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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18 views

Notation for parametric family of joint densities

This is copied from my textbook; Assume that the statistical model for the MVR $\textbf{Y}=(Y_{1},Y_{2},\ldots , Y_{n})^{T}$ is given by the parametric family of joint densities: $$\{ ...
0
votes
1answer
20 views

Notation for vector space of polynomials of bounded degree

Is there standard notation for the vector space of polynomials in $n$ variables with coefficients in a field $F$ and with degree at most $D$? Without bounding the degree, it is $F[x_1, \ldots, x_n]$. ...
0
votes
0answers
10 views

Notation for mimimal sum when choosing elements from two sets

I'd be grateful for any pointers on the following I am wondering if there is any standard notation (or neat suggestions) for the following. I have two sets $\{t_1, t_2, \ldots , t_k\}$ and $\{s_1, ...
0
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0answers
15 views

Notation of axis

I have a graph where I rescaled the axis by dividing by 10. In the label on the axis, should I put "(x10)" or "(/10)"? I don't know the correct semantics of these labels in graphs.
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0answers
13 views

Probabilistic Graphical Model Diagram Notation, what does the box mean?

I'm just learning about probabilistic graphical models, I know the circles represent random variables, shaded being observed and unshaded being latent variables. But what does the box mean?!
7
votes
1answer
82 views

What does $\frac12(D_{2p}\times D_{2p})$ mean in group theory?

Reading a thesis, I have come across the (unexplained) notation $$\frac{1}{2}(D_{2p}\times D_{2p})\cong (p\times p):2,$$ where $D_{2p}$ is a dihedral group. What does this "$\frac12$" notation mean? ...
1
vote
0answers
23 views

Statistical symbols: should greek letters be used for population or for a sample?

When finding mean and the stansard deviation, do you use the Greek symbols for a population, or a sample. When do you use "s" and xbar, for a population, or a sample? (I am taking AP Statistics)
2
votes
1answer
71 views

Why we use $\mathbb{R}^{m \times n}$ notation instead of $\mathbb{R}^{n \times m}$?

I just realised, that I use all the time the notation $\mathbb{R}^{n \times m}$, and all books and papers use $\mathbb{R}^{m \times n}$. $\mathbb{R}^{n \times m}$ is more sympathetic for me, because I ...
0
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1answer
42 views

Integral notation

I have encountered the following integral: $\int_{x-d}^{x+d}f(y)dy$ I am trying to figure out what is the role of $d$ in this integral. Is the $d$ at the beginning of the integral the same as the ...
3
votes
0answers
12 views

Equivalent to proportionality sign for additive constants

Short question Is there an equivalent to the proportionality sign $\propto$ for additive constants? The proportionality relation $y\propto x$ implies that $y=kx$ for some constant $k$. Is there a ...
6
votes
2answers
394 views

Meaning of a set in the exponent

Let $ D = 2^\mathbb{N} $, i.e., D is the set of all sets of natural numbers. What's the meaning of this definition? Intuitively, I would suggest that $ D = \{1,2,4,...\} $ but the explanation ...
2
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0answers
37 views

notation for minimum and maximum?

I'm trying to figure out the correct notation for this situation for use in Machine Learning. I have various ratings (for texts): ...
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vote
1answer
44 views

Standard Notation For The Set of All the Morphisms Of A Category

Let $\mathscr C$ be a category. Let $\text{Ob}(\mathscr C)$ be the set of all the objects of $\mathscr C$. Is there a standard notation for $\bigcup_{A,B\in\text{Ob}(\mathscr C)}\text{Mor}(A,B)$? ...
7
votes
5answers
479 views

Functional Notation.

I have some doubts regarding function notation: First If I present a function I write:$f(x)$ If I write it's inverse:$f^{-1}(x)$ So why doesn't$f(f(x))=f^2(x)$ Second If $\frac{df(x)}{dx}=f'(x)$ ...
1
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1answer
40 views

Just a translation issue.

I'm italian and my professor of spectral theory wrote the list to the arguments to be studied in italian. The problem is that all the literature is in english and often the translation are a bit ...
5
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2answers
76 views

What is this notation for a function? I've never seen it written like this before.

What does this mean? $$ f=\{ (x,y): y= x+2 \}$$ I don't understand what "$(x,y):$" means in regard to the problem. Also why is the $y$ inside of the $f(x)$ function. Isn't it supposed to be outside? ...
0
votes
1answer
91 views

Does “arbitrarily small” mean very close to zero or very negative?

In mathematical writing, does “arbitrarily small” mean very close to zero (like $0.000001$) or very negative (like $-1000000$)? Are there better phrases to distinguish these two cases?
0
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1answer
31 views

What notation to use for a sequence of integers that end with digit 5?

I need to solve a low high school home work and I ask a question about the most correct notation. The problem is to build a set of circles with $r$ and $d$ such that $d=5, 15, 25, 35,...d_{+_1}$ and ...
1
vote
1answer
35 views

Lerch transcendent

While messing around with something I got a result on WolframAlpha with a notation like this $$\text{LerchPhi}^{(0,1,0)}\left(\frac{1}{2}, 0, 2\right)$$ I know that ...
0
votes
1answer
12 views

Unknown notation explanation

In a control theory textbook I saw the following notation : $$f(t)\in L_{\infty}$$ Since I am not familiar with this kind of notation could someone explain What does it mean?
15
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9answers
1k views

Is there an interval notation for complex numbers?

Just as $$\{x \in \mathbb{R}: a \leq x \leq b\}$$ can be written in the more-compact form $[a,b],$ is there an analogous notation for $$\{z \in \mathbb{C}:z=x+yi, x \in[a,b], y \in[c,d]\} \quad ?$$ ...
2
votes
1answer
56 views

Understanding the notation of a book when derivating

I'm trying to understand the notation that the book uses. The book says $(1)$ $y=a\cdot \sin x$ and then the derivate of $(1)$ is $(2)$ $\frac{d^2y}{dx^2}=-a \cdot \sin x$ I don't get what to do ...
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0answers
47 views
+50

Notation for the set of all arguments corresponding to local minima.

The notation $$\mathop{\mathrm{arg\, min}}_{x \in X} f(x)$$ is sometimes used for the set of all $x \in X$ corresponding to global minima of the function $x \in X \mapsto f(x).$ Is there notation for ...
2
votes
2answers
48 views

Writing solutions of inequalities: $3<x$ versus $x>3$

My son wrote a solution to a number line graph as 3 < x instead of what his teacher said was the correct answer of x > 3. When he brought his paper back in to bring it up he was told that the ...
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0answers
80 views
+50

Meaning of notation $\operatorname{ord}_Q(g)$ in “Algebraic Curves” by Fulton

I didn't understand this notation in the chapter 7 page 93 of Fulton's algebraic curves book: What the author means by $\text{ord}_Q(g)$? Maybe he would like to say $\text{ord}_Q(G) := ...
3
votes
0answers
51 views

Etiquette for proper usage of Greek letters and other notation

I've progressed to the "output" point in my mathematics career and have run into a slightly embarrassing problem while writing a paper. Clearly, certain Greek letters are suitable for some situations ...
2
votes
3answers
196 views

Why are variables in integration by substitution so counter intuitive?

Integration by substitution is defined as something like $\displaystyle\int_a^b f(\phi(t))\phi'(t)dt = \int_{\phi(a)}^{\phi(b)} f(x)dx$ But for my taste, the variables $x$ and $t$ are exactly ...
0
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0answers
66 views

What does $X:Y\to x(t)$ mean?

Relatively new into math and working my way into it. I need some help understanding the statement below. X:Y -> x(t). Can someone please help me with what does it mean? So just to clarify I have a ...
2
votes
1answer
13 views

Consider a symmetric matrix $X$ with eigendecomposition $X=UVU^T$, how to call $\sum_{v_{k,k}>0}v_{k,k}u_ku_k^T$?

Consider a symmetric matrix $X$ with eigendecomposition $X=UVU^T$ How do people call $\sum_{v_{k,k}>0}v_{k,k}u_ku_k^T$? Sum of positive components of $X$? The positive semi definite part of $X$? ...
0
votes
2answers
25 views

Sigma notation: number columns with sum > 0 of binary matrix

I'm trying to formulate a Sigma notation formula which would yield the count (sum) of columns which themselves have a non-zero sum. $\begin{bmatrix} 1 & 0 & 0 & 0 & 0\\ 1 & 1 ...
0
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0answers
34 views

Hyperbolic sinc function

Cardinal sine function or sinc function is defined by: \begin{equation} \mathrm{sinc}x=\begin{cases}\frac{\sin x}{x}, & x \neq 0,\\ 1, & x = 0,\end{cases} \end{equation} Is there any ...
0
votes
1answer
26 views

Notation for show that a variable is binary?

Are there a "math letter" that represent the set of binary variable $\{0,1\}$? Like, when writing e.g., $a \in \mathbb{R}$, we know $a$ is real. I only know this notation $a \in \{0,1\}$, but is this ...
2
votes
0answers
37 views

On group-theoretic shorthand notation

I have often seen shorthand notation used in group-theoretic contexts and I believe it is called ATLAS notation. However, even with some searching I have not been able to find a satisfactory summary ...
4
votes
1answer
65 views

Notational issues on differential equations

I am studying dynamical systems and I have some trouble in understanding the notation used for differential equations. For example when I read $$\overset{..}{x}=F(x),$$ how should I interpret ...
0
votes
2answers
51 views

How to represent the ceiling function using mathematical notation?

How to represent the ceiling function using mathematical notation? I need an equation to input in a program because it doesn't except the ceiling function so it has to be some sort of mathematical ...
2
votes
3answers
41 views

Is there another meaning of this notation?

In a book I found the following notation: Let $c,d\in \mathbb{Z}$ such that $c\mathbb{Z}+d\mathbb{Z}=\mathbb{Z}$. For me, this means that $\gcd(c,d)=1$. If $\gcd(c,d)=1$, then there is $z,u\in ...
1
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0answers
27 views

In regards to metric spaces, does $d^\star$ have an accepted name, or notation? Do any authors use it?

(I write $\omega$ for the set $\{0,1,2,\ldots\}$.) Let $X$ denote a metric space with metric $d$. Define a function $d^{\star} : X^\omega \times X^\omega \rightarrow [0,\infty]^\omega$ by writing ...
0
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0answers
22 views

Creating a formula (notation) from series of equations

I need some help with "shrinking" of few equations I have a couple of categories of circles. For each one of these, a certain equation, which represents the circle radii is written: for 1st ...
1
vote
1answer
60 views

A sigma notation but with multiplication instead of addition?

I am not a mathematician, so I apologize if this question will sound stupid. I am wondering is there some sort of notation which will resemble the one of sigma notation, but with multiplication ...
1
vote
0answers
31 views

Weird derivative computation

I found the following formulas in a control theory textbook : $$s(x,t)=\left(\frac{d}{dt}+\lambda\right)^{(n-1)}\varepsilon $$ where $\varepsilon(t)=T\left(\frac{e(t)}{p(t)}\right)$ and ...
0
votes
2answers
45 views

What is this lower number?

I was taught that the lower number in math would be the base, but you can't have base 0 (can you?) I'm looking at some derivatives and it looks something like this. $$x^2_0$$ Sorry for the stupid ...
1
vote
1answer
18 views

Notation for a Line Segment

I have a straight line segment joining two points ($i$ and $j$). I have a third point, $k$, that has a perpendicular distance to the line segment $\kappa_{\bot}$ (call this line segment of length ...
0
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2answers
42 views

Combinaision of two functions

Let us denote $X_0 = \{x, y\}$ and $X_1 = \{a, b\}$ two disjoint sets of variables; let us denote $V$ a set of values. I have two functions $f_0 : X_0 \rightarrow V$ and $f_1 : X_1 \rightarrow V$, ...
1
vote
0answers
75 views

Simplex Notation

Let $\left(V,T\right)$ denote an affine space and let $v_0, \dots v_n$ denote some affine independent points of $V$. A $m$-simplex $s$ with vertices $v_0, \dots v_m$ can be represented by ...
1
vote
1answer
15 views

How do I express the concept of the highest “place” of a number so that I could use it in further calculations as part of an expression

So if I had the number "123" (which would be the result of an expression of terms), I would get 100 since the highest place digit used is the hundreds place. I would also get 100 for 285 and for 999, ...
0
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1answer
77 views

Notation used in the book “Opera de Cribro” by Freidlander and Iwaniec

In the book Opera de Cribro by Freidlander and Iwaniec, the notation $\tau_r(n)$ is used for a certain function related to the number of divisors less than $n$, $\tau(n)$. The only information I know ...
1
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2answers
24 views

Notation for all permutations of a set

Suppose I have a finite set $X$. Is there a standard notation to denote the set of all possible permutations of the elements of $X$? P.S. something like the power set notation for all subsets.
0
votes
0answers
22 views

Is there accepted notation and/or terminology for the smallest cover of $S$ with cells from $P$?

Let $X$ denote a set. Then for $S \subseteq X$ and $P$ a partitioning of $X$, define $P \diamond S$ as the smallest cover of $S$ with cells from $P$. Explicitly: $$P \diamond S = \bigcup\{Q \in P ...
0
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1answer
46 views

A mathematical symbol question [closed]

In the problem it says $$y_t=E_t y_{t+1} +i_t+u_t\,\text{ where }\,t=t_0, t_1, t_2, \dots$$ and I wonder if $t=t_0$, then $y_{t+1}$ means $y_{t_0+1}$ or $y_{t_1}$?
0
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0answers
20 views

Product of tuples vs cartesian product of set

If $\left ( X_{i} \right )_{1\leq i\leq n}$ is an ordered n-tuple of sets their Cartesian product is defined as: $$\prod_{i=1}^{n}X_{i}:=\left \{ (x_{i})_{1\leq i\leq n} :x_{i}\in (X_{i}) \; \text{ ...