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
2answers
62 views

What is the symbol ≙ most commonly used for in a mathematical or math-related context?

What is the symbol most commonly used for in a mathematical or math-related context? LaTeX produces the symbol with \hateq. ...
1
vote
2answers
52 views

Does $A\setminus B = A\setminus C$ imply $B=C$?

Let $A, B, C$ be sets with $B \subset C$ and $C \subset A$. Does $A\setminus B = A\setminus C$ imply $B=C$? I am not sure what the \ means, so I don't know how to solve this.
1
vote
1answer
343 views

mathematical symbol for vector appending

Given a vector v=<1,2,3>, now I want to have a new vector v', which is the vector v, appends with a number 4, how should I represent v' mathematically? What I wish to have is something like ...
0
votes
1answer
58 views

What does the notation $H=\{ a | a^2=e \}$ mean? [closed]

What is the meaning of notation $H=\{ a | a^2=e \}$? Is it the same as $H=\{a,a^2=e\}$? (Here $a$ is an element of some group, with identity $e$.)
2
votes
1answer
41 views

Is the way I simplify my notation?

Do you agree with how I simplify this equation notation $$\sum_{i=1}^n \phi_{v_i} \left(\sum_{i=1}^m \phi_{l_i}\right)=\sum_{(i,j)\in \mathcal{S}}\phi_{v_i}\phi_{l_j},$$ where I define ...
2
votes
0answers
48 views

Cleaning Up Messy Product Notation

Suppose I have the following: Let $N_1<...<N_m$. Let $T_{N_k}(x)=\sum_{i=0}^{N_k}{\frac{x^i}{i!}},$ $ t(i,j,x)=(T_{N_i}-T_{N_j})(x)$ I'm trying to define a polynomial $p_{k,m}(x)$ like ...
4
votes
2answers
55 views

Is there any symbol for “undefined”?

For example we have $\frac{0}{0}$ which is undefined or we have a multiplication of $2\times2$ and $3\times3$ matrices which is also undefined. Is there any symbol for representing it?
5
votes
1answer
83 views

Why is $\mathrm{arctan}(0)$ not infinity?

$\arctan x$ is defined as: $$\arctan x = \frac{1}{\tan(x)} = \frac{1}{\frac{\sin(x)}{\cos(x)}}$$ if I now have $x = 0$ I should get: $$\frac{1}{\frac{\sin(0)}{\cos(0)}} = \frac{1}{\frac{0}{1}} = ...
1
vote
1answer
39 views

What is $\langle I\rangle$ in this text?

I've read the following: It is easy to see that given any independent set $I$ in $V$, the vertices of $V-I$ form a covering of $G$. Conversely, if $V-I$ forms a covering, then $\langle I\rangle$ ...
0
votes
0answers
46 views

Has anyone proposed a “maximum subset” symbol?

From a ZFC perspective, there is a unique set $\emptyset$, which is the empty subset of every set. Further, every set has a maximum subset, namely itself. However from a structural perspective, there ...
3
votes
1answer
2k views

Scientific notation and negative numbers

My daughter is learning scientific notation in school, and her textbook says something to the effect of this: Scientific notation is a method of writing numbers as the product of two factors ...
1
vote
1answer
34 views

Interpreting limit notations

My question is: Are the following notations equivalent or not: $$(1)\;\;\;\;\;\;\text{When}\;||\textbf{x}||\rightarrow 0,\;\text{then}\;\;\;\frac{f(\textbf{x})}{||\textbf{x}||}\rightarrow0$$ ...
5
votes
3answers
476 views

Why is Multiplicative Notation Used for Groups (Instead of Additive)?

In documents relating to group theory it seems common to use a multiplicative notation to represent the group operation. For example, I'm reading Herstein's "Topics in Algebra" and looking for some ...
2
votes
1answer
821 views

what does mean of notation comma?

I confused the notation comma. I know that the comma means 'AND' in Set theory as gate($a$^$b=a$ AND $b$), But we write solution of equaiton as $x=1,2$ (the equation: $x^2-3x+2=0$) the question is ...
0
votes
0answers
29 views

Laplace transform notation

I'm confused about the notation used, pretty much everywhere, to describe what a Laplace transform it. Wikipedia says something along the lines of "..Laplace transform of a function $f(t)$..", ...
0
votes
0answers
5 views

Partial derivative notation inside an integral - what would be normal?

What would be the most idiomatic way of writing the following idea? $$x^{t+u} = \int_0^x\int_0^{x}\frac{\partial (y^t)}{\partial y}\cdot \frac{\partial (z^u)}{\partial z}dz dy$$ for $\Re(x)>0$. ...
11
votes
6answers
1k views

Is there a notation for being “a finite subset of”?

I would gladly use a notation for "A is a finite subset of B", like $$A\sqsubset B \text{ or } A\underset{fin}{\subset} B,$$ but I have never seen a notation for that. Are there any? While ...
0
votes
1answer
51 views

A basic question of basic writing

When we define some term by a notation starting with the word "define" or "let", which of the following is correct? Define $A=x+2y$; or, define $A \equiv x+2y$.
1
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0answers
29 views
0
votes
0answers
19 views

what does this notation exactly mean? $(x)_{+}$

So the question is already given in the title: I see in some mathematics proof, the following notation is used: $x=(z)_+$ and we know that $x$ should be greater than or equal to zero, i.e. $x\geq ...
23
votes
2answers
500 views

What is the Coxeter diagram for?

I understand that Coxeter diagrams are supposed to communicate something about the structure of symmetry groups of polyhedra, but I am baffled about what that something is, or why the Coxeter ...
0
votes
2answers
34 views

If and only if with two conditions?

Would it make sense to write a statement saying that, for example: $A = B$ if and only if $f(A,B) = 1$ or $g(A,B) = 2$ ?
2
votes
0answers
40 views

For all/Exists in both ways

Is there a more compact expression to write (without repeating the "same" sentence and using the conjunction): $\forall a \in A \exists b\in B | d(a,b) < 100 \wedge \forall b \in B \exists a \in A ...
0
votes
1answer
33 views

Understanding relation between vector valued function and function objective in an multi objective optimization problem

I try to understand the relation between "vector-valued function" and "function objective" as used in optimization problem. I understand that objective function in a multi-objective problem can be ...
3
votes
4answers
134 views

What is the meaning of $(2n)!$

I came across something that confused me $$(2n)!=?$$ What does this mean: $$2!n!, \quad 2(n!)$$ or $$(2n)!=(2n)(2n-1)(2n-2)...n...(n-1)(n-2)...1$$ Which one is right? The exercise is to show that ...
0
votes
0answers
40 views

Are ratio notations always equivalent?

Is there any case where the following ratio notations are not equivalent? For cases where the notations are equivalent, under what circumstances would the first notation be preferred? First ...
0
votes
0answers
26 views

How do I specify a function without a defined argument?

A function $f$ with the argument $x$ is commonly written $f_x : A\to B, x\mapsto f(x)$, or $f_x : \mathbb{R} \to \mathbb{R}, x\mapsto x^2$, but say I don't want to specify the argument, how would I ...
2
votes
1answer
19 views

Notation to express affine relationship

As you know, if we have a linear relationship between two variables $x$ and $y$ : $y=ax$, this is usually denoted by , $y\varpropto x $ y is proportional to x. The question is if they are affinely ...
0
votes
1answer
36 views

Single variable true or false statements

If I have a true or false statement S, depending on a varible x, is there some standard function or opperation in formal logic, that takes the statement S and the variable x, and outputs $1$ if ...
1
vote
2answers
104 views

Matrix notation of vectors?

My linear algebra book says that a vector is a one-column matrix. However, in the context of what we are studying (linear equations) it would make more sense if a vector was of the form of the ...
-1
votes
2answers
42 views

Notation of coordinate representation in Lee

In Lee's Introduction to Smooth Manifolds he writes $$ \omega = \omega_i dx^i$$ where $\omega$ is a differential form. See for example page 293. What does $\omega_i dx^i$ stand for? According ...
0
votes
0answers
38 views

Different vector notations

I'm in multi-variable calculus right now, studying vectors. For calculus, the notation is completely different that what I have previously dealt with in linear algebra and discrete mathematics, or ...
2
votes
1answer
27 views

Why is the sample set notated with $\chi$ in statistics?

My professor of statistics based his lesson notations on H. Georgii's work 'Stochastics'. The sample set is thereby notated as $\chi$, instead of the usual $\Omega$. I don't really understand the ...
1
vote
0answers
38 views

Why aren't placeholders for arguments more common?

When learning about differentiation and integration, one often deals with functions, and it's common to use $D(x^2) = 2x$ as a function instead of $D(x\mapsto x^2) = (x\mapsto 2x)$, while it would ...
0
votes
0answers
25 views

Turing machine notation question.

I'm a bit confused on some of the notation being used for turing machines in one of our exercises in class. The question gives us a string α ϵ {0,1}* and the function int(α) that changes a binary ...
-2
votes
0answers
27 views

Multiple products of submodules

NOTE: This is part of a homework, so only worry about the question regarding notation. We have the following conditions: $R=\mathbb{Z}$, $I = \mathbb{Z}_{>0}$, and $M_i = \mathbb{Z} / i ...
0
votes
1answer
48 views

A question about a notation

Let $A$ be a non-singular square matrix. Which of the following notations is correct? $${A^2}^{-1} \qquad \text{or} \qquad A^{-2}$$
1
vote
0answers
21 views

Different notation for Jacobi symbol

Is there a different, sort of established, notation for the Legendre / Jacobi / Kronecker symbol $\left(\frac{a}{b}\right)$? If yes, where is it used (in which texts)? I'm asking, because I ...
1
vote
1answer
85 views

What is the mathematical notation for representing a maximum number output?

For example, something like the following: LowerOfTheTwo(a × b,1000) = c So, if a = 100 and ...
0
votes
3answers
47 views

The meaning of dot centered vertically, as in $3\cdot 5$

I just went to a site to practise some maths as I am studying some maths on my OU course in computing and IT and I ran into some symbols that I did not understand The questions were solve ...
2
votes
1answer
60 views

Why is arcsin represented with the ^(-1) notation?

So in trigonometry, we have sin, secant (which is one over sin) and arcisn. Why is arcsin sometimes represented with sin^-1? sin^2 means sin to the second power, but sin^-1 explicitly does not mean ...
2
votes
3answers
61 views

Is modular arithmetic defined for all rational numbers (with denominators coprime to modulus)?

In the expression $\frac{1}{b}\pmod m$, where $(b,m)=1$, is $\frac{1}{b}$: a) a rational number (and so rational numbers are defined in modulo arithmetic using multiplicative inverses)? b) just ...
1
vote
1answer
56 views

What is the meaning of the notation $]1, 1[$? [duplicate]

This may look like a silly question but I am struck in my work with this notation in one of the papers. What is meant by $]1,1[$ ?
4
votes
4answers
75 views

Question about $x\mapsto f(x)$ notation.

I'm trying to learn this notation, but I have some questions regarding its uses: Why is a "$:$" used instead of "$=$" when defining the function, e.g. $f: x\mapsto f(x)$ isntead of $f = x\mapsto ...
10
votes
2answers
18k views

multiplication equivalent of the summation symbol

I was curious (even though this is a very amateur question)... what would the multiplication equivalent of sigma (the summation symbol) be? $$\sum$$ I want to do a series of multiplication of ...
0
votes
0answers
10 views

List of hundreds of elements

In a formal writing I need to list the following elements in order: $a_1=[x_1,x_2,x_3],a_2=[x_1,x_3,x_2],a_3=[x_2,x_1,x_3],a_4=[x_2,x_3,x_1],a_5=[x_3,x_1,x_2],a_6=[x_3,x_2,x_1]$. ...
1
vote
4answers
136 views

When an equation has no solutions, denote it with $x\in\varnothing$.

My teacher claims that when an equation in variables $x_1,x_2,\ldots,x_n$ has no solutions, you should denote this fact with $(x_1,x_2,\ldots,x_n)\in\varnothing$. An empty set can't have an element ...
0
votes
0answers
14 views

Notation Explanation

Here, page $3$, there is this notation $\bar{P}^{\beta X}$. I know that $\beta X$ is the stone-Cech compactification of $X$, but authors do not define what is $\bar{P}^{\beta X}$. Is it the set of all ...
0
votes
2answers
27 views

Big-O math Question

I'm having trouble with this question: Suppose that $f(x), g(x)$ and $h(x)$ are functions such that $f(x)$ is $O(g(x))$ and $g(x)$ is $O(h(x))$. Prove that $f(x)$ is $O(h(x))$. I have tried ...
2
votes
2answers
68 views

Is there a better way of writing differentiation and integration?

Differentiation is commonly written simply with a prime mark and an equation, as $(x^2)' = 2x$. Although I find this confusing and think it'd better be written $D(x\mapsto x^2) = x\mapsto 2x$, as ...