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.
12,707
questions
0
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1
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27
views
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 ...
2
votes
1
answer
90
views
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 &...
- 390
3
votes
0
answers
100
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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 ...
- 63
2
votes
1
answer
113
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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 $0$.
- 23
0
votes
1
answer
80
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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=\...
- 313
0
votes
0
answers
44
views
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 ...
- 215
-1
votes
0
answers
22
views
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 ...
- 39
2
votes
0
answers
40
views
$\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 ...
- 165
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0
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36
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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,...
- 718
1
vote
1
answer
63
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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$, ...
- 1,788
0
votes
0
answers
21
views
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,...
- 173
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votes
1
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61
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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$ ...
- 2,145
1
vote
0
answers
23
views
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)$....
- 1,057
1
vote
1
answer
66
views
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 ...
- 107
0
votes
1
answer
19
views
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(...
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.
- 9
0
votes
0
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32
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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 ...
- 71
-4
votes
1
answer
56
views
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.
- 1
1
vote
1
answer
34
views
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{...
- 3,003
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votes
1
answer
70
views
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 ...
- 5,553
-2
votes
0
answers
19
views
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
...
0
votes
0
answers
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{...
- 3,003
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{...
- 3,003
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 ...
- 728
2
votes
0
answers
35
views
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.
- 39
-1
votes
0
answers
47
views
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 $G\cong H\times K$ ...
- 3,003
0
votes
1
answer
47
views
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 ...
1
vote
0
answers
13
views
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 ...
- 8,521
1
vote
1
answer
66
views
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 $\textit{cyclic}$ ...
- 3,003
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
$$0\to M'\...
- 3,003
-1
votes
0
answers
47
views
Polynomial quotient ring notation [duplicate]
I'm currently studying a bit of abstract algebra due to it's usefulness in cryptography and encountered a notation that is a little unclear to me:
$$ \mathbb{Z}[x]/(x^N -1) $$
I understand that this ...
- 143
0
votes
0
answers
31
views
Notation for referring to specific graph colourings
Consider the following four graphs where $k$ represents the number of colours used to colour the vertices of each graph.
Here cycle graphs are used to represent regular polygons, in this specific case ...
- 722
0
votes
0
answers
46
views
What’s the logic behind this labelling of conjugacy classes of groups which seems common?
On the website GroupNames here that lists groups with orders below $500$ as well as the ATLAS of finite group representations (and other places I’m sure I’ve stumbled upon and forgotten about), ...
- 1,739
1
vote
0
answers
60
views
Turnstile followed by 'nothing' [duplicate]
In the literature, I came across the statement "A, ¬A ⊢." I'm uncertain about its meaning. Could this mean that any conclusion can be derived from having both A and its negation, ¬A, as ...
- 235
0
votes
2
answers
53
views
Big-Oh notation question
When we have a question like so:
What is the smallest integer $n$, such that $f(x) = x^{5.7}(\log x)^{1.2}$ is $O(x^n)$?
Would we go about the question as so: round up $x^{5.7}$ to become $x^6$.
Since ...
0
votes
1
answer
31
views
Notation for powerset with cardinality condition [duplicate]
Given a set $X=\{x_1, \ldots, x_n\}$ I would like to denote the set of all distinct subsets of $X$ which have cardinality $k\le n$.
I am aware that the set of all subsets (of any cardinality) is ...
- 135
0
votes
0
answers
62
views
Difference in these notations
Let $\Omega$ denote a bounded domain. I am wondering which is the difference between the notations
$$1. \quad\mathbb R^n\setminus\Omega $$
and
$$2. \quad\mathbb R^n\setminus\mathring{\Omega}$$
and
$$3....
- 454
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 (...
- 651
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votes
0
answers
46
views
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 ...
- 3,003
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 ...
- 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 $\textit{...
- 3,003
0
votes
0
answers
32
views
does linearly dependency or independency have a symbol?
whenever we talk about the concept, we always write "$\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 ...
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 ...
- 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:
$${\...
0
votes
0
answers
66
views
What's the purpose of $δx$ here?
Why is the $δx$ here necessary? I'm going through Knuth's Concrete Math, and in the section on finite calculus, it says that it's akin to the $\mathrm{d}x$ of continuous integrals, but wouldn't it ...
3
votes
0
answers
40
views
Is there a standard notation for the measure $E \mapsto \mu(E \cap S)$?
If $\mu$ is a measure and $S$ is $\mu$-measurable, it is easy to see that the measure $E \mapsto \mu(E \cap S)$ defines a measure on the $\sigma$-algebra where $\mu$ is defined. I have been using the ...
- 1,010
0
votes
0
answers
35
views
What is the difference between using set to make equation or not?
What is the difference between $x = a, b, c$ and $x \in \{a, b, c\}$?
Which expression should I use?
- 1
0
votes
0
answers
32
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notation : $f_{X|Y=y}(x)$ instead of $f_{X|Y}(x|y)$?
I just have a notation question. The density $f_{X|Y}(\cdot, y)$ is defined by $$\mathbb{P}(X\in A|Y=y)=:\int_A f_{X|Y}(x|y)dx$$ would the notation $f_{X|Y=y}(x)$ instead of $f_{X|Y}(x|y)$ also be ...
- 1,187
2
votes
3
answers
99
views
How to express an invalid argument such as "affirming the consequent" in propositional logic?
For example, say you want to write a symbolic statement for affirming the consequent. You could write it in the following two ways
$$
(P \to Q, Q) \to P
$$
or
$$
\frac{P \to Q, Q}{P}
$$
Which one ...
- 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 ...
- 319