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

Other than $\setminus$ and $-$, are there any other notations for the set-theoretic difference of sets?

Let $X$ denote a set, and suppose that $B$ and $A$ are subsets thereof. Then the set-theoretic difference of $B$ and $A$ may be denoted in any of the following ways: $$B \setminus A, \qquad B - A, ...
2
votes
1answer
15 views

Notation for the set of the subgroups of a group?

Given a group $G$, is there a "standard notation" to denote the set of the subgroups of $G$?
0
votes
0answers
38 views

If d/dx is an operation in functions, why do we need f(x)? [on hold]

This might be a little pedantic, but I need to sort out my terminology. Point 1:When mathematicians think of a function, they think of a mapping: $f:x \mapsto f(x)$. $f$ is a function that maps a ...
0
votes
1answer
18 views

Can the “$\forall x\in X $” be moved in this statement? “$\Gamma$ satisfiable $\implies \exists v:v(\alpha)=1 \forall \alpha \in \Gamma$”.

Can the "$\forall x\in X $" be moved in this statement? "$\Gamma$ satisfiable $\implies \exists v:v(\alpha)=1 \forall \alpha \in \Gamma$". I mean, is this the same than to write "$\Gamma$ ...
1
vote
1answer
24 views

Theory of Computation Notation Proof

The Question: Show that if $f(n) = \mathcal{O}(g(n))$ and $g(n) = \mathcal{O}(f(n))$, then $f(n) = \Theta(g(n)).$ I know that since $\Theta$ is a stronger notation than $\mathcal{O}$, then: $f(n) = ...
1
vote
1answer
36 views

Iverson Brackets

I would appreciate some feedback on my notation. I'm using Iverson brackets, which I'm sort of new to as a concept, but it seems simple enough. The degree of a vertex $v_n$ is given by the sum of the ...
0
votes
2answers
37 views

Basic question on math notation of max and min

When we write $\text{max}\left \{x,y \right \}$ and $\text{min}\left \{x,y \right \}$ then what do we actually mean? Does it mean the maximum and minimum of both the things that are inside $\left \{ ...
-2
votes
1answer
27 views

Notation methods for the following things? [on hold]

I go to a high school that rushes concept and does not ever talk about notation. I want to be prepared for college, and not be swamped by all this notation I don't know. From SE, I would like to know ...
2
votes
3answers
54 views

Notation: $f(A)$ when $f$ is a function $f:A\to B$.

I've seen the following notation with no previous clarification: $f(A)$, when $f$ is a function $f:A\to B$. Am I correct to assume $f(A)$ should be the image of $f$? E: I'd appreciate downvoters ...
4
votes
1answer
53 views

What does the notation $11\mid a^2$ mean?

What does the notation $11\mid a^2$ mean as used in this answer: http://math.stackexchange.com/a/948251/13230 I am trying to understand the proof that $\sqrt{11}$ is an irrational number, but am ...
-4
votes
0answers
99 views

Do “my” notations already exist or not?

Because I'm a bit slow to write my lessons, when I was in classroom, especially in maths, I created my notations as the same way as notations normaly used. For example in maths we prefer write ...
0
votes
2answers
34 views

Inverse functions: what is the difference between $\tan^{-1}(x)$ and $\tan(x)^{-1}$?

I’ve never really been taught about inverse functions, and I figured this is a pretty simple question, but I couldn’t find any explanation in my math textbook about this. What is the difference ...
1
vote
0answers
26 views

Problem with statistics notation for a density function

I'm reading a paper about partitioning of driving data and producing synthetic driiving profiles and I'm uncapable of understanding some of its equations. Just to give an example, if we consider the ...
2
votes
0answers
22 views

Generalised equation/Notation for writing down products of sets of combinations

I am trying to write a generalized equation to solve a fairly simple probability problem (c & k are constants) $$y_{1} = (1 - cx_{1})^k$$ $$y_{2} = \frac{(1 - cx_{2})^k - ...
1
vote
0answers
26 views

Abbreviating the definition of a tangent vector field?

Let $A \subset \mathbb{R}^{n}$ be open in $\mathbb{R}^{n}$ and let $F: A \to \mathbb{R}^{n} \times \mathbb{R}^{n}$ be continuous. Then $F$ is called a tangent vector field on $A$ if and only if $F(x) ...
1
vote
1answer
24 views

Notation and name for this function?

Let $k \geq 1$; let $V,W$ be vector spaces; and let $T: V \to W$ be linear. Then how do we call and denote the function $(v_{1},\cdots, v_{k}) \mapsto (T(v_{1}), \cdots, T(v_{k})): V^{k} \to W^{k}$?
0
votes
1answer
22 views

Understanding function's notation

I have been given a question on the following pdf: Suppose the random variable, X, follows a uniform distribution on the interval (0, θ). The pdf of X is $f(x;θ)$ = $1/θ$, $if$ $0≤x≤θ$, $θ>0$, ...
0
votes
1answer
27 views

Complex conjugate of $z$ as a different variable

Can a complex conjugate be represented by a different letter than $z$? As in: Let $y$ be a complex number satisfying $|y|<1$. Find the set of all complex numbers $z$ satisfying ...
7
votes
3answers
767 views

Exponent of an exponent?

If I have an expression that gives 2^3^4, would I compute this as $(2^3)^4$ or as $2^{(3^4)}$? The two answers are wildly different. My TI gives the former but Wolfram gives the latter and I don't ...
-1
votes
1answer
48 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
3answers
69 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
41 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
18 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
55 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
30 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
15 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
19 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
32 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
42 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
33 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
16 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
13 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
votes
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
49 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 ...