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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0
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1answer
18 views

Notation for all k-tuples that can be constructed from a set

Is there a generally accepted notation for a $k$-tuple that is constructed from a set? I have a set $\mathcal{A}$, and need to sum over all possible $k$-tuples (denoted $t_k$). Right now, I'm using ...
2
votes
1answer
19 views

Notation to express affine relationship

As you know, if we have a linear relationship between two variables $x$ and $y$ : $y=ax$, this is usually denoted by , $y\varpropto x $ y is proportional to x. The question is if they are affinely ...
4
votes
3answers
91 views

Why is $\mathbb{Z}^{+}$ sometimes used to denote the natural numbers?

This does not really make sense to me for several reasons: The integers are usually constructed using a given construction of the natural numbers Historically natural numbers were conceived of ...
2
votes
1answer
105 views

When was contemporary logical notation established

When contemporary fundamental logical notation was established? I mean basic symbols as used nowadays $\iff\implies\land\lor\lnot\forall\exists\vdash\models$.
1
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1answer
36 views

Summation with two running indices

I don't understand the notation of the following summation. $$ \sum_{i,j=1}^m \gamma_i \cdot \beta_{ij} \cdot \alpha_j$$ I first thought $ i, j $ would be increased simultaneously, but that would ...
0
votes
0answers
13 views

Notation for Markov Model

I have a statement that says: "Show that conditional on $X_m = i$, $(X_{m+n})_{n \in \mathbb{N}}$ is Markov($\delta_i, p$) independent of $X_1, \ldots X_m$". What does the notation Markov($\delta_i, ...
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3answers
47 views

What does this summation notation denote?

I am having trouble figuring out how this notation works, specifically how the intersection relates to the rest of the summation. It's just stuck there after it. I would greatly appreciate any help ...
1
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1answer
29 views

Comma vs pipe/vertical line in notation for conditional probability

What is the difference between the following expressions: $$P(X_1 < X_2 \mid \min(X_1, X_2) = t) \qquad \text{and}\qquad P(X_1 < X_2, \min(X_1, X_2) = t)$$ For context, I am trying to ...
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votes
0answers
33 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
votes
1answer
38 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
votes
1answer
57 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: $$^2\log\bigg(\frac 15\bigg)$$ ...
0
votes
2answers
39 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
35 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 ...
0
votes
2answers
21 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, ...
1
vote
0answers
31 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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vote
1answer
44 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 ...
0
votes
2answers
38 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
votes
1answer
44 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
votes
1answer
51 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?
0
votes
2answers
87 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 ...
0
votes
1answer
20 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
67 views

Summation verification

I have a particular polynomial $$ 1-10x+35x^2-50x^3 $$ Which can be written nicely as $$1-(1+2+3+4)x+(1\cdot2+1\cdot3+1\cdot4+2\cdot3+2\cdot4+3\cdot4)x^2$$ ...
1
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1answer
29 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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vote
1answer
46 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
55 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 ...
0
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2answers
87 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 ...
0
votes
1answer
49 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
48 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
60 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 ...
1
vote
1answer
43 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 ...
0
votes
1answer
33 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.
0
votes
2answers
50 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\}$
2
votes
2answers
33 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 $5!$ ...
0
votes
3answers
36 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
42 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
65 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, $S=k[T_0,\ldots,T_r]$, ...
1
vote
1answer
33 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 ...
1
vote
1answer
28 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
votes
1answer
28 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
41 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
votes
1answer
24 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
42 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
68 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
votes
0answers
39 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
48 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
23 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
147 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
27 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
141 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 + ...