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.
8,256 questions
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1answer
29 views
what is $W^{-1,2}$?
I have been reading about the weak Poincare lemma in the book "Linear and Nonlinear Functional Analysis with Applications" by P.G. Ciarlet.
Let $\Omega$ be a simply connected domain in $\mathbb R^n$...
2
votes
0answers
25 views
Clarification of notation used in differential games
I'm working through Rufus Isaacs's work on differential games and I need clarification on the notation used. Some context: The Value of the game is to be the minmax of the payoff which symbolically is ...
1
vote
1answer
11 views
Upper and Lower shapes in Perlin Noise Generated Terrain
I am trying to learn about Perlin Noise and procedural generation. I am reading through an online tutorial about generating landscapes with noise, but I don't understand part of the author's ...
3
votes
1answer
81 views
What does this physics paper mean by having a matrix in a denominator?
I am not familiar with any notation used in physics. The paper "Non-hermitian random matrix theory: Method of hermitian reduction" by
Joshua Feinberg and A. Zee (Nuclear Physics B, 1997) states:
A ...
3
votes
1answer
31 views
Notation of Probability space
Assume we have red and a black cube (normal cubes with 6 sides). We roll these two dice. Is it true that the sample space is
$$\Omega = \left\{ (r,s) \mid r \in \{ 1, \dots, 6\}, s \in \{ 1, \dots, 6\...
1
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1answer
35 views
Notation for “congruent to a member of”
Is it acceptable to write $x\in S\pmod m$ to denote "$x$ is congruent to a member of $S$ modulo $m$"? Are there any established alternatives to this notation?
An example of use: "When $m\ge 5$ is ...
-2
votes
1answer
22 views
Index (x_i) with two rows in latex [on hold]
I have following problem in latex formatting:
I want to write for a matrix : $ (a_{ij})_{\underset{j=1,\ldots , n}{i=1,\ldots ,m}} $ but I want the $i=\ldots$ and $j=\ldots$ to be the same size...
...
2
votes
1answer
34 views
Is there a symbol to mean “$x$ fits completely $v$ times in $y$”?
Is there a simpler way to write "$x$ fits completely $v$ times in $y$," i.e. is there a mathematical symbol or way to write for example:
"32 fits 0 times completely in 4" or for example "32 fits 1 ...
0
votes
2answers
40 views
Editor asks me to define arg lim min
I have recently submitted a paper to IEEE Trans. on Information Theory. I got the reviewer comments and one reviewer seemed to me like he/she was obsessive with the notations. For example he was ...
1
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1answer
24 views
Regarding notation, for $f(x,y)$ are $f_x(x,g(x))$ and $\frac{\partial}{\partial x}f(x,g(x))$ interpreted differently?
More specifically, I see $\frac{\partial}{\partial x}f(x,g(x))$ as meaning take the derivative of $f(x,g(x))$ w.r.t $x$.
On the other hand, I see $f_x(x,g(x))$ as meaning the partial derivative of $f(...
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15 views
Notation: limit with no variable under it next to infimum with variable under it
My statistics text has the following definition for a uniform asymptotic confidence interval:
$$\lim \inf_{n \to \infty} \inf_{\theta \in \Theta} \mathbb{P}(\theta \in C_n) \geq (1-\alpha)$$
How do ...
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0answers
29 views
Solving equations over multiple lines: notational convention
Consider, for example, the following equation:
\begin{align}
x^2 - 2x = 1.
\end{align}
I'd like to solve the equation for $x$ in detail and am wondering how to write it down.
Let me offer two ...
0
votes
1answer
58 views
What does $5\mathbb{Z}_{25}$ mean? (Notation help)
Does $5 \mathbb{Z}_{25}$ refer to the numbers in $\mathbb{Z}_{25}$ multiplied by $5 $ -- i.e., there are 25 elements -- or does it refer to multiples of $5$ in $\mathbb{Z}_{25}$ -- i.e., there are $5$ ...
1
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1answer
22 views
What does this Markov Chain notation mean?
So, I don't know the meaning of much of the notation present in the following slide.
I know basically what a Discrete Markov Chain and a Transitional Probability Matrix are, but I'd like to what ...
0
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2answers
38 views
How to correctly write the set of all vectors of the form $(a,b,c)$, where $a+2b-c=0$
I'm not 100% sure if this is where this should go, but my LA prof wants us to practice writing more mathematically using correct notation. this is one of our homework problems and I wrote down the ...
0
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1answer
17 views
Matrix notation for double sum of row and column with the same index
a biologist/ecologist here,
I never took any courses in algebra (definitely missing in my education) but I am working with matrices all day.
For one paper, I have to write the matrix formulation but ...
2
votes
1answer
70 views
What does this notation mean? $\Phi(x) \downarrow, \Phi(x) \uparrow$
I'm not sure how I am supposed to know this, I have never used notation like this in my previous school. Is this notation logic or is it something I should have learned in math class? What I am ...
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0answers
21 views
Decipephering Notation and plugging in values for ellipse formula
Premise
I had asked a question on stats exchange about calculating error ellipses for a given scatter plot. I got an answer that seems acceptable, but I'm having trouble implementing it because my ...
0
votes
1answer
39 views
How to put an arrow above a letter? [closed]
Can anyone help me put $\rightharpoonup$ above $C_3$ in latex? Need to do so to indicate line integral for Green's Theorem.
Any help would be appreciated.
1
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1answer
59 views
Looking for a proper math notation to deal with intervals
Say we have two sets like this:
$A = \{a_1,a_2,a_3,a_4,a_5,a_6,a_7,a_8,a_9,a_{10}\}$ and $B = \{b_1,b_2,b_3,b_4,b_5,b_6,b_7,b_8,b_9,b_{10}\}$
I want to be able to build something like this: $[(a_{1},...
1
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0answers
54 views
Notational way to say that something is a set
When you want to say, for example, that $a$ is an integer, you write it as $a \in \mathbb{Z}$, which is read as "$a$ is an element of the set of all integers".
But, because of the notorious ...
0
votes
3answers
43 views
Composite versus square notation in functions
What is meaning of $f^2(x)$ ? There seems to be confusion in its interpretation.
Is $f^2(x)$ same as $(f(x))^2$ or $f\circ f$?
0
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2answers
27 views
About indexed family of sets and their products
An indexed family of sets is a function $A=(i\mapsto A_i)_{i\in I}:I\to E$ for some $I\ne \emptyset$ and some $E$, where each $A_i$ is a set.
I suppose $E$ is a set that contains all $A_i$ and ...
0
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0answers
19 views
Notation of density functions
Assume two jointly normally distributed variables X,Y.
Then what I often see is that densities are written as follows:
$f_X(x)$ as the density of X, $f_Y(y)$ as the density of Y, $f_{X,Y}(x,y)$ as ...
0
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0answers
24 views
Are there time where, instead of writing a function as $f(w,x,y,z)$ we would instead write it with more complicated arguments like $f(w,x,y-z,z)$?
By "complicated arguments " I mean where the arguments are themselves functions (like $f(x,x^2,y,z)$ or something)
As a rough example, would we ever write $f(x,y)= (x-y)^2+x$ as $f(x-y,x)$ instead (...
0
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1answer
28 views
Notation for “or” in inclusion-exclusion formula
Suppose that I have a set $A$ and I want to compute the probability that this set contains at least one of the elements $x_1,\dots, x_n$. In other words,
$p(x_1 \in A \text{ or } \dots \text{ or } ...
0
votes
1answer
33 views
What is the standard asymptotic notation when $x\rightarrow 0$
I understand big "$\mathcal{O}$” and little "o" notation but every definition I have seen is for $n\rightarrow\infty$. But what about something like $f(x)\in o(g(x))$ for $x\rightarrow 0$? Is there a ...
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0answers
29 views
Doubt of geometric notation about vertices and polygons
If ABCD is a quadrilateral, does this notation imply that vertex B is connected with vertex A and with vertex C?
3
votes
2answers
65 views
The hookrightarrow and its meaning
Very weirdly I found a $\hookrightarrow $ in my Algebra book just like that. Could someone please just tell me what it means? Sorry for this maybe stupid question in advance but very much appreciate ...
2
votes
1answer
52 views
Summing over set of sets
I am having trouble trying to understand an expression based on the multivariate Taylor series which is used to generate a system of residual equations. The expression is from Chauhan (2017) ...
1
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1answer
26 views
Having trouble notating an equation determining how much XP is to be given to players while referencing variables found in our database.
In the game being developed, players will be playing best-of-three matches against one another. XP will be given out depending on their score vs the average score and will receive a bonus for whether ...
0
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0answers
37 views
Notation for random point on an area
Given that $S $ is a surface area.
What is a good notation to indicate that a variable (position) $x_0$ is set to a random point on $S$.
For now my solution is to simply write $x_0 \gets rnd(S)$, ...
2
votes
1answer
23 views
How to distinguish argument parentheses and grouping parentheses?
$$s(a+b)$$
Does it mean s times a+b, or is s a funtion and take a+b as arguments?
$$(s(a+b))(c+d)$$
Does it mean s(a+b) times (c+d), or is s a high order function and s(a+b) return a function which ...
3
votes
0answers
62 views
+50
Confusion regarding the notation of associated operator of a PDE.
I'm given the following PDE: $$u_{tt}-u_{xx}+u^3=0$$ My source says that the associated operator is $$L:=\frac{\partial^2}{\partial t^2}-\frac{\partial^2}{\partial x^2}+u^2$$ which is arrived at ...
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0answers
17 views
Difference between notation in the derivation of Maxwell's equations
This question is more about the mathematical notation and little about physics.
I have two books, Tipler and Halliday, when studying the derivation of Maxwell's equations they use the same example ...
2
votes
5answers
64 views
Why write $\exp(x)$, instead of $e^x$?
Why write $\exp(x)$, instead of $e^x$?
I would have thought that if $x$ is a long expression, $\exp(x)$ would be preferred, so that it is clear? But I have seen that this is not the case.
0
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1answer
42 views
How to understand such a complex event $\left((a\cap\grave{b})\cup(b\cap\grave{a})\right)$ in probability?
What is the meaning of the event $\left((a\cap\grave{b})\cup(b\cap\grave{a})\right)$ in probability?
0
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0answers
30 views
Meaning of symbol $\looparrowright$ in math
Is there a conventional meaning for the symbol $\looparrowright$ when used in math.
I came across this symbol in here (see slide 2 for e.g.).
10
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3answers
2k views
What is the dot in “$1.2.4$”.
I am not a mathematician. I did additional maths O’level back in the stone age but did not pursue maths further (much to my regret).
I am reading David Acheson’s fascinating book ‘The Story of ...
1
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0answers
51 views
Why we care only about $\Pi_1$ parameters in axiom schemes?
There is exist tradition to formulate axiom schemes such as induction, comprehension or replacment in a way like "for each formula $\phi(y,\overline{x})$ with free variables $y$ and $\overline{x}=x_1,....
0
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1answer
17 views
Correct notation for broadcasting operation
In Python numpy a row vector $u \in \mathbb{R}^n$ and its transposed $u^T$ can be added, multiplied or subtracted, yielding a $\mathbb{R}^{n\times n}$ matrix, where each element $(i,j)$ is the ...
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0answers
30 views
Is the codomain part of the function?
If functions are defined as sets of ordered pairs, then how does it make sense to talk about the codomain of a function, or talk about a function being surjective (rather than saying something like “...
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0answers
14 views
How do I evaluate this limit: $\max \{\lim_{x,k \to \infty} G_k(x)\}$
Let $$G_k(x)=A(x)B_k(x)=\pi(x)^{\frac{1}{\log(x)}}\pi(k-x)^{\frac{1}{\log(k-x)}},$$
where $\pi(x)$ is the prime counting function.
What is $$\max \{\lim_{x,k \to \infty} G_k(x)\}?$$
This is what I ...
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vote
2answers
14 views
Infinitesimal squared in metrics
Metrics are often formulated by appealing to the square of an infinitesimal quantities. Examples of such are:
$$
(ds)^2=(dx)^2+(dy)^2
$$
or
$$
ds^2=dx^2+dy^2
$$
or
$$
d(s^2)=d(x^2)+d(y^2)
$$
...
2
votes
1answer
44 views
Representing Iterations in Math
I'm coming from a software engineering background and not a mathematical one. You may have to explain the exact notation to me but I would really appreciate it. I want to represent one of my processes ...
0
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0answers
9 views
Correct formulation of all unordered subindeces
Suppose we have an index set $\{1, \dots, n\}$. Now I want to take all the subindices. For example, if the set $\{1, 2, 3\}$, I want to a collection of $\{1\}, \{2\}, \{3\}, \{1, 2\}, \{2, 3\}, \{1, 3\...
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1answer
23 views
Notation for number sets
Variables a and b assume values of two number sets as part of a grid search.
a assumes the first 21 multiples of 1440, b assumes values from 0 to 1 in steps of $\dfrac{1}{100}$. To clarify ... $$a = [...
0
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0answers
38 views
Is there any math notation for `be denoted by`?
https://mathoverflow.net/questions/325185/is-there-any-math-notation-for-be-denoted-by
The sentence s "In many supervised learning problems one has an output variable $y$ and a vector of input ...
1
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3answers
65 views
What does the notation $A^{-2}$ mean if $A$ is a matrix?
$A^2$ means to multiple the matrix by itself, and $A^{-1}$ refers to the matrix's inverse. Would $A^{-2}$ be the square of the inverse or the inverse of the square?
1
vote
2answers
35 views
How to read/interpret $\hat{f}(y)(x)$
I'm currently in a point-set topology class and was presented with the following definition on a homework assignment.
If $f: X\times Y\to Z$ is a continuous function, we can define $\hat{f}: Y\to \...
