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.

learn more… | top users | synonyms

1
vote
2answers
96 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
37 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
31 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 ...
1
vote
0answers
33 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
40 views

A question about a notation

Let $A$ be a non-singular square matrix. Which of the following notations is correct? $${A^2}^{-1} \qquad \text{or} \qquad A^{-2}$$
0
votes
0answers
12 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
81 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 ...
2
votes
1answer
57 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 ...
0
votes
3answers
45 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 ...
1
vote
1answer
54 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
71 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 ...
0
votes
0answers
9 views

List of hundreds of elements

In a formal writing I need to list the following elements in order: $a_1=[x_1,x_2,x_3],a_2=[x_1,x_3,x_2],a_3=[x_2,x_1,x_3],a_4=[x_2,x_3,x_1],a_5=[x_3,x_1,x_2],a_6=[x_3,x_2,x_1]$. ...
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
0answers
31 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
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 $y$?
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
64 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 ...
2
votes
4answers
124 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 ...
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 ...
-1
votes
1answer
28 views

Big-O Math Problem [on hold]

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
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
22 views
+50

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 ...
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...
0
votes
1answer
44 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 ...
5
votes
2answers
308 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: $\sum_{k_1} \sum_{k_2} \underbrace{\dots}_n \sum_{k_n} f(\mathbf k)$?
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 ...
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
0answers
21 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

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
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: $ ...
0
votes
1answer
23 views

what is the name of this operation: $x^T\otimes B$

So the question is simple: how the following operation is commonly called? $x^T\otimes B$, each element of matrix B is multiplied by the array $x^T$, so the result is a matrix. I'm not even sure if I ...
1
vote
1answer
33 views

A quickie about set theory notation

I'm reading the first chapters of my discrete mathematics textbook and I couldn't help but wonder (perhaps I haven't seen enough examples) -- is it more appropriate to write that $a$ is an integer and ...
1
vote
1answer
27 views

What is the operator priority in set theory?

Say I have three arbitrary sets $A,B,C$. Which statement is true ? $A \times B \cup C = (A \times B) \cup C $ $\quad $ or $\quad$ $A \times B \cup C = A \times (B \cup C) $ And the same ...
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 + ...
0
votes
1answer
15 views

Summation notation with ambiguous subscripts

I'm reading a paper which has the following description; Say we have a time series of correlated sequential observations of the random variable $X$ denoted $\{x_n\}_{n=1}^N$ from a stationary, time ...
1
vote
1answer
28 views

Need help with notation — finite set of random primes

I need help with notation for a finite set of random primes. Edit I've inserted my take on the format from the answer. Does it work? My attempt:$$\{X\in\binom{\mathbf P_{3,100}}{20}\},$$ ...
0
votes
0answers
24 views

is it okay in a journal to express the vector-scalar division like this

Assume you want to show that a vector is divided by a scalar and then the norm is taken, i.e. $\|\frac{x}{c}\|$ where x is the vector, and c is the scalar. So is it okay to show it like this? I ...
1
vote
0answers
27 views

Notating the components of the $\hat{\beta}$ matrix when $\hat{Y}$ is multidimensional

This is a question on The Elements of Statistical Learning. We have from the linear model $$\hat{Y} = X^{T}\hat{\beta}$$ where $\hat{Y}^{T} = \begin{bmatrix} \hat{Y}_1 & \hat{Y}_2 & \cdots ...
1
vote
3answers
140 views

What Does $y=A\exp(6x)$ mean?

So my professor used this and I don't really know what this equation means. $A$ is a positive constant, different $A$'s give different curves and these curves form a family $\mathcal{F}$. Given a ...
0
votes
1answer
49 views

Why is $(f(x))'$ shortened $f'(x)$

Why is $(f(x))'$ shortened $f'(x)$? This makes the chain rule look awkward, as $(f(g(x)))'\neq f'(g(x))$, but rather $f'(g(x))\!\times\! g(x)$, and makes it difficult to remember. It's also an ...
3
votes
1answer
99 views

What does a standalone $dx$ mean?

Some literature uses $dx$, in the context of differential equations, in a confusing way without defining what it really stands for: $Mdx + Ndy = 0$ Does it mean one of the following or something ...
-1
votes
1answer
44 views

$\bigcup_{i \in I} \mathcal{P} (A_i)$

This is Velleman 3.7, Problem 4 Below is the problem, verbatim. Suppose $ \{ A_i \mid i \in I\}$ is a family of sets. Prove that if $\mathcal{P}(\bigcup_{i \in I} A_i) \subseteq \bigcup_{i \in I} ...
0
votes
1answer
50 views

What is the name of this graph operation? (creating $k$ connected copies)

I'm looking for the name of this natural graph operation, which is kinda similar to Cartesian product, but not quite, as the copies of the graphs are not fully connected. Instead, it creates a $k$ ...
34
votes
6answers
3k views

What do mathematicians mean by “equipped”

I am a mathematical illiterate so I do not know what people mean when they say equipped. For example, I say that Hilbert space is a vector space equipped with a inner product. What does that ...
0
votes
3answers
40 views

What does the notation $\min_x$ mean?

I have a problem in which I need to find $\min_x(f(x))$. What does this notation mean?