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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2
votes
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): ...
1
vote
1answer
47 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
494 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
vote
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
votes
2answers
77 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
96 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
votes
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
39 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 ...
1
vote
1answer
27 views

Explanation of notation $f(t)\in L_{\infty}$ in a control theory textbook

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
votes
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
57 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 ...
4
votes
4answers
135 views

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
52 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 ...
2
votes
1answer
117 views

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
201 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
votes
0answers
67 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
27 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
votes
0answers
37 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
27 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
66 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
52 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
43 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
vote
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
votes
0answers
24 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
63 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
19 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
votes
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
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
votes
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
vote
2answers
25 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
votes
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
votes
0answers
23 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{ ...
0
votes
0answers
25 views

Is there a standard symbol that denotes the set of relational operators

I am writing a research paper, and I would like to somehow denote the set of relational operators $$ \left\{ =,>,<,\leq,\geq,\neq\right\} $$ Before I use some random symbol for that purpose, ...
0
votes
1answer
41 views

how to tell a fraction in denominator or numerator should be substituted with its integer equivalent

Suppose we have equations as follows (A, C and B are all integers and $\gcd$=greatest common divisor). $$R_1 = \frac{A\times C}{B} \hspace{2cm} R_2 = ...
3
votes
0answers
178 views

Identities for Sieve of Eratosthenes collisions.

Edited to define the last two tables Three Questions: 1) Is all notation correct? 2) Is there a symbol for flatten? 3) How would we prove the identities: the sum of the divisors in the symmetric ...
1
vote
1answer
49 views

Count of matched items in multiple sets

I do apologize if this is a duplication. I did find a question that appears close to describing something of what I'm looking for, but I'm just not "seeing" the complete picture (maybe): Counting ...
7
votes
2answers
97 views

Why does the sign $\times$ vanish in mathematical expressions?

I just would like to know whether or not there exists an historical reason to prefer the expression $a b$ to $a \times b$. Why does the sign $\times$ vanish (whereas $+$ stays)? I thought that ...
1
vote
0answers
37 views

Solve for ? - undetermined inequality symbol

So I was solving a problem in Rudin (chapter 3 #16, to be specific) and I realized how convenient it would be to have a symbol that represented an undetermined equivalence relationship. As an example ...
1
vote
3answers
36 views

Notation: the set of two-element subsets of $\Bbb N$

Let $\{a,b\}\subseteq \Bbb N$. Is there a special name or notation for sets of this type, for example $\Bbb N^{2\ge}$? Any subset size may be used, but the specific size and denoting that order does ...
4
votes
1answer
109 views

How do you write an integral and why

A. Year 1 Calculus Student Approach $$ F(x) = \int f(x') dx\, $$ B. Random math paper you find online approach $$ F(x) = \int dx f(x') \, $$ C. Spivak $$ F(x) = \int f(x) \, $$ D. ??? (Edit) ...
0
votes
0answers
51 views

Alternatives to the notation $\|x\|$ for the norm of $x$?

For aesthetic reasons, I don't like the notation $\|x\|$ for the norm of $x$. Have any alternatives been proposed?
0
votes
1answer
40 views

tuple of tuples notation

Is the following notation right for indicating a $\mathit{m}-$tuple of $\mathit{n_{j}}-$tuples (I mean that each tuple of the $\mathit{m}-$tuple has a different number of elements)? ...
4
votes
4answers
761 views

Why don't we indicate the variable to summed as we do for integrals?

When integrating over a certain variable $x$, we make sure to end the integral with $dx$, like so: $$\int_{1}^{\infty}\frac{1}{x^2}dx$$ The reason for this of course becomes more clear as one goes ...
0
votes
1answer
42 views

Is there a name for a property defined in terms of open sets?

We know that if a property is defined in terms of open sets then the property is preserved under a homeomorphism. Is there a name for such a property?