Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [notation]

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.

0
votes
1answer
16 views

total of non zero value

I want to write a math formula that represents the average of non zero value e.g. if I have 4 numbers, one of them is zero, then the sum of the numbers will be divided by 3. Is it correct to say: $$ \...
-1
votes
2answers
31 views

What is the difference between the summations?

What is the difference between the summation $$\sum_{1 \leq i<j \leq n} f(i,j)$$ and $$\sum_{1\leq i} \sum_{<j \leq n} f(i,j)?$$
0
votes
0answers
18 views

Typographic conventions for subscripts?

I was wondering if there were any sort of consistent rules or guidelines for how to properly format subscripts on variables? The primary aims should be to have clear meaning, and consistency with what ...
2
votes
2answers
22 views

Probability theory - Logic, Notation, simulation

i need some help in probability theory. The thing is im not sure if im thinking about this correctly and if i express my thoughts correctly. I really got lost in all the dice examples of the internet. ...
1
vote
1answer
19 views

Operator precedence in addition and subtraction

Customary operator precedence has addition prior to subtraction. Apart from historical convention and notational consistency, is there a rationale for this?
0
votes
4answers
41 views

What is the meaning of $\binom {i+j+k}{i,j,k}$

In an answer to a question (https://math.stackexchange.com/a/288999/172737) this combinatoric symbol was used $$\binom {i+j+k}{i,j,k}$$ I can't determine its meaning, though I've searched. I ...
0
votes
1answer
38 views

What is the difference between “for every $x$ there exists a $y$” and “for all $x$ there exists a $y$”?

Is there any difference between them? or are they same? I was going through the definition of uniform continuity, which uses the term "for every". Can someone explain me the difference between the two ...
1
vote
1answer
44 views

What does $\vee$ mean in the context of group theory?

What does $\vee$ mean in the context of group theory? In particular, I am trying to figure understand:
2
votes
1answer
23 views

Notation of countable disjunction in infinitary logic

Let $L_{\omega_1}$ be a propositional infinitary language. The subscript $\omega_1$ in $L_{\omega_1}$ indicates that disjunctions and conjunctions of all lengths $<\omega_1$ are allowed. In other ...
1
vote
1answer
29 views

Notation for countable union

I sometimes see the following notation for a countable union of sets: $\bigcup_{n\in\omega}E_n$ Is this notation strictly synonymous with the more standard $\bigcup_{n\in\mathbb{N}}E_n$?
2
votes
0answers
14 views

mathematical notation for the sum of all the elements of the individual diagonals above the secondary diagonal.

What is the notation of the sum of the elements above the secondary diagonal for a generic nxn square matrix? I do not mean the sum of all the elements above the secondary diagonal, but rather the ...
0
votes
0answers
23 views

Dyadic Function

I have the following formula in the beginning of the basics of probability theory. The notes only say that we define this function. What does this function serve to ? What does it tell ? What is 1 and ...
0
votes
0answers
12 views

function with vector argument notation

I have some questions on functions that take real-valued vectors as arguments which I would like to resolve. Given $x \in \mathbb{R}^a, y\in \mathbb{R}$. I know the notation $g: \mathbb{R}^a \...
1
vote
1answer
55 views

Multiplicative quotient - what's the correct notation? Does a quotient group contain singletons or cosets?

I want to learn the correct notation and language with which to communicate clearly about a quotient on the multiplicative group $G=(\Bbb Q^+,\times)$ In particular, I want to know the notation with ...
0
votes
1answer
28 views

How to denote that something is a subalgebra?

According to Wikipedia, for a given group $G$, the relation of its subgroup $H$ to $G$ is usually denoted by $H\le G$ (or $H\lt G$ for a proper subgroup). What about algebras? What is the most ...
1
vote
0answers
12 views

Big O notation with -n near zero

Given a function of the form $$f(x)= \frac{c_1}{x} + \frac{c_2}{x^2} \,+ \,...+\, \frac{c_n}{x^n}$$ where $c_1,c_2,...,c_n \epsilon \mathbb{R}$ are constants, as $x$ approaches $0$ it is clear that $...
1
vote
0answers
28 views

What does a semi-colon mean within a function expression?

I am trying to understand how to implement gradient mapping for a parametric max-type function $f(t;x)$ defined such that $$f(t;\bar{x};x)=\max_{1\leq i\leq m}\{f_0(\bar{x} + \langle f'_0(\bar{x}),x-\...
2
votes
2answers
48 views

Exact notation of the domain of a function

For example, we have $f(x)=\frac{1}{x^2-1}$ Would the domain be $$\mathcal D(f)=\{x\in\mathbb{R}\mid x\neq(1,-1)\}$$ or rather $$\mathcal D(f)=\{x\in\mathbb{R}\mid x\neq \{1,-1\}\}$$ or $$ D(f)=\{x\...
1
vote
2answers
39 views

Small o notation PROOF [closed]

It's probably a vey silly question, but I'm confused. I should proof the small o notation with lim but i don´t know how $(\ln n)^a = o(n^b )$ how do i solve this and do i need to proof it for $a<...
0
votes
0answers
8 views

Notation of Payoff functions in the Selten game

The pictures are from Narahari's textbook, Game theory and Mechanism Design. Could anyone explain to me the last line (the definition of payoff functions)? I haven't seen this notation ever before ...
0
votes
0answers
27 views

How do you type formatting commands from LaTeX in this community? [closed]

My question is, how do you type formatting commands from LaTeX in boxes like these in this community? For example, document{article} or ...
0
votes
1answer
35 views

A question on $G=S_5$ concerning notation

I think there must be a misprint in a question I've been asked.It has written on it ; $$|G|=S_5$$ but of course this notation is nonsense as a real number cant be equal to a set. Do you think it ...
-1
votes
5answers
41 views

What does this set mean: $ \{ g \mid g : \{0,1\} \rightarrow \mathbb{N} \} $

I have an excercise and there is the set $ \{ g\mid g : \{0,1\} \rightarrow \mathbb{N} \} $. Now I wanted to know, that this set mean? What's the content of it? I know normal sets very well but in my ...
1
vote
2answers
36 views

Little-o notation for $\ln(x)$

I want to Show the following: $\ln(x) = o (e^{\sqrt{\ln x}})$ (Little-o Notation). So I need to Show that: $\displaystyle{\lim_{x \rightarrow \infty} \frac{\ln(x)}{e^{\sqrt{\ln x}}}=0}.$ Can you help ...
1
vote
0answers
21 views

Use of the notation $a\ll b$ for $a,b$ maybe not positive

$|x| \ll 1$ is understood as "$x$ sufficiently small (in norm)", i.e. $|x|<C$ for some unspecified constant $C$. Similarly, $|x| \gg 1$ is understood as "$x$ sufficiently big". Has anyone used ...
0
votes
0answers
7 views

Notation clarification

I came across the following notation, but I don't understand it's meaning... Given some discrete domain $\mathcal{X}$ and a distribution $\mathcal{D}$ over $\mathcal{X}$. For $S\subseteq \mathcal{...
2
votes
0answers
18 views

Overbar over range of possible values

In a research paper I stumbled upon the formula $x =\overline{0 \dots 2^n-1}$. As far as I understand from the context of the paper this means that $x$ can have a value between $0$ and $2^n - 1$, but ...
0
votes
0answers
12 views

Mnemonic/intuition behind lattice notation? [duplicate]

For lattices, the least upper bound of $a,b$ is denotes $a\lor b$ and the greatest lower bound is $a\land b$. Is there an intuition behind this notation? Is there a similarity with the logical ...
1
vote
0answers
19 views

Confusion on equivalence class $[a]=${$(x_a,z);∀z∈C$} meaning

For equivalence class $[a]=${$(x_a,z);∀z∈C$} means $[a]=${$x_a$}$×C$ where $z∈C$. Am I defining it correctly?
-1
votes
0answers
36 views

How do I handwrite a comma in mathematics without confusing it for the number one? [closed]

When I handwrite vectors using component form, my commas look like the number one. How do I handwrite a comma in mathematics without confusing it for the number one? This is the closes link I could ...
3
votes
1answer
68 views

Is $f$ integrable?

Exercise 11.21 in Real Analysis for... by Richard Bass says: Suppose $f: \mathbb{R}^n : \rightarrow \mathbb{R}$ is measurable, $c>0$, and $p<n$? If $|f(x)| \leq c|x|^{-p} \chi_{B(0,1)}(x)$ a.e, ...
0
votes
0answers
23 views

Notation of vector space containing line segments

I have been trying to learn about vectors by myself. So far I understand that a vector space is a set of elements that follow certain axioms and each element in that set is a vector. I read that a ...
1
vote
1answer
38 views

Notations concerning polynomials over and extensions of rings

I find it hard to keep overview over the notations for sets of polynomials, evaluations of polynomials, and extensions of rings and so on. Let $R$ be a ring, and $E/R$ an extension of $R$. ...
0
votes
1answer
40 views

Help interpret notation $\sum_{j_1+j_2+\cdots+j_m=n}a^{j_1}_1a^{j_2}_2\cdots a_m^{j_m}$

I read somewhere that this sum can be written as: $$\sum_{r+s=n}a_rb_s=\sum_{r=0}^na_rb_{n-r}\tag1$$ This means to create all possible orders of $(r,s)$ and add these together. Now, my question is ...
2
votes
0answers
37 views

List of standard notation of concrete categories

Is there somewhere a relatively big list of concrete catiegories with their standard notations? Here is a list of some of them, but for example the category of affine spaces is missing from here. Is ...
0
votes
1answer
67 views

A goat is tied to a shed with a barn next to it. [duplicate]

A rectangular shed measuring 4 feet by 5 feet is located along the side of a barn. The barn is 20 feet wide and 45 feet long. A 3 year old goat is tethered to a corner of the shed, not against the ...
1
vote
1answer
47 views

Which is the difference between these two sets?

I am studying The large scale structure of space-time by Hawking and Ellis. They use the sets $\partial A$ and $\dot{A}$; they seem to be both some kind of border of the set $A$, but they are ...
1
vote
1answer
42 views

Big-O notation: Prove that $3^x$ is $O(3^x - 2^x)$

I have to show that $3^x$ is $O(3^x - 2^x)$. I'm just starting to learn the basics of Big-Oh notation. I'm thinking you have to take logarithms here, but am stuck on how to show this is true once I ...
0
votes
0answers
23 views

Prove equality with cross products using Einstein notation

Notice that throughout this question I will be using Einstein's summation notation. Let $v(x):\mathbb{R}^3 \to \mathbb{R}^3$ be a vector field and define $$2\mathbb{W}(v) = \nabla v - \nabla v^T$$ ...
1
vote
1answer
34 views

Why is overhat notation used both for a unit vector, $\hat{x}$, and for the closest vector, $\hat{x}$, in the best approximation theorem?

vector notation - why is overhat notation used both for a unit vector, $\hat{\mathbf x} = {\mathbf x \over || \mathbf x ||}$, and for the closest vector in a subspace $\hat{\mathbf x}$ to a vector $\...
1
vote
1answer
20 views

Projection of a vector, notation for

Consider an unit vector $\vec d$ (X coordinate) and another vector $\vec v$. All vectors are on a plane. The X coordinate of $\vec v$ is given by the formula $\vec{d}\cdot\vec{v}$. I need to write a ...
1
vote
1answer
28 views

Is there a way to think about Probability rules with multiple variables?

I am working through Intro to AI, and several times so far Sebastian makes a jump from a rule defined in 2 variables to using the rule with three variables. There seems to be some understanding he is ...
0
votes
1answer
23 views

Prove the big O of this function $f(n) = n^4 + 10n^3\log(n)$ is $f(n) = O(n^4)$

Use the formal definition of Big-O notation to prove his function $f(n) = n^4 + 10n^3\log(n)$ is $f(n) = O(n^4)$. I understand how to prove the Big O notation on polynomials mainly thanks to this post:...
0
votes
2answers
28 views

How to symbolically define set of all real numbers (R) in set-builder notation?

Can we define R using set-builder notation without language semantics (purely in math symbols)? Is it valid to do the following: $\{x\in\mathbb{R}|x\}$
2
votes
1answer
42 views

What does 'N × Q' represent in this relation?

In relation {(x, y) ∈ N × Q | y = √x} what does 'N × Q' represent?
1
vote
2answers
26 views

Correstness of the mathematical expression

I have a question regarding some strange mathematical expression defined in the set of positive integers - N : g(N) - greatest power of 2 that divides N. e.g. <...
1
vote
1answer
21 views

What is this codomain?

I was presented with a function $f:X$-->$2^X$ and I'm not sure what is meant by the codomain $2^X$. Any ideas?
1
vote
0answers
30 views

Meaning of notation $\{0,1/2,1\}^V$.

In the context of studying a polyhedral search space I am asked to prove that the set of extremal points is a subset of $\{0,1/2,1\}^V$? I do vaguely remember having seen this before, in algebra, ...
0
votes
0answers
8 views

notation - binary cross entropy

I have a loss where I would like to use binary cross entropy. Let's say I define $BCE$ as: $BCE(x, y) = - \left[ y \cdot \log x + (1 - y) \cdot \log (1 - x) \right]$ Then when expressing the loss, I ...
0
votes
1answer
48 views

In set theory, is a bar above a letter the same as the tilda?

Is an A with a horizontal line above it the same as an A with a tilda before it? eg: ~A So, are they both the complement (opposite) of A?