $|||x|||$ rather than $||x||$?

I am familiar with the notation $||x||$ meaning some norm of $x$. I have just come across the notation $|||x|||$ (in a text that also uses the former for norms). What is the difference?
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2answers
85 views

Why “thin groupoids” are not ubiquitous?

Google search for "thin groupoid" finds surprisingly few (namely 7) pages. But "thin groupoid" is a term to denote an important notation of a groupoid with every loop being the identity. I met it ...
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1answer
19 views

Average Distance of an element and a set of elements

Let $a$ be an element and $B$ be a set of elements $\{b_1,\dots,b_n\}$ which would be the best notation to represent the average distance between $a$ and all the elements of $B$? One way to describe ...
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0answers
63 views

Summation verification

I have a particular polynomial $$ 1-10x+35x^2-50x^3 $$ Which can be written nicely as $$1-(1+2+3+4)x+(1\cdot2+1\cdot3+1\cdot4+2\cdot3+2\cdot4+3\cdot4)x^2$$ ...
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1answer
21 views

Expressing the nth element of a set

Let's say I have a set $S$ of infinite length. How can I express a function that returns the nth element in the set?
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1answer
40 views

In graph theory, what does $o(G)$ usually mean?

I'm completing a graph theory assignment, and one of the problems states, Prove that a tree $T$ has a perfect matching if and only if $o(T-v) = 1$ for every $v \in V (T)$. I'm not asking for ...
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votes
2answers
50 views

Pitfalls/subtleties of $O$ notation

What are some examples of $O$ subtleties? I'm not only thinking of the asymmetry of the $O$ relation, but of the ways in which $O$ constants can depend on nearby parameters, and the fact that the ...
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2answers
60 views

Is there any shorthand for $\text{span}\{v_1, \ldots,v_n\}$ which doesn't conflict with any notation in linear algebra?

Some people use $\langle \cdot \rangle $ as a shorthand of $\text{span}$ (e.g. the German wiki), i.e. $$\langle \{ v_1, \ldots,v_n \} \rangle := \text{span}\{v_1, \ldots,v_n\},$$ yet the notation ...
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1answer
47 views

Definition of the set of independent r.v. with second moment contstraint

I am trying to nice write the definition of the following set. Def: The set of all distributing of the pair $(X_1,X_2)$ such that $X_1$ and $X_2$ are independent Have second moment constraint ...
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1answer
43 views

What is the meaning of V\U?

What is the meaning of U \ V when it comes to graph? I try to understand Markov property on DGM with below document but for me it is hard to search. ...
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3answers
58 views

Expressing a number that doesn't exist [closed]

How can one express something like $x \in \pi$ where $\pi$ is a set of prime numbers and $d$ is some divisor such that $\pi = \lbrace n:d|n\rbrace = \lbrace {1, p}\rbrace$? Or should I do something ...
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1answer
40 views

Notation: May or may not be?

Searched it on Google and couldn't find it. Consider the following literal statement: If there exists a supremum M for A, where A is a set contained within the one dimensional continuum R, then M may ...
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votes
1answer
31 views

In a binary vector $ x \in \{0,1\}^{k}$ what does the $^{k}$ mean?

In a binary vector $ x \in \{0,1\}^{k}$ what does the $^{k}$ mean? I understand that $\in$ means 'is a possible outcome' or 'in' so x can be 0 or 1, but I'm not sure what the $^{k}$ means.
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0answers
11 views

notation or symbol for truncated vector

I don't think that the title was clear! Consider you have a vector y=[y1 y2 ... yN] During your notes you need to use the last M elements of y: $\tilde{y}=[y_{N-M}, ... y_N]$ what is the best and ...
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2answers
28 views

symbol for maximum number in an array or vector

As we know $\|x\|_{\infty}$ returns the maximum "absolute" value through the vector . I'm looking for a symbol to show the actual value that can be also negative: $ ?x?=\max\{x_1,...x_N\}$
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2answers
31 views

Summation notation for divided factorial.

I have the following sum $$5\cdot4\cdot3+5\cdot4\cdot2+5\cdot4\cdot1+5\cdot3\cdot2+5\cdot3\cdot1+$$$$5\cdot2\cdot1+4\cdot3\cdot2+4\cdot3\cdot1+4\cdot2\cdot1+3\cdot2\cdot1$$ It is basically $5!$ ...
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votes
3answers
35 views

What does $\left \lbrace r, l,0 \right \rbrace ^{\mathbb{Z}^2}$ mean?

What is the meaning of this notation? $$ \left\{a, b\right\}^{[c, d]} $$
4
votes
1answer
40 views

What is the meaning of the notation $\mathbb{R}^3/\mathbb{Z}^3$?

In Terence Tao's piece on Kolmogorov's Law (http://terrytao.wordpress.com/2014/05/15/kolmogorovs-power-law-for-turbulence/) he uses the notation for the fluid velocity $$u: \mathbb{R} \times ...
0
votes
2answers
63 views

What is $S_d$ in algebraic geometry?

I'm trying to read algebraic geometry on my own by doing homeworks on course hold in 2003. One of the problem is the following: Let $k$ be a field, $S=k[T_0,\ldots,T_r]$, ...
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1answer
32 views

Is there such an expression?

I saw some notation on my friends notebook. What does that L shaped two lines mean? Goes below a1, a2 and a1-a2. I couldn't find anything related online. May this be about complex numbers? Can someone ...
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1answer
24 views

Select some particular elements to a set

What I am asking is not a math "problem" but something about presenting the problem in math language. Assume $0<a_{i}<1, i=1,2,3,...,N$ and $a_{i} \neq a_{j}$, I want to have a set $A$ which ...
0
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1answer
22 views

Bold 1 with interval as subscript in function definition - what does it mean?

I am sitting on an exercise. My prof gave me this function: $$f(a) := \frac{1}{3} \cdot \textbf{1}_{(-\infty,\ 0]} (a) \frac{1}{2} e^{a/2} +\frac{2}{3} \cdot \textbf{1}_{(0,\ \infty]}(a) \frac{1}{5} ...
0
votes
1answer
34 views

Notation: Polynomial of the Differential Operator

I having difficulty with some notation relating to control theory. Given that $H(s)$ is a strictly proper, scalar transfer function (i.e. a ratio of polynomial functions with a higher degree in the ...
0
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1answer
23 views

$\bot$ operator for integers?

Quote from a proof on page 9 of this paper: Let $\hat{w}$ be the $\mathbf{(s[j] \bot 1)st}$ write by $p_i$. (emphasis mine) $s[j]$ is an integer. My initial guess was that this was typo/misprint ...
0
votes
3answers
40 views

Notation for asymptotic approximation

I was reading Stirling's approximation and got quite confused with the idea of asymptotic formula. So in Wikipedia it says that a function $F(n)$ of $n$ is asymptotic formula for $P(n)$ if $P(n)$ is ...
3
votes
2answers
58 views

How do I learn all the weird symbols and notations?

I'm really fond of math, and would have studied that, if I didn't find software development even more interesting. Even though I don't study math, I do sometimes come across stuff I want to learn ...
2
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0answers
36 views

Why are there so many different symbols to represent the Heaviside (unit step) function

In signal processing, the unit step function is typically written as $u(t)$. In other references though I have seen it represented as $H(t)$ and even $\theta(t)$. The unit impulse is fairly ...
2
votes
1answer
46 views

Sets and Notation.

There is a set like: $V = \{f : R \to R \mid f(x) = ax + c \text{ with } a, c \in \mathbb{R} \}$ I do not know what "$:$" means. I do not know what "$|$" means. I think the meaning is something ...
0
votes
1answer
22 views

Equivalency of Set Notation

This is a very simple question. Let's say there is $ Z_{1} \cup Z_{2} $ Where $ Z_{1} = \emptyset $ and $ Z_{2} $ = $ \left\{ x \mspace{4mu} | \mspace{4mu} x \in \mathbb{R},\mspace{4mu} 9<x ...
3
votes
5answers
141 views

How do I succinctly note the sum of $(n-1)+(n-2)+…$?

I was playing with numbers and wanted to see how many possible connections there are in a network of $n$ nodes. I found that the answer was equal to ...
0
votes
1answer
23 views

Expressing a hypercube subset definition using set notation

The definition of a hypercube is this: The $n $-dimensional hypercube $Q_n$ is the graph with $V = \left\{{ (e_1,\dots,e_n)|e_i \in \left\{{0,1}\right\}(i=1,\dots,n)}\right\}$ in which two ...
0
votes
1answer
27 views

What does it mean when you have $\operatorname{Pr}\limits_{h\in \mathcal{H}}$

I'm asked to prove that a family of hash functions is $2$-wise independent. I'm told that: $\mathcal{H}$ is $k$-wise independent if for any $k$ inputs $x_1,...,x_k$ and hash values $v_1,...,v_k$, ...
2
votes
3answers
134 views

What is the difference between $\omega$ and $\aleph_0$?

The book I'm using says that the cardinality of a set $X$ is the least ordinal $\alpha$ such that $|X| = |\alpha|$. So then $\omega = \aleph_0$, but $\omega + \omega \ne \omega$, while $\aleph_0 + ...
2
votes
1answer
46 views

Is this notation for inverse functions bad?

I'm trying to find useful notation for inverse functions that isn't too much in conflict with other notation already in use, but I'm wondering if this notation will come back and bite me in the ...
1
vote
1answer
51 views

What does it mean to have a lone plus sign in the exponent/superscript (Modified Weiszfeld algorithm)

I was skimming through Vardi & Zhang's paper on "A modified Weiszfeld algorithm for the Fermat-Weber location problem". It is available at http://www.stat.rutgers.edu/home/cunhui/papers/43.pdf ...
1
vote
1answer
34 views

Angular bracket operation in differential geometry?

There is an angular bracket operation in geometry, which looks like $$\langle X,Y\rangle$$ where $X$ and $Y$ are apparently $(0,1)$ tensors. It appears for instance in the answer to the following ...
2
votes
1answer
27 views

Since a function is $f$, not $f(x)$, how do you denote $\int f(x,y)g(y)dy$?

It's usually stated that the correct symbol of a function should be $f$, because $f(x)$ is the value of $f$ at the point $x$. I tend to follow this convention, but there are ocassions when this ...
0
votes
2answers
21 views

set notation, find min

I have the following problem: I have two set of operators $S_1$, $S_2$. Each operator has a cost, which we find it by $Cost(o)$, where $o$ is an operator. Now I need to find the cheapest operator ...
3
votes
2answers
386 views

What is the meaning and difference of { } and ( )

I know that $(1,2,3) \ne (3,2,1)$ but {1,2,3} = {3,2,1}. But what does it mean actually? And maybe some explanation on why 1. Ø subset of {0} is true? 2. {x} element of {x} is false?
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votes
4answers
67 views

How $a_{13}=0$ in $\begin{bmatrix} {2}&{1}&{0}\\ {1}&{3}&{5} \end{bmatrix}$?

I'm reading Artin's Algebra. $$\begin{bmatrix} {2}&{1}&{0}\\ {1}&{3}&{5} \end{bmatrix}$$ It says that $a_{ij}$ is the matrix entry such that $i$ is the horizontal coordinate and $j$ ...