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.
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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:
$$
\...
-1
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2answers
31 views
What is the difference between the summations?
What is the difference between the summation $$\sum_{1 \leq i<j \leq n} f(i,j)$$ and $$\sum_{1\leq i} \sum_{<j \leq n} f(i,j)?$$
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0answers
18 views
Typographic conventions for subscripts?
I was wondering if there were any sort of consistent rules or guidelines for how to properly format subscripts on variables? The primary aims should be to have clear meaning, and consistency with what ...
2
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2answers
22 views
Probability theory - Logic, Notation, simulation
i need some help in probability theory. The thing is im not sure if im thinking about this correctly and if i express my thoughts correctly. I really got lost in all the dice examples of the internet.
...
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1answer
19 views
Operator precedence in addition and subtraction
Customary operator precedence has addition prior to subtraction. Apart from historical convention and notational consistency, is there a rationale for this?
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4answers
41 views
What is the meaning of $\binom {i+j+k}{i,j,k}$
In an answer to a question (https://math.stackexchange.com/a/288999/172737) this combinatoric symbol was used
$$\binom {i+j+k}{i,j,k}$$
I can't determine its meaning, though I've searched.
I ...
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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
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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:
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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 ...
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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
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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 ...
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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 ...
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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 \...
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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 ...
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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 ...
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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}$$
where $c_1,c_2,...,c_n \epsilon \mathbb{R}$ are constants, as $x$ approaches $0$ it is clear that $...
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0answers
28 views
What does a semi-colon mean within a function expression?
I am trying to understand how to implement gradient mapping for a parametric max-type function $f(t;x)$ defined such that
$$f(t;\bar{x};x)=\max_{1\leq i\leq m}\{f_0(\bar{x} + \langle f'_0(\bar{x}),x-\...
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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 $$ D(f)=\{x\...
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2answers
39 views
Small o notation PROOF [closed]
It's probably a vey silly question, but I'm confused.
I should proof the small o notation with lim but i don´t know how
$(\ln n)^a = o(n^b )$
how do i solve this and do i need to proof it for
$a<...
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0answers
8 views
Notation of Payoff functions in the Selten game
The pictures are from Narahari's textbook, Game theory and Mechanism Design.
Could anyone explain to me the last line (the definition of payoff functions)? I haven't seen this notation ever before ...
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0answers
27 views
How do you type formatting commands from LaTeX in this community? [closed]
My question is, how do you type formatting commands from LaTeX in boxes like these in this community? For example, document{article} or ...
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1answer
35 views
A question on $G=S_5$ concerning notation
I think there must be a misprint in a question I've been asked.It has written on it ;
$$|G|=S_5$$
but of course this notation is nonsense as a real number cant be equal to a set.
Do you think it ...
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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 ...
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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 ...
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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 ...
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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
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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 ...
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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 ...
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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?
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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 ...
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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, ...
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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 ...
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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$.
...
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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$$
This means to create all possible orders of $(r,s)$ and add these together.
Now, my question is ...
2
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0answers
37 views
List of standard notation of concrete categories
Is there somewhere a relatively big list of concrete catiegories with their standard notations? Here is a list of some of them, but for example the category of affine spaces is missing from here. Is ...
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1answer
67 views
A goat is tied to a shed with a barn next to it. [duplicate]
A rectangular shed measuring 4 feet by 5 feet is located along the side of a barn. The barn is 20 feet wide and 45 feet long. A 3 year old goat is tethered to a corner of the shed, not against the ...
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1answer
47 views
Which is the difference between these two sets?
I am studying The large scale structure of space-time by Hawking and Ellis. They use the sets $\partial A$ and $\dot{A}$; they seem to be both some kind of border of the set $A$, but they are ...
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1answer
42 views
Big-O notation: Prove that $3^x$ is $O(3^x - 2^x)$
I have to show that $3^x$ is $O(3^x - 2^x)$. I'm just starting to learn the basics of Big-Oh notation. I'm thinking you have to take logarithms here, but am stuck on how to show this is true once I ...
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0answers
23 views
Prove equality with cross products using Einstein notation
Notice that throughout this question I will be using Einstein's summation notation.
Let $v(x):\mathbb{R}^3 \to \mathbb{R}^3$ be a vector field and define
$$2\mathbb{W}(v) = \nabla v - \nabla v^T$$
...
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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
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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 ...
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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 ...
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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:...
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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: $\{x\in\mathbb{R}|x\}$
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1answer
42 views
What does 'N × Q' represent in this relation?
In relation {(x, y) ∈ N × Q | y = √x}
what does 'N × Q' represent?
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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. <...
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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?
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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, ...
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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
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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?
