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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-1
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1answer
45 views

Full stop as mutiplication sign

I have often seen, that users of this forum use "$.$" (full-stop) as a multiplication sign, e.g. $4.5=20$ I have thought, that this notation is the american style. But a user of this forum told me ...
4
votes
4answers
65 views

What do following asymptotic symbols mean?

What do these symbols mean? I see them in analytic number theory. $$\ll$$ $$\gg$$ $$\ll_\epsilon$$ $$\gg_\epsilon$$ $$\asymp$$ $$\sim$$ All these appear in here ...
1
vote
0answers
32 views

Why do we use r to represent vector-valued functions?

Many standard calculus texts use r as the default function name when defining vector-valued functions, e.g., $\textbf{r}(t)=\langle x(t),y(t),z(t)\rangle$. For scalar-valued functions, we default to ...
0
votes
2answers
39 views

How to express open interval in roster notation? [on hold]

For example, an open interval such as $(a, b)$ means $a$ and $b$ are not included. If I have $[a, b)$ I know $a$ is included but $b$ is not. I need to express this in roster notation, which is a list ...
3
votes
1answer
45 views

Why do we write $df/dx$ instead of $df/dx(x)$?

I was just thinking about how, i.e., if $f\colon\mathbb R\to\mathbb R$ is defined by $f(x) = x^2$, then it's customary to write $$ \frac{df}{dx} = 2x. $$ But since the derivative is itself a function ...
0
votes
2answers
23 views

null empty set has 2 subsets?

The question in the book was: How many subsets does $\{\emptyset\}$ have? a) 0, b) 1, c) 2, d) 3. The answer was c. How can an empty set have 2 subsets?
3
votes
0answers
20 views

Characterize in terms of fibre

I am not familiar with the notion "characterize" in the following context. Does this mean to redefine or?.... Any help would be appreciated. Thank you. For a function $f:X\to Y$, and y an element of ...
0
votes
0answers
15 views

Tensors, indices and matrix notation - is there a common convention?

For a tensor named T with two indices, there are four possibilities: $T_{ij}$ , $T_i^{\ j}$, $T^i{\ _j}$ and $T^{ij}$. Is there a common convention as to how these tensors would be represented as ...
0
votes
0answers
11 views

Notation for the ith row and column of a matrix

When noting the $i^{th}$ scalar of a vector $\mathbf{x}$ one usually does it as $x_i$, since it is a scalar When doing this for matrices that are being denoted in bold, let's say $\mathbf{A}$, how ...
0
votes
2answers
54 views

Is there a mathematical symbol for “and”? [duplicate]

I have a statement as such: $\mathbb{Z_+} \triangle E = \{ x \in \mathbb{Z_+} : x \space \% \space 2 \neq 0 \space and \space x \in \mathbb{Z} : x < 0 \space and \space x \space \% \space 2 = 0 ...
0
votes
1answer
30 views

Is there a notation for “Bounded Kleene star”?

I understand that Kleene star is defined as: $$V^*=\bigcup_{i = 0 }^\infty V_i = V_0 \cup V_1 \cup V_2 \cup V_3 \cup \ldots.$$ (given $V$ is a formal language, $V_0 = \{\varepsilon\}$, and $V_k$ is ...
2
votes
2answers
29 views

Integration of a scalar function with respect to a vector

I have a scalar function that takes $n$ arguments, $f(x_1, x_2,x_n) = f(\mathbf{x})$, and two vectors also with $n$ elements, $\mathbf{z} = (z_1, z_2\cdots,, z_n)$, and $\Delta\mathbf{z} = (\Delta ...
0
votes
0answers
13 views

How to deduce this fact from the existence of factorized regular conditional probabilities and disintegration of probability measures?

In the lecture we had a theorem about the disintegration of probability measures in the following formulation: Theorem: Given two standard Borel spaces $(S_i,\mathscr S_i),i=1,2$ let $(S,\mathscr ...
0
votes
1answer
37 views

For two functions $f,g$ from $X$ to $\mathbb R$ how should I interpret $f \wedge g$?

For two functions $f,g$ from $X$ to $\mathbb R$ how should I interpret $f \wedge g$? I came to such a term while reading the axioms of fuzzy topology.
3
votes
2answers
72 views

Notation: $\varphi$ and $\phi$

Is it bad style to use $\phi$ and $\varphi$ in the same paper (for different things, of course)? I'd like to use $\phi$ for a function and $\varphi$ for a particular function value.
0
votes
1answer
18 views

Notation: Codomain of a probability density function

I need some help with the correct notation for the codomain of a probability density function. Consider the following problem. Let $$ F : V \to (0,1), \, x \mapsto \int\limits_{\inf V}^{x} f(t) \, ...
0
votes
0answers
31 views

Notation for does not converge?

Is it okay to write that $x_n \not \rightarrow x$ to indicate that the sequence $(x_n)$ does not converge to $x$? Or should this notation be discouraged?
2
votes
2answers
40 views

Index notation interpretation for matrices

I want to understand the how to interpret the matrices which are represented by index notation. Here is my matrix $𝜎_{𝑖𝑗}+𝜎_{𝑖𝑘}𝑤_{𝑘𝑗}−𝑤_{𝑖𝑘} 𝜎_{𝑘𝑗}$ All the matrices in the equation ...
1
vote
0answers
32 views

Abuse of notation ? $(A\mid M_{n\times p})$ to denote a set of matrices…

Let $A\in M_{n\times m}$. Would it be considered an abuse of notation to write $$\left(A\mid M_{n\times p}\right)\subseteq M_{n\times (m+p)},\tag{1}$$ where $\mid$ denotes matrix augmentation ? By ...
1
vote
0answers
14 views

Notation for compactly supported functions

I teach a course in real analysis and applications to partial differential equations in which I spend some weeks talking about Sobolev spaces. I have always used the symbol $C_0^\infty(\Omega)$ to ...
0
votes
1answer
12 views

Definition of a function whose codomain is set of probability measure over cartesian product with dependency between sets in the product

I am thinking about the following function: $$ p : A \to \Delta \big( F(x, y(t) ) \times T \big) ,$$ where $t \in T$ denotes continuous time, and $\Delta (X)$ denotes the set of all probability ...
0
votes
0answers
21 views

$\mapsto$ functional notation and probability distributions

I have a question concerning mathematical writing. If we have a function $f: X \to Y$, we can write it \begin{align} f: \ & X \to Y \\ & x \mapsto f(x), \end{align} where $f(x)$ can ...
0
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0answers
11 views

Notation of multivariate functions and parameters

I have some trouble having a standard notation for multivariate functions and parameters. I'm dealing with the derivation of the Master equation. Some authors write the probability density function ...
0
votes
1answer
36 views

Is this “truncating” matrix function well known?

I'm working with a kind of "truncating" matrix function $\tau_r:M_{n\times n}\to M_{n\times r}$, where $r\leq n$, defined by $\tau_r(A)=B$, where $b_{ij}=a_{ij}$ for $j\leq r$. Is this a well known ...
1
vote
2answers
37 views

Notation Question $n$ $ < <$ $m$

What does the following notation mean: $n< < m$ , where $n$ and $m$ are numbers?
0
votes
0answers
23 views

If $C^H$ is the conjugate transpose of $C$ then what is meant by $C^{-H}$?

If $C^H$ is the conjugate transpose of $C$, i.e., $C^H=\overline{C^T}$ then what is meant by $C^{-H}$?. Assume that $C$ is a square matrix. I can't find a definition for this anywhere?. Can anybody ...
2
votes
1answer
48 views

A Type of Union I do not understand

I am not able to read this following union. Could someone please help me to understand it? $\bigcup\limits_ {k \geq n}${${x \in X: |f_k(x)-f(x)|\geq q} $ }
1
vote
1answer
77 views

What does $\propto$ mean in the following equation?

I have seen this question but I still have problem with the meaning of this symbol. From this book: The time-dependent angle may be defined from the components of the wave vector in order to ...
1
vote
3answers
66 views

Acronyms and words as variables and in mathematical notation

I am unsure if this question is warranted. Often mathematical symbols and objects are represented by a single character, e.g. variables are most often single characters like $x$, and often to ...
0
votes
1answer
31 views

What is the “T” set?

I am reading an engineering paper and it references a "T" set in the same way that one would reference the set of complex numbers with $\mathbb{C}$, or the set of real numbers with $\mathbb{R}$". What ...
1
vote
0answers
34 views

Notation/definition problem for commutative binary operation

I'm trying to describe/define the commutative binary operation on a three-element set which when the operands are the same, gives the same element and when they are different gives the element which ...
1
vote
1answer
69 views

Use of exclamation point

I'm quite puzzled by the use of an exclamation point in this paper. The authors introduce the following linear constraints to a quadratic program: $ \sum_k a^{(l)}_k b_j (\mathbf{x}_k) = r_j^{(l)} $ ...
2
votes
2answers
105 views

What does $e$ mean in this expression?

I've seen this formula $$1RM = \frac{100 \cdot w}{48.8 + 53.8 \cdot e^{-0.075 \cdot r}}$$ but I don't know what does the $e$ means. The $w$ stands for weight. The $r$ for repetitions but I think ...
0
votes
1answer
24 views

Meaning of $^sB$, s an element, B a subgroup

Let $G = SL_2(\mathbb{F}_q)$, $B$ the subgroup of all upper triangular matrices, $s = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$. What does $^sB$ mean? I read it from page 4 of C. ...
0
votes
1answer
15 views

Notation in Kronecker-Weber theorem

Sorry for the dumb question but I don't understand a notation. I'm reading the notes of Culler about the Kronecker Weber theorem (see here) and at page 3 we have a finite extension of number field ...
0
votes
0answers
25 views

Mathematical notation for first and second maximum

I have a vector $f_x = f_{x_1}, f_{x_2},\cdots, f_{x_n} $ having the frequencies for bin $x = x_1,x_2,\cdots,x_n$. Now I want to address two bins having highest frequencies. I address the highest ...
1
vote
0answers
14 views

What is the mapping of Z-transform?

Recall that given a series $x(k)$, the Z-transform $\mathcal{Z}$ is defined as: $$\mathcal Z(x(k)) = \sum_{k =0}^{\infty} x(k) z^{-k}$$ where $x(k)$ satisfies $|x(k)| \leq M\rho^k$, $M, \rho$ real ...
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votes
0answers
24 views

Function notation of y [closed]

could you expain what the following function means in layman terms: y(x ; W) Cheers
2
votes
2answers
44 views

Notation of expectation and random variables

I'm trying to understand the notation used at p18 of The Elements of Statistical Learning. I suspect errors in notation. What do the authors mean and, if any notational errors, what would be the ...
3
votes
0answers
42 views

Standard notation for indices in group theory?

I've seen three notations for indices in group theory, namely $(G:H)$, $[G:H]$ and $|G:H|$. Is there any of these notations that is standard?
1
vote
0answers
16 views

Notation or theory on functions which reorder sequences

I wanted to come up with a simple way of reordering the elements in some sequence $a=\left[ a_{0}, a_{1} \cdots a_{n} \right]$ in a specific way. My solution was to have a sequence of integers ...
0
votes
0answers
14 views

Notation for functions returning probability distributions

Let $A$ and $B$ be two sets. If $f$ is a (deterministic) function from $A$ to $B$, I can write $f : A \rightarrow B$. What if $f$ was a stochastic function and could take different values for a ...
0
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0answers
35 views

Does anyone use the notation $\mathrm d^3(x,y,z)$?

I am working on a LaTeX package for typesetting differentials (yes, I know it will be only one of many). I aim at covering many different situations that may arise when dealing with differentials. I ...
2
votes
1answer
79 views

Question about notion $d\mu = fdv$ in Real Analysis of Folland

I'm reading the book Real Analysis of Folland, chapter 3 about signed measure, and there's some notion that confused me. In this book, he defines that $dv = fd\mu$ if $v(E) = \int_E{fd\mu}$, and ...
0
votes
0answers
11 views

What is the notation for 'asymptoticly approximate mapping'? If any…

I've learned about the notation 'maps to': $\mapsto$ And also asymptotic approximation: $\simeq$ Is it valid to suggest the notion of 'asymptoticly approximate mapping'? If so, what is ...
2
votes
1answer
35 views

How to correctly write definite time integration of this function?

Last time I saw an integral was something like 10 years ago, and I am having doubts about the notation I should use. I want to describe the evolution of the volume difference between two cylinders ...
3
votes
1answer
64 views

Does writing $f(x)\sim \ell$ have a sense?

If $\lim_{x\to a}f(x)=\ell$, is it correct to say that $f(x)\sim_a \ell$ ? I would say yes since $\lim_{x\to a}\frac{f(x)}{f(a)}=1$, but on a test I wrote $e^{-t}\sim_0 1$ and the corrector said that ...
1
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1answer
35 views

How to simplify the equation of combination?

If there are three random variables and three related thresholds, how to simplify the following expression by summation or multiply or other operators? Thank you. ...
1
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1answer
32 views

Has anyone ever suggested a name or notation for this operation on multisets?

A basic multiset identity says: $$A+B = (A \cap B) + (A \cup B)$$ Allowing ourselves to use negative multiplicities and rearranging: $$A-(A \cap B) = (A \cup B)-B$$ But since $A \supseteq (A \cap ...
1
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0answers
44 views

What if there is $\downarrow$ or $\uparrow$ notation in the limit instead of $\rightarrow$?

I saw a different notation in a limit in the book Elementary Differential Geometry by A N Pressley : what do both of $\downarrow$ and $\uparrow$ mean?