Questions tagged [notation]

Questions 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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Is there a special notation for sets of matrices? [duplicate]

So, I know that you can write $\mathbb{R}^n$ to express the set of all n-tuples with real components. Is there a similar notation for the set of all $m\times n$ matrices, something like $\mathbb{R}^{m ...
Arthur Prudius's user avatar
2 votes
1 answer
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What does $a \ne b \ne c$ mean?

Does $a\ne b \ne c$ mean $a \ne b \land b \ne c$ or $a \ne b \land b \ne c \land a\ne c $ ? These are two distinct statements when 2 $\;\not\!\!\!\implies(a \ne c)$, yet I am unaware if one is &...
Neptune's user avatar
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Notation used within "Prime ideal structure in commutative rings" by M. Hochster

I was reading through this paper and I came across some rather confusing notation in the proof of Theorem 4. It says Proof. ...$Y$ is finite, and it is clear that the image of the restriction of any ...
AVP Neelam's user avatar
2 votes
1 answer
113 views

Is my notation correct?

$\{x : x \le 75, \in \mathbb{Z}_+ \cup \{0\}\}$ Is this notation correct? I'm going for positive integers less than or equal to $75$ including $0$.
ℤ_INT's user avatar
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Is $\circledcirc\equiv\omega *$? Or is $\omega * \in \circledcirc$?

In Winning Ways Volume 2 (pg. 398) : $\circledcirc$ (sunny) is used "instead of $0\star\rightarrow$" as "the collection $0, \star1, \star2, \star3, \star4,...$" eg. $$\circledcirc=\...
stargirl's user avatar
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Meaning of Φ : Y → X

I am reading the book "Advances in Intelligent Systems and Computing" and I cannot understand a paragraph. Parametric approaches include the classical SOM and its probabilistic counterpart ...
tahasozgen's user avatar
-1 votes
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notation conventions

I have a quite trivial question for many of you, but not for me. I have a summation of the type $ΣF_x= p_{x_{j,i}} + q_{x_{j,i}} + s_{x_{j,i}} + p_{x_{j,i+1}} + q_{x_{j,i+1}} + s_{x_{j,i+1}} = 0$ I ...
Sibel's user avatar
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2 votes
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$\models P \wedge Q \iff \neg ( \neg P \vee \neg Q )$ is a valid argument

I have to show that $\models (P \wedge Q) \iff \neg ( \neg P \vee \neg Q )$ is a valid argument. However, I have no idea how to interpret a $\models$ symbol WITHOUT a LHS. I have always seen it like ...
GeekOverdose's user avatar
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Question on the notation of Supremum

Assume you have a real valued function $f(x,y)$ defined on some domain $X\times Y$. When people write $\sup\limits_{x \in X}\sup\limits_{y\in Y} |f(x,y)|$ is that actually the same as $\sup\limits_{(x,...
MackeyTopology's user avatar
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Meaning of $\overline{ab}$ in rings with unity

Let $R$ be a ring with unity. An element $x \in R$ is called $\textit{nilpotent}$ if $x^m = 0$ for some $m \in \mathbb{N}$. a.) Show that if $n=a^kb$ for some integers $a,b$, and $k$ where $k \neq 0$, ...
David C. Huang's user avatar
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write cubic spline as a sum of the local splines times interpolation values

Not sure if this is the right place to ask. If so, please let me know. I am performing cubic spline interpolation to produce a globally $C^2([a,b])$ function $S(x)$ on the one-dimensional interval $[a,...
Simon's user avatar
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What does $\mathbf{1}$ mean in $\frac{1}{n} \sum_{m=0}^{n-1} \mathbf{1}${$X_m=i$} here?

In the below passage, I was wondering what $\mathbf{1}$ signifies: How much time does a Markov chain spend in state $i$, in the long term? That is, what is the long term fraction of time that $X_n=i$ ...
Princess Mia's user avatar
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Notation for $k$-partitions of $n$ containing at least one summand equal to $s$

I am looking for whether there is any notation for the $k$-partition number of $n$ where the partitions must include some summand $s$. An example of the kind of notation I am looking for is $P_k^s(n)$....
user110391's user avatar
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1 vote
1 answer
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Consequences of using left-to-right composition

Personally, I find left to right composition much more natural, but I have seem to come across an instance where using this notation gives different results. Let $G$ be a group and define $\phi: G \to ...
Shaikh Ammar's user avatar
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1 answer
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Nash Equilibrium Notation

Is this representation an accurate one for the Nash Equilibrium? $$\{\nexists s_1^{'} \in S_1 : u_1(s_1^{'},s_2) \geq u_1(s_1,s_2)\} \ \wedge\ \{\nexists s_2^{'} \in S_2 : u_2(s_1,s_2^{'}) \geq u_2(...
Tunay Sabri Yüksel's user avatar
0 votes
1 answer
110 views

What is the difference between $[0, 2\pi)$ and $[0,2\pi]$? [closed]

What is the difference in solving trig equations in the interval $[0, 2\pi)$ or $[0,2\pi]$? There seems to be no difference.
fred59's user avatar
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Annihilator notation $M^{00}$ in Roman's Advanced Linear Algebra

I have a fairly simple question. Roman's Advanced Linear Algebra on pg. 102 defines the annihilator of a set $M$ in the vector space $V$ as $$ M^0 = \{f \in V^* \ | \ f(M) = \{0\}\} $$ which is easily ...
Steven Cripe's user avatar
-4 votes
1 answer
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What does this notation in this image mean? [closed]

Question Source $$(x, y, z) \mapsto \dbinom{x}{1} + \dbinom{x+y+1}{2} + \dbinom{x+y+z+2}{3}$$ I'm a high school student. I'm confused on what this notation means.
happya's user avatar
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1 vote
1 answer
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Meaning of projection onto one factor in $0\to A^{r-1}\to A^r\to A\to 0$

The following is taken from: $\textit{Partial Differential Control Theory Vol 1: Mathematical tools}$ by J F. Pommaret $\color{Green}{Background:}$ $\textbf{Definition 1.50.}$ $M$ is call a $\textit{...
Seth's user avatar
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Why do we fix an extension of valuation of $K$ to $\overline{K}$?

Let $K$ be a valuation field. Let $v$ be a valuation of $K$. Let $K_v$ be completion of $K$ at $v$. I often encounter an expression. Fix an extension of $v$ to $\overline{K}$, which serves to fixes ...
Pont's user avatar
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-2 votes
0 answers
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Forcing lowercase in macros under MathJax [closed]

I have a bunch of manuscripts, where I used a collection of custom macros to enforce a bunch of notation by semantically describing my equations. A simple example would be ...
Robert Bock's user avatar
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45 views

Which one is the right morphism in the following exact sequence: $0\to A^{r-1}\to A^r\to A\to 0$

The following is taken from: $\textit{Partial Differential Control Theory Vol 1: Mathematical tools}$ by J F. Pommaret $\color{Green}{Background:}$ $\textbf{Definition 1.50.}$ $M$ is call a $\textit{...
Seth's user avatar
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0 votes
1 answer
32 views

Unclear about the notation $A^n\to M:(1,0,\ldots,0)\to x_1,\ldots,(0,\ldots,0,1)\to x_n$ in Proposition 1.55

The following is taken from: $\textit{Partial Differential Control Theory Vol 1: Mathematical tools}$ by J F. Pommaret $\color{Green}{Background:}$ $\textbf{Definition 1.50.}$ $M$ is call a $\textit{...
Seth's user avatar
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1 vote
1 answer
24 views

Wigner's Surmise delta function notation, which law of probability

I have three independent random variables, $x_1, x_2$ and $x_3$ with $x_1,x_2\cong N(0,1)$ and $x_3 \cong N(0, 1/2)$. I have $s:= \sqrt((x_1-x_2)^2 + 4x_3^2)$. How do I write down an integral for the ...
ttt's user avatar
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2 votes
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Proper notation of a nested square root - is there a notation akin to tetration which extends to roots

In the way in which $x^{x^{x^{x}}}$ can be written as $x$ tetrated to 4 is there such a method to writing $\sqrt[...\sqrt{2}]{2}$ extending out to the left.
MrMez's user avatar
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-1 votes
0 answers
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Should $G\ncong H\times K$ if $G$ is indecomposable? [closed]

The following is taken from: Hungerford's Algebra $\color{Green}{Background:}$ $\textbf{Exercise 1:}$ A group $G$ is indecomposable if and only if $G\neq \langle e \rangle$ and $G\cong H\times K$ ...
Seth's user avatar
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0 votes
1 answer
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Using and Rather than Implies

I am trying to understand the difference between and $\wedge$ and $\rightarrow$. Consider $$x=y\Longleftrightarrow \forall z(z\in x \ \rightarrow z \in y)$$ However, I think we can use and notation ...
Tunay Sabri Yüksel's user avatar
1 vote
0 answers
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Graphical notation for easy visual operations on multivariate polynomials

Vector and matrix notation is an excellent graphical scheme for doing elementary operations on degree 1 multivariate equations. Adding one equation to another is made easy by ordering the variables ...
Mitch's user avatar
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1 vote
1 answer
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Is $k$ in $\textit{Ann}_R(x)=p^k R$ fixed?

The following is taken from $\textit{Module Theory An Approach to Linear Algebra}$ By: T.S.Blyth $\color{Green}{Background:}$ $\textbf{Exercise 4.1.}$An $R-$module $M$ is said to be $\textit{cyclic}$ ...
Seth's user avatar
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0 votes
1 answer
30 views

What does the following notation mean in the enclosed commutative diagram for exact sequence?

The following is taken from: $\textit{Partial Differential Control Theory Vol 1: Mathematical tools}$ by J F. Pommaret $\color{Green}{Background:}$ $\textbf{Proposition 1.59.}$ Let $$0\to M'\...
Seth's user avatar
  • 3,003
-1 votes
0 answers
47 views

Polynomial quotient ring notation [duplicate]

I'm currently studying a bit of abstract algebra due to it's usefulness in cryptography and encountered a notation that is a little unclear to me: $$ \mathbb{Z}[x]/(x^N -1) $$ I understand that this ...
Ymi's user avatar
  • 143
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0 answers
31 views

Notation for referring to specific graph colourings

Consider the following four graphs where $k$ represents the number of colours used to colour the vertices of each graph. Here cycle graphs are used to represent regular polygons, in this specific case ...
Astrid's user avatar
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What’s the logic behind this labelling of conjugacy classes of groups which seems common?

On the website GroupNames here that lists groups with orders below $500$ as well as the ATLAS of finite group representations (and other places I’m sure I’ve stumbled upon and forgotten about), ...
Robin's user avatar
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1 vote
0 answers
60 views

Turnstile followed by 'nothing' [duplicate]

In the literature, I came across the statement "A, ¬A ⊢." I'm uncertain about its meaning. Could this mean that any conclusion can be derived from having both A and its negation, ¬A, as ...
Mijito's user avatar
  • 235
0 votes
2 answers
53 views

Big-Oh notation question

When we have a question like so: What is the smallest integer $n$, such that $f(x) = x^{5.7}(\log x)^{1.2}$ is $O(x^n)$? Would we go about the question as so: round up $x^{5.7}$ to become $x^6$. Since ...
For Website's user avatar
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1 answer
31 views

Notation for powerset with cardinality condition [duplicate]

Given a set $X=\{x_1, \ldots, x_n\}$ I would like to denote the set of all distinct subsets of $X$ which have cardinality $k\le n$. I am aware that the set of all subsets (of any cardinality) is ...
user160623's user avatar
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0 answers
62 views

Difference in these notations

Let $\Omega$ denote a bounded domain. I am wondering which is the difference between the notations $$1. \quad\mathbb R^n\setminus\Omega $$ and $$2. \quad\mathbb R^n\setminus\mathring{\Omega}$$ and $$3....
Physics user's user avatar
1 vote
0 answers
34 views

Notation for expressing a straight chain of $n \choose 2$ identity statements

Given the glossary $Dx$: $x$ is a dog, we can make the following translations: "there is at least one dog" - $\exists x Dx$. "there are at least two dogs" - $\exists x \exists y (...
user51462's user avatar
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0 answers
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Question about the maps: $K\to F$ and $L\to F$ in proof of proposition 1.59 concerning finitely presented module.

The following is taken from: $\textit{Partial Differential Control Theory Vo 1: Mathematical tools}$ by J F. Pommaret $\color{Green}{Background:}$ $\textbf{Definition 1.49.}$ If $M$ is a module over ...
Seth's user avatar
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0 votes
0 answers
23 views

Notaional question about the projection map $A^n\to M$ and short exact sequence $A^m\to A^n\to M\to 0.$

The following is taken from: $\textit{Partil Difgferential Control Theory Vo 1: Mathematical tools}$ by J F. Pommaret $\color{Green}{Background:}$ $\textbf{Definition 1.49.}$ If $M$ is a module over ...
Seth's user avatar
  • 3,003
4 votes
0 answers
111 views

Notation questions about $A^{r-1}\to A^r, A^n\to M:(1,0,\ldots,0)\to x_1,\ldots,(0,\ldots,0,1)\to x_n$ in Proposition 1.55 concerning free module [closed]

The following is taken from: $\textit{Partial Differential Control Theory Vol 1: Mathematical tools}$ by J F. Pommaret $\color{Green}{Background:}$ $\textbf{Definition 1.50.}$ $M$ is call a $\textit{...
Seth's user avatar
  • 3,003
0 votes
0 answers
32 views

does linearly dependency or independency have a symbol?

whenever we talk about the concept, we always write "$\alpha_1,\alpha_2,\cdots,\alpha_r$ linearly independent" which is a really long line. it takes so much time to write and read. is there ...
ZhenRanZR's user avatar
0 votes
0 answers
46 views

How to denote square uniquely in Euclidean $\mathbb{R}^2$?

I am eager to know how one can denote a square in the $\mathbb{R}^2$ Euclidean space. I mean I can write as $[\text{centre of square}, \text{dimension}]$ but how would I know its orientation then. Is ...
Userhanu's user avatar
  • 571
0 votes
0 answers
30 views

how to use the combinations of k elements of n (binomial coefficients) in a formula

Let's assume set $$S = (2,3,4,5)$$ I like to express the sum of the products of all possible unique combinations of $k$ (distinct) elements of $S$. I know the binomial coefficient is equal to: $${\...
Pim Dumans's user avatar
0 votes
0 answers
66 views

What's the purpose of $δx$ here?

Why is the $δx$ here necessary? I'm going through Knuth's Concrete Math, and in the section on finite calculus, it says that it's akin to the $\mathrm{d}x$ of continuous integrals, but wouldn't it ...
Arthur Prudius's user avatar
3 votes
0 answers
40 views

Is there a standard notation for the measure $E \mapsto \mu(E \cap S)$?

If $\mu$ is a measure and $S$ is $\mu$-measurable, it is easy to see that the measure $E \mapsto \mu(E \cap S)$ defines a measure on the $\sigma$-algebra where $\mu$ is defined. I have been using the ...
BBBBBB's user avatar
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0 votes
0 answers
35 views

What is the difference between using set to make equation or not?

What is the difference between $x = a, b, c$ and $x \in \{a, b, c\}$? Which expression should I use?
Junee's user avatar
  • 1
0 votes
0 answers
32 views

notation : $f_{X|Y=y}(x)$ instead of $f_{X|Y}(x|y)$?

I just have a notation question. The density $f_{X|Y}(\cdot, y)$ is defined by $$\mathbb{P}(X\in A|Y=y)=:\int_A f_{X|Y}(x|y)dx$$ would the notation $f_{X|Y=y}(x)$ instead of $f_{X|Y}(x|y)$ also be ...
edamondo's user avatar
  • 1,187
2 votes
3 answers
99 views

How to express an invalid argument such as "affirming the consequent" in propositional logic?

For example, say you want to write a symbolic statement for affirming the consequent. You could write it in the following two ways $$ (P \to Q, Q) \to P $$ or $$ \frac{P \to Q, Q}{P} $$ Which one ...
Kalcifer's user avatar
  • 556
1 vote
1 answer
49 views

When the fraction bar symbol is used with polynomial expressions does it have the same meaning, as it does when it is used with numbers?

If g(x) and f(x) are polynomial functions, does the rational function g(x)/f(x) mean g(x) ÷ f(x) ? So can g(x) / f(x) be evaluated by the long division of the polynomials, where g(x) is the divident ...
Alice 's user avatar
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