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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4
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4answers
194 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
61 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
146 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
69 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
267 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 ...
2
votes
1answer
18 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
76 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
139 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
214 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
58 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 ...
5
votes
1answer
88 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
214 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
49 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 ...
2
votes
0answers
42 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 ...
3
votes
1answer
105 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
2answers
51 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
34 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
51 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
17 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
91 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 ...
2
votes
2answers
56 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
28 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
0answers
47 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
58 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 = ...
1
vote
1answer
56 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 ...
8
votes
3answers
154 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 ...
6
votes
1answer
165 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
66 views

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

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
126 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
1answer
71 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
802 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
47 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?
0
votes
1answer
30 views

Ever thought of differentiate brackets for function and for order of operations?

Now parentheses "()" is used for both function, e.g. $f(x)$, and for order of operations, e.g. $(3+5)*2$. Ever in math history be suggested to differentiate? for example square bracket "[]" can be ...
1
vote
1answer
151 views

Why abstract index notation should not be confused with the Ricci calculus?

Considering this answer, it is mentioned that the range of indices $a, b, c,\dots$ are seen as abstract and coordinate-free and linear operations can be represented with them; and the range of indices ...
1
vote
0answers
25 views

Notation for vectors that exclude zero

Is there a conventional notation for the set of all vectors of length $n$ such that not one element of the vector is equal to zero? Right now I have to write out something like "vector $B$ blah blah ...
1
vote
1answer
93 views

How can $A \supset B$ be a synonymous of $A \Rightarrow B$? [duplicate]

From time to time, although not so commonly, I see $A \supset B$ written with seemingly the same meaning as $A \Rightarrow B$. Ex. in Constructive Type Theory and Interactive Theorem Proving, on page ...
2
votes
0answers
64 views

What does the notation $\textbf{x} \langle\textbf{Y} \rangle $ mean if $\textbf{Y} \subseteq \textbf{X}$ for random variables?

I was reading daphne's Probabilistic Graphical Models book and she introduces some notation about sets of random variables that I am confused about (on page 21 section 2.1.3.2). Before I ask my ...
0
votes
1answer
51 views

How to make clear a letter is a function?

How should I make clear that a symbol is a function? Usually a function is denoted by the letter $f$ or $g$, or is directly applied to arguments (e.g. $c(x,y)$) or is implied to be a function by an ...
0
votes
2answers
127 views

Clever Substitution Notation for Logic Formulae

Assume I have a first order- ($\mathsf{FO}$-) formula $ \varphi(x)$ with free variable $x$ and bounded variables $x',x''$. Then, $\varphi(x) \in \mathsf{FO}^3$ since it has $3$ distinct variables. ...
4
votes
0answers
97 views

Why not defining a measure as a function on functions?

A measure $\mu$ is a function to $\left[0,\infty\right]$ on the sets belonging to a $\sigma$-algebra. Then for integrable functions $f$ the integral $\int fd\mu$ comes in, having nice properties ...
1
vote
1answer
41 views

Notation for rounding function

The Wikipedia article http://en.wikipedia.org/wiki/Nearest_integer_function mentions the following notation for the rounding or "nearest integer" function. (That is, the function that corresponds to ...
0
votes
2answers
592 views

Usage of capital and small letters

Are there rules for when small, capital and greek symbols are used? Simple example: The volume left in a cube with a sphere in it is V=C-S with capital standard latin letters, meaning "if you don't ...
1
vote
3answers
38 views

Writing down solutions notation

How do you write solutions to a simple equation in set notation? For example: - the solution to $x-4=0$ - the solutions to $x^2-x=0$? Thanks in advance.
2
votes
1answer
66 views

Notation for the subcategory of commutative $R$-algebras

Let $R$ be a commutative ring (with identity) and let $R\mathbf{Alg}$ denote the category of $R$-algebras. My question: Is there a suitable notation for the full subcategory of commutative ...
0
votes
2answers
66 views

Very simple notation question

What notation is it called when a number is represented as a series of additions, for example: 124 = 100 + 20 + 4 This is a very simple question obviously but I don't remember what it's called! ...
0
votes
2answers
49 views

Which letters to use as index in sequences?

Usually the latin letters $i,j,k,l,m,n$ are used as indexes in sequences or sets with $k$ elements ($A = \{ a_1,...,a_k \} $). But when we already used all these letters is there any recommendation? ...
0
votes
1answer
26 views

Using $\pm$ to express “in the range of” statement.

Does it make sense to write: $x = \left\{A\pm B\right\}$ To mean that $x$ falls in the range of $\left\{A-B,A+B\right\}$? If not, what would be the correct way of expressing this? Many thanks!
0
votes
1answer
797 views

What is the difference between single and double modulus signs. Do they both mean magnitude?

What's the difference between a set of single modulus and a set of double modulus signs? On textbooks I have seen the magnitude of two vectors vector as $|\mathbf{x} - \mathbf{y}|$ but I've seen ...
0
votes
2answers
2k views

Probability notation P versus Pr

I have come across both $P(…)$ and $Pr(…)$ being used to represent probabilities. Is there any difference in the meaning of these notations, or are they just different shorthands? I seem to come by ...
0
votes
1answer
74 views

Max/Min Notation Question

In a paper I'm currently reading it gives alpha to be the following value. $\alpha = \max_t \min_{t_j \in T_N} ||t-t_j||_2$ I am wondering what exactly this means? I have the following code: ...