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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5
votes
5answers
356 views

Is there a notation for being a finite subset?

I would use a notation for being a finite subset, like $$A\sqsubset B \text{ or } A\underset{fin}{\subset} B,$$ but I have never seen a notation for that. Are there any? While waiting for a ...
0
votes
2answers
30 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
38 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
32 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
131 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
37 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
24 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
34 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
100 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
39 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
35 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
35 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
21 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
42 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
15 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
82 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
58 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
58 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
55 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
9 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
135 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
26 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
66 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 ...
0
votes
1answer
45 views

How to notate higher anti-derivatives?

We can represent the $nth$ derivative of $y$ with the following notation: $$\frac{d^ny}{dx^n}$$ How can we represent the $nth$ anti-derivative of $y$?
2
votes
4answers
127 views

Meaning of symbols $\vdash$ and $ \models$

I'm confused about the use of symbols $\vdash$ and $ \models$. Reading the answers to Notation Question: What does $\vdash$ mean in logic? and What is the meaning of the double turnstile symbol ...
3
votes
2answers
121 views

Can interval notation be used to describe a set?

If $x$ is an element of the set of integers between 4 and 14 inclusive, some might say $ x \in Z \hspace{1mm} , \hspace{1mm} 4\le x\le14 $ or $ x \in $ { $4,5,...,14$} I wonder whether this ...
1
vote
2answers
85 views

Are the definitions of dot product and cross product the wrong way round?

This is something that has been bugging me since I started studying again. It seems to me that the definitions and symbols for the dot and cross products are backwards. When I first learnt ...
6
votes
0answers
50 views

Does anyone use $\subset$ for proper subset anymore?

I belong the the group of people who still write (not necessarily proper) subset as $\subseteq$ to avoid any confusion with proper subset, which I notate $\subsetneq$; I usually do not use $\subset$ ...
0
votes
1answer
17 views

Substitution in Big-O notation

If I have two statements, one of the form $f\sim g$ and the other of the form $f=O(g)$ of which the definitions are: $$f\sim g\implies\lim_{x \to \infty}\left|\frac{f(x)}{g(x)}\right|=1 ...
0
votes
2answers
46 views

What is the difference between $[H, g]$ and $[h, g]$?

I am working on this problem, where $[H, g]$ is the commutator group: Let $H$ be a subgroup of $G$, show that $[H, g] = [H, \langle g \rangle]$. Before solving it, I need to understand the ...
2
votes
3answers
75 views

Proving with Big O Notations

Is there a way I can prove that $O(3^{2n})$ does NOT equal $10^n$? How would that be done? Also, is it okay to simplify $O(3^{2n})$ to $O(9^n)$ to do so?
0
votes
1answer
45 views

What does $f(u)=\min!$ mean in calculus of variations?

I have a very simple notation related question. There are notes to calculus of variations [specifically: Zeidler's book "Nonlinear Functional Analysis and its Applications II/B" page 506] which states ...
-1
votes
1answer
28 views

Big-O Math Problem [closed]

I'm having trouble with a hard question, so, say 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 $O(h(x))$.
1
vote
1answer
18 views

Vector notation question

Just a short question regarding notation: If this matrix represents a vector and I want to solve it for $t=2$, may I write it as follows: $ \left( \begin{array}{ccc} vt\\ vt-gt\\ \end{array} ...
2
votes
4answers
131 views

Using “$\cdot$” as variable placeholder

I've occasionally come across the use of "$\cdot$" as placeholder for a variable, most recently in a paper on radial basis functions, which were defined as $$ s(\cdot) = p(\cdot) + \sum_{i=1}^N ...
2
votes
0answers
19 views

A question about a notation used in the Folland Real Analysis

This is the exercise 11 in the Folland Real Analysis. Could anyone tell me what it means by f(x,・) and f(・,y)? I have never seen such notations before...
5
votes
2answers
310 views

What is the proper notation for a general number of nested summations?

A sum over one index: $\sum_i f(i)$ A sum over two indices: $\sum_i \sum_j f(i,j)$ A sum over many indices: $\sum_{k_1} \sum_{k_2} \underbrace{\dots}_n \sum_{k_n} f(\mathbf k)$?
1
vote
0answers
25 views

Mathematical Notation: Bracket [closed]

{M + 0.5[(24F/45) - M], M} For this formula, why is there a ", M}" What does that and the curly brackets mean? Someone told me it is a form of mathematical notation?
1
vote
1answer
31 views

What does “$C^{\infty}$” convergence mean?

I'm studying first notions about several complex variables. As a consequence of the (generalized form) of the Cauchy esteem for holomorphic functions, the book says that in the space $\mathcal ...
1
vote
0answers
22 views

Name the maps in a commutative diagram

When writing a formal paper sometimes one needs to construct complicated commutative diagrams, such as My question is, should one always give names to all maps in the diagram (perhaps except those ...
1
vote
1answer
31 views

Can one use the following notation in integrals?

I read from theoretical physics lecture notes the following: http://theory.physics.helsinki.fi/~fymmi/Luennot4_1-9.pdf $$\Gamma(p)\Gamma(q)=4\int_0^\infty dr r^{2p+2q+1}e^{-r^2}\int_0^{\pi/2}d\varphi ...
0
votes
0answers
6 views

Bring $ P(z_k | z_1, \ldots, z_{k-1},z_{k+1},\ldots,z_N) = e^\mathbf{z^Tb} / \sum_{z_k \in \{0,1\}} e^\mathbf{z^Tb} $ into sigmoidal form

Let $\mathbf{z} = \{z_1,\ldots,z_N\}$ be a state vector consisting of binary elements $z_i \in \{0,1\}$. Assume that I already did some work and found for a specific conditional distribution this: $ ...
1
vote
0answers
34 views

Mathmatical notation for a term of a polynomial

If I have a polynomial $f(x) = ax^n + bx^{n-1} + cx^{n-2} \ldots zx^0$, is there any mathematical notation for one term, such as the $x^3$ term. For example, if I have a polynomial of $f(x) = x^6 + ...